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240d113062
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<head>
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<head>
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<!-- 2021-01-08 ven. 15:53 -->
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<!-- 2021-01-08 ven. 15:30 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Stewart Platform - Decentralized Active Damping</title>
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<title>Stewart Platform - Decentralized Active Damping</title>
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<meta name="generator" content="Org mode" />
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<meta name="generator" content="Org mode" />
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@ -42,25 +42,25 @@
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<li><a href="#orgddaf52f">1. Inertial Control</a>
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<li><a href="#orgddaf52f">1. Inertial Control</a>
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<ul>
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<ul>
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||||||
<li><a href="#org933440d">1.1. Identification of the Dynamics</a></li>
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<li><a href="#org933440d">1.1. Identification of the Dynamics</a></li>
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||||||
<li><a href="#org2875dd1">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#orged6d23c">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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||||||
<li><a href="#org0cea759">1.3. Obtained Damping</a></li>
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<li><a href="#org533c409">1.3. Obtained Damping</a></li>
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||||||
<li><a href="#orga866100">1.4. Conclusion</a></li>
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<li><a href="#orgc76021e">1.4. Conclusion</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#orgf8ed544">2. Integral Force Feedback</a>
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<li><a href="#orgf8ed544">2. Integral Force Feedback</a>
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<ul>
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<ul>
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<li><a href="#orga2d019b">2.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org7b81fe5">2.1. Identification of the Dynamics with perfect Joints</a></li>
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||||||
<li><a href="#org6ac04ee">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#org3dca396">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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||||||
<li><a href="#org06e1086">2.3. Obtained Damping</a></li>
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<li><a href="#org7044ed4">2.3. Obtained Damping</a></li>
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<li><a href="#orgfa832d6">2.4. Conclusion</a></li>
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<li><a href="#org9c769b9">2.4. Conclusion</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#orgabec4e1">3. Direct Velocity Feedback</a>
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<li><a href="#orgabec4e1">3. Direct Velocity Feedback</a>
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<ul>
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<ul>
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<li><a href="#org19cbcee">3.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#orga2d019b">3.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org0fabf01">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#org2875dd1">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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||||||
<li><a href="#org6c74c9a">3.3. Obtained Damping</a></li>
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<li><a href="#org0cea759">3.3. Obtained Damping</a></li>
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||||||
<li><a href="#org81b2156">3.4. Conclusion</a></li>
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<li><a href="#orga866100">3.4. Conclusion</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#orgc7e2089">4. Compliance and Transmissibility Comparison</a>
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<li><a href="#orgc7e2089">4. Compliance and Transmissibility Comparison</a>
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@ -90,7 +90,7 @@ The following decentralized active damping techniques are briefly studied:
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<a id="org709d56c"></a>
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<a id="org709d56c"></a>
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</p>
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</p>
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<div class="note" id="org1ae7526">
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<div class="note" id="org8a14d8c">
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<p>
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<p>
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||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_inertial.m">here</a>.
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The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_inertial.m">here</a>.
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</p>
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</p>
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@ -106,44 +106,44 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
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<h3 id="org933440d"><span class="section-number-3">1.1</span> Identification of the Dynamics</h3>
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<h3 id="org933440d"><span class="section-number-3">1.1</span> Identification of the Dynamics</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<div class="org-src-container">
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<pre class="src src-matlab">stewart = initializeStewartPlatform();
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<pre class="src src-matlab"> stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
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stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
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stewart = generateGeneralConfiguration(stewart);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart);
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stewart = initializeStrutDynamics(stewart);
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stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
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stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
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stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
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</pre>
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</pre>
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</div>
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</div>
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<div class="org-src-container">
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<div class="org-src-container">
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<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
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<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
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payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
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payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
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controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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</pre>
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</pre>
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</div>
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</div>
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<div class="org-src-container">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options = linearizeOptions;
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options.SampleTime = 0;
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options.SampleTime = 0;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'stewart_platform_model'</span>;
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mdl = <span class="org-string">'stewart_platform_model'</span>;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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clear io; io_i = 1;
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clear io; io_i = 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Vm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute velocity of each leg [m/s]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Vm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute velocity of each leg [m/s]</span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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||||||
G = linearize(mdl, io, options);
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G = linearize(mdl, io, options);
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||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
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G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
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||||||
G.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
|
G.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
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||||||
</pre>
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</pre>
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||||||
</div>
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</div>
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||||||
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@ -159,17 +159,17 @@ The transfer function from actuator forces to force sensors is shown in Figure <
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</div>
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</div>
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||||||
</div>
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</div>
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||||||
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||||||
<div id="outline-container-org2875dd1" class="outline-3">
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<div id="outline-container-orged6d23c" class="outline-3">
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||||||
<h3 id="org2875dd1"><span class="section-number-3">1.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
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<h3 id="orged6d23c"><span class="section-number-3">1.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
||||||
<div class="outline-text-3" id="text-1-2">
|
<div class="outline-text-3" id="text-1-2">
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||||||
<p>
|
<p>
|
||||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
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||||||
<pre class="src src-matlab">stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
<pre class="src src-matlab"> stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||||
Gf = linearize(mdl, io, options);
|
Gf = linearize(mdl, io, options);
|
||||||
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Gf.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
|
Gf.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
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||||||
</pre>
|
</pre>
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||||||
</div>
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</div>
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||||||
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||||||
@ -177,10 +177,10 @@ Gf.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string"
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|||||||
We now use the amplified actuators and re-identify the dynamics
|
We now use the amplified actuators and re-identify the dynamics
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeAmplifiedStrutDynamics(stewart);
|
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||||
Ga = linearize(mdl, io, options);
|
Ga = linearize(mdl, io, options);
|
||||||
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Ga.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
|
Ga.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -196,8 +196,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org0cea759" class="outline-3">
|
<div id="outline-container-org533c409" class="outline-3">
|
||||||
<h3 id="org0cea759"><span class="section-number-3">1.3</span> Obtained Damping</h3>
|
<h3 id="org533c409"><span class="section-number-3">1.3</span> Obtained Damping</h3>
|
||||||
<div class="outline-text-3" id="text-1-3">
|
<div class="outline-text-3" id="text-1-3">
|
||||||
<p>
|
<p>
|
||||||
The control is a performed in a decentralized manner.
|
The control is a performed in a decentralized manner.
|
||||||
@ -222,10 +222,10 @@ The root locus is shown in figure <a href="#orgaea8656">3</a>.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orga866100" class="outline-3">
|
<div id="outline-container-orgc76021e" class="outline-3">
|
||||||
<h3 id="orga866100"><span class="section-number-3">1.4</span> Conclusion</h3>
|
<h3 id="orgc76021e"><span class="section-number-3">1.4</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-1-4">
|
<div class="outline-text-3" id="text-1-4">
|
||||||
<div class="important" id="org91c21ee">
|
<div class="important" id="org37b8ef0">
|
||||||
<p>
|
<p>
|
||||||
We do not have guaranteed stability with Inertial control. This is because of the flexibility inside the internal sensor.
|
We do not have guaranteed stability with Inertial control. This is because of the flexibility inside the internal sensor.
|
||||||
</p>
|
</p>
|
||||||
@ -242,7 +242,7 @@ We do not have guaranteed stability with Inertial control. This is because of th
|
|||||||
<a id="org1f0d316"></a>
|
<a id="org1f0d316"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="org30f755d">
|
<div class="note" id="org54cec4b">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_iff.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_iff.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -254,31 +254,31 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orga2d019b" class="outline-3">
|
<div id="outline-container-org7b81fe5" class="outline-3">
|
||||||
<h3 id="orga2d019b"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
|
<h3 id="org7b81fe5"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||||
<div class="outline-text-3" id="text-2-1">
|
<div class="outline-text-3" id="text-2-1">
|
||||||
<p>
|
<p>
|
||||||
We first initialize the Stewart platform without joint stiffness.
|
We first initialize the Stewart platform without joint stiffness.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -286,18 +286,18 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
And we identify the dynamics from force actuators to force sensors.
|
And we identify the dynamics from force actuators to force sensors.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Taum'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensor Outputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Taum'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensor Outputs [N]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
G.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -313,17 +313,17 @@ The transfer function from actuator forces to force sensors is shown in Figure <
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org6ac04ee" class="outline-3">
|
<div id="outline-container-org3dca396" class="outline-3">
|
||||||
<h3 id="org6ac04ee"><span class="section-number-3">2.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
<h3 id="org3dca396"><span class="section-number-3">2.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
||||||
<div class="outline-text-3" id="text-2-2">
|
<div class="outline-text-3" id="text-2-2">
|
||||||
<p>
|
<p>
|
||||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
<pre class="src src-matlab"> stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||||
Gf = linearize(mdl, io);
|
Gf = linearize(mdl, io);
|
||||||
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Gf.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
Gf.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -331,10 +331,10 @@ Gf.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string"
|
|||||||
We now use the amplified actuators and re-identify the dynamics
|
We now use the amplified actuators and re-identify the dynamics
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeAmplifiedStrutDynamics(stewart);
|
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||||
Ga = linearize(mdl, io);
|
Ga = linearize(mdl, io);
|
||||||
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Ga.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
Ga.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -350,8 +350,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org06e1086" class="outline-3">
|
<div id="outline-container-org7044ed4" class="outline-3">
|
||||||
<h3 id="org06e1086"><span class="section-number-3">2.3</span> Obtained Damping</h3>
|
<h3 id="org7044ed4"><span class="section-number-3">2.3</span> Obtained Damping</h3>
|
||||||
<div class="outline-text-3" id="text-2-3">
|
<div class="outline-text-3" id="text-2-3">
|
||||||
<p>
|
<p>
|
||||||
The control is a performed in a decentralized manner.
|
The control is a performed in a decentralized manner.
|
||||||
@ -383,10 +383,10 @@ The root locus is shown in figure <a href="#orgce5d8d8">6</a> and the obtained p
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgfa832d6" class="outline-3">
|
<div id="outline-container-org9c769b9" class="outline-3">
|
||||||
<h3 id="orgfa832d6"><span class="section-number-3">2.4</span> Conclusion</h3>
|
<h3 id="org9c769b9"><span class="section-number-3">2.4</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-2-4">
|
<div class="outline-text-3" id="text-2-4">
|
||||||
<div class="important" id="orgad0c17b">
|
<div class="important" id="orged36719">
|
||||||
<p>
|
<p>
|
||||||
The joint stiffness has a huge impact on the attainable active damping performance when using force sensors.
|
The joint stiffness has a huge impact on the attainable active damping performance when using force sensors.
|
||||||
Thus, if Integral Force Feedback is to be used in a Stewart platform with flexible joints, the rotational stiffness of the joints should be minimized.
|
Thus, if Integral Force Feedback is to be used in a Stewart platform with flexible joints, the rotational stiffness of the joints should be minimized.
|
||||||
@ -404,7 +404,7 @@ Thus, if Integral Force Feedback is to be used in a Stewart platform with flexib
|
|||||||
<a id="org63027d0"></a>
|
<a id="org63027d0"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="orgadea9d6">
|
<div class="note" id="orgfb739d8">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_dvf.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_dvf.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -416,31 +416,31 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org19cbcee" class="outline-3">
|
<div id="outline-container-orga2d019b" class="outline-3">
|
||||||
<h3 id="org19cbcee"><span class="section-number-3">3.1</span> Identification of the Dynamics with perfect Joints</h3>
|
<h3 id="orga2d019b"><span class="section-number-3">3.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||||
<div class="outline-text-3" id="text-3-1">
|
<div class="outline-text-3" id="text-3-1">
|
||||||
<p>
|
<p>
|
||||||
We first initialize the Stewart platform without joint stiffness.
|
We first initialize the Stewart platform without joint stiffness.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -448,22 +448,22 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
And we identify the dynamics from force actuators to force sensors.
|
And we identify the dynamics from force actuators to force sensors.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -480,17 +480,17 @@ The transfer function from actuator forces to relative motion sensors is shown i
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="outline-container-org0fabf01" class="outline-3">
|
<div id="outline-container-org2875dd1" class="outline-3">
|
||||||
<h3 id="org0fabf01"><span class="section-number-3">3.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
<h3 id="org2875dd1"><span class="section-number-3">3.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
||||||
<div class="outline-text-3" id="text-3-2">
|
<div class="outline-text-3" id="text-3-2">
|
||||||
<p>
|
<p>
|
||||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
<pre class="src src-matlab"> stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||||
Gf = linearize(mdl, io, options);
|
Gf = linearize(mdl, io, options);
|
||||||
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -498,10 +498,10 @@ Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string"
|
|||||||
We now use the amplified actuators and re-identify the dynamics
|
We now use the amplified actuators and re-identify the dynamics
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeAmplifiedStrutDynamics(stewart);
|
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||||
Ga = linearize(mdl, io, options);
|
Ga = linearize(mdl, io, options);
|
||||||
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Ga.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
Ga.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -517,8 +517,8 @@ The new dynamics from force actuator to relative motion sensor is shown in Figur
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org6c74c9a" class="outline-3">
|
<div id="outline-container-org0cea759" class="outline-3">
|
||||||
<h3 id="org6c74c9a"><span class="section-number-3">3.3</span> Obtained Damping</h3>
|
<h3 id="org0cea759"><span class="section-number-3">3.3</span> Obtained Damping</h3>
|
||||||
<div class="outline-text-3" id="text-3-3">
|
<div class="outline-text-3" id="text-3-3">
|
||||||
<p>
|
<p>
|
||||||
The control is a performed in a decentralized manner.
|
The control is a performed in a decentralized manner.
|
||||||
@ -543,10 +543,10 @@ The root locus is shown in figure <a href="#org0436b4d">10</a>.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org81b2156" class="outline-3">
|
<div id="outline-container-orga866100" class="outline-3">
|
||||||
<h3 id="org81b2156"><span class="section-number-3">3.4</span> Conclusion</h3>
|
<h3 id="orga866100"><span class="section-number-3">3.4</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-3-4">
|
<div class="outline-text-3" id="text-3-4">
|
||||||
<div class="important" id="orgb486ca9">
|
<div class="important" id="org2640d3c">
|
||||||
<p>
|
<p>
|
||||||
Joint stiffness does increase the resonance frequencies of the system but does not change the attainable damping when using relative motion sensors.
|
Joint stiffness does increase the resonance frequencies of the system but does not change the attainable damping when using relative motion sensors.
|
||||||
</p>
|
</p>
|
||||||
@ -567,17 +567,17 @@ Joint stiffness does increase the resonance frequencies of the system but does n
|
|||||||
We first initialize the Stewart platform without joint stiffness.
|
We first initialize the Stewart platform without joint stiffness.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -585,9 +585,9 @@ stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</spa
|
|||||||
The rotation point of the ground is located at the origin of frame \(\{A\}\).
|
The rotation point of the ground is located at the origin of frame \(\{A\}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -600,9 +600,9 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
Let’s first identify the transmissibility and compliance in the open-loop case.
|
Let’s first identify the transmissibility and compliance in the open-loop case.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
<pre class="src src-matlab"> controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
[T_ol, T_norm_ol, freqs] = computeTransmissibility();
|
[T_ol, T_norm_ol, freqs] = computeTransmissibility();
|
||||||
[C_ol, C_norm_ol, freqs] = computeCompliance();
|
[C_ol, C_norm_ol, freqs] = computeCompliance();
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -610,11 +610,11 @@ Let’s first identify the transmissibility and compliance in the open-loop
|
|||||||
Now, let’s identify the transmissibility and compliance for the Integral Force Feedback architecture.
|
Now, let’s identify the transmissibility and compliance for the Integral Force Feedback architecture.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'iff'</span>);
|
<pre class="src src-matlab"> controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'iff'</span>);
|
||||||
K_iff = (1e4<span class="org-type">/</span>s)<span class="org-type">*</span>eye(6);
|
K_iff = (1e4<span class="org-type">/</span>s)<span class="org-type">*</span>eye(6);
|
||||||
|
|
||||||
[T_iff, T_norm_iff, <span class="org-type">~</span>] = computeTransmissibility();
|
[T_iff, T_norm_iff, <span class="org-type">~</span>] = computeTransmissibility();
|
||||||
[C_iff, C_norm_iff, <span class="org-type">~</span>] = computeCompliance();
|
[C_iff, C_norm_iff, <span class="org-type">~</span>] = computeCompliance();
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -622,11 +622,11 @@ K_iff = (1e4<span class="org-type">/</span>s)<span class="org-type">*</span>eye(
|
|||||||
And for the Direct Velocity Feedback.
|
And for the Direct Velocity Feedback.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
|
<pre class="src src-matlab"> controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
|
||||||
K_dvf = 1e4<span class="org-type">*</span>s<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>5000)<span class="org-type">*</span>eye(6);
|
K_dvf = 1e4<span class="org-type">*</span>s<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>5000)<span class="org-type">*</span>eye(6);
|
||||||
|
|
||||||
[T_dvf, T_norm_dvf, <span class="org-type">~</span>] = computeTransmissibility();
|
[T_dvf, T_norm_dvf, <span class="org-type">~</span>] = computeTransmissibility();
|
||||||
[C_dvf, C_norm_dvf, <span class="org-type">~</span>] = computeCompliance();
|
[C_dvf, C_norm_dvf, <span class="org-type">~</span>] = computeCompliance();
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -661,7 +661,7 @@ K_dvf = 1e4<span class="org-type">*</span>s<span class="org-type">/</span>(1<spa
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:53</p>
|
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
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|
||||||
</html>
|
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|
||||||
|
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.org-query-replace { /* query-replace */ color: #b0e2ff; background-color: #cd00cd; }
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.org-secondary-selection { /* secondary-selection */ background-color: #ffff00; }
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.org-shadow { /* shadow */ color: #7f7f7f; }
|
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.org-show-paren-match { /* show-paren-match */ background-color: #40e0d0; }
|
||||||
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.org-show-paren-mismatch { /* show-paren-mismatch */ color: #ffffff; background-color: #a020f0; }
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.org-tool-bar { /* tool-bar */ color: #000000; background-color: #bfbfbf; }
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.org-tooltip { /* tooltip */ color: #000000; background-color: #ffffe0; }
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|
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|
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1095
docs/css/readtheorg.css
Normal file
1095
docs/css/readtheorg.css
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Load Diff
@ -3,7 +3,7 @@
|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:52 -->
|
<!-- 2021-01-08 ven. 15:30 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Cubic configuration for the Stewart Platform</title>
|
<title>Cubic configuration for the Stewart Platform</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -45,34 +45,34 @@
|
|||||||
<li><a href="#org6359f2f">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
|
<li><a href="#org6359f2f">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
|
||||||
<li><a href="#org5c37be2">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
|
<li><a href="#org5c37be2">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
|
||||||
<li><a href="#org32ac59a">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
|
<li><a href="#org32ac59a">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
|
||||||
<li><a href="#orgeb8ae82">1.5. Conclusion</a></li>
|
<li><a href="#org4e88cdb">1.5. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org312b7d4">2. Configuration with the Cube’s center above the mobile platform</a>
|
<li><a href="#org312b7d4">2. Configuration with the Cube’s center above the mobile platform</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org4983654">2.1. Having Cube’s center above the top platform</a></li>
|
<li><a href="#org4983654">2.1. Having Cube’s center above the top platform</a></li>
|
||||||
<li><a href="#orge53b7f6">2.2. Size of the platforms</a></li>
|
<li><a href="#orge53b7f6">2.2. Size of the platforms</a></li>
|
||||||
<li><a href="#org52825e8">2.3. Conclusion</a></li>
|
<li><a href="#org561a2bc">2.3. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org2387b96">3. Cubic size analysis</a>
|
<li><a href="#org2387b96">3. Cubic size analysis</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org3647f9f">3.1. Analysis</a></li>
|
<li><a href="#org3647f9f">3.1. Analysis</a></li>
|
||||||
<li><a href="#org701701b">3.2. Conclusion</a></li>
|
<li><a href="#org948a425">3.2. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org174af3a">4. Dynamic Coupling in the Cartesian Frame</a>
|
<li><a href="#org174af3a">4. Dynamic Coupling in the Cartesian Frame</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgdb33aa6">4.1. Cube’s center at the Center of Mass of the mobile platform</a></li>
|
<li><a href="#orgdb33aa6">4.1. Cube’s center at the Center of Mass of the mobile platform</a></li>
|
||||||
<li><a href="#org49b330b">4.2. Cube’s center not coincident with the Mass of the Mobile platform</a></li>
|
<li><a href="#org49b330b">4.2. Cube’s center not coincident with the Mass of the Mobile platform</a></li>
|
||||||
<li><a href="#orgf407e4d">4.3. Conclusion</a></li>
|
<li><a href="#org7d50eae">4.3. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org7831cff">5. Dynamic Coupling between actuators and sensors of each strut</a>
|
<li><a href="#org7831cff">5. Dynamic Coupling between actuators and sensors of each strut</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org38e9e8f">5.1. Coupling between the actuators and sensors - Cubic Architecture</a></li>
|
<li><a href="#org38e9e8f">5.1. Coupling between the actuators and sensors - Cubic Architecture</a></li>
|
||||||
<li><a href="#org21d40d3">5.2. Coupling between the actuators and sensors - Non-Cubic Architecture</a></li>
|
<li><a href="#org21d40d3">5.2. Coupling between the actuators and sensors - Non-Cubic Architecture</a></li>
|
||||||
<li><a href="#org0348380">5.3. Conclusion</a></li>
|
<li><a href="#orgeb8ae82">5.3. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org3ce1c89">6. Functions</a>
|
<li><a href="#org3ce1c89">6. Functions</a>
|
||||||
@ -128,7 +128,7 @@ In this document, the cubic architecture is analyzed:
|
|||||||
<a id="org6bc5f56"></a>
|
<a id="org6bc5f56"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="org783c5d6">
|
<div class="note" id="org6a03293">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_stiffnessl.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_stiffnessl.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -182,21 +182,21 @@ The Jacobian matrix is estimated at the location of the center of the cube.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = <span class="org-type">-</span>H<span class="org-type">/</span>2; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = <span class="org-type">-</span>H<span class="org-type">/</span>2; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
Hc = H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
Hc = H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
||||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
|
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
|
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -291,21 +291,21 @@ The Jacobian matrix is not estimated at the location of the center of the cube.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = 20e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = 20e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
Hc = H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
Hc = H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H<span class="org-type">/</span>2; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H<span class="org-type">/</span>2; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
||||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
|
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
|
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -400,21 +400,21 @@ The Jacobian is estimated at the cube center.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 80e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 80e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = <span class="org-type">-</span>30e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = <span class="org-type">-</span>30e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
Hc = 100e<span class="org-type">-</span>3; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
Hc = 100e<span class="org-type">-</span>3; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
||||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
|
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
|
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -520,21 +520,21 @@ The center of the cube from the top platform is at \(z = 110 - 175 = -65\).
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = <span class="org-type">-</span>H<span class="org-type">/</span>2; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = <span class="org-type">-</span>H<span class="org-type">/</span>2; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
Hc = 1.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
Hc = 1.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H<span class="org-type">/</span>2 <span class="org-type">+</span> 10e<span class="org-type">-</span>3; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H<span class="org-type">/</span>2 <span class="org-type">+</span> 10e<span class="org-type">-</span>3; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
||||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
|
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 215e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 195e<span class="org-type">-</span>3);
|
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 215e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 195e<span class="org-type">-</span>3);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -620,10 +620,10 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgeb8ae82" class="outline-3">
|
<div id="outline-container-org4e88cdb" class="outline-3">
|
||||||
<h3 id="orgeb8ae82"><span class="section-number-3">1.5</span> Conclusion</h3>
|
<h3 id="org4e88cdb"><span class="section-number-3">1.5</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-1-5">
|
<div class="outline-text-3" id="text-1-5">
|
||||||
<div class="important" id="orgb449c4a">
|
<div class="important" id="org2fc62c4">
|
||||||
<p>
|
<p>
|
||||||
Here are the conclusion about the Stiffness matrix for the Cubic configuration:
|
Here are the conclusion about the Stiffness matrix for the Cubic configuration:
|
||||||
</p>
|
</p>
|
||||||
@ -644,7 +644,7 @@ Here are the conclusion about the Stiffness matrix for the Cubic configuration:
|
|||||||
<a id="org419cdb0"></a>
|
<a id="org419cdb0"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="orge405fbc">
|
<div class="note" id="orgd5c0d4d">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_above_platforml.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_above_platforml.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -676,8 +676,8 @@ Thus, we want the cube’s center to be located above the top center.
|
|||||||
Let’s fix the Height of the Stewart platform and the position of frames \(\{A\}\) and \(\{B\}\):
|
Let’s fix the Height of the Stewart platform and the position of frames \(\{A\}\) and \(\{B\}\):
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = 20e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = 20e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -697,8 +697,8 @@ However, the rotational stiffnesses are increasing with the cube’s size bu
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Hc = 0.4<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
<pre class="src src-matlab"> Hc = 0.4<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -783,8 +783,8 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
|
|||||||
</table>
|
</table>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Hc = 1.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
<pre class="src src-matlab"> Hc = 1.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -870,8 +870,8 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
|
|||||||
</table>
|
</table>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Hc = 2.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
<pre class="src src-matlab"> Hc = 2.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1049,10 +1049,10 @@ For a small cube:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org52825e8" class="outline-3">
|
<div id="outline-container-org561a2bc" class="outline-3">
|
||||||
<h3 id="org52825e8"><span class="section-number-3">2.3</span> Conclusion</h3>
|
<h3 id="org561a2bc"><span class="section-number-3">2.3</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-2-3">
|
<div class="outline-text-3" id="text-2-3">
|
||||||
<div class="important" id="orgc3fb4db">
|
<div class="important" id="orga24e443">
|
||||||
<p>
|
<p>
|
||||||
We found that we can have a diagonal stiffness matrix using the cubic architecture when \(\{A\}\) and \(\{B\}\) are located above the top platform.
|
We found that we can have a diagonal stiffness matrix using the cubic architecture when \(\{A\}\) and \(\{B\}\) are located above the top platform.
|
||||||
Depending on the cube’s size, we obtain 3 different configurations.
|
Depending on the cube’s size, we obtain 3 different configurations.
|
||||||
@ -1102,7 +1102,7 @@ Depending on the cube’s size, we obtain 3 different configurations.
|
|||||||
<a id="org53ade24"></a>
|
<a id="org53ade24"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="org6ff8a60">
|
<div class="note" id="orgfd32e5a">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_size_analysisl.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_size_analysisl.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -1132,8 +1132,8 @@ We only vary the size of the cube.
|
|||||||
We initialize the wanted cube’s size.
|
We initialize the wanted cube’s size.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Hcs = 1e<span class="org-type">-</span>3<span class="org-type">*</span>[250<span class="org-type">:</span>20<span class="org-type">:</span>350]; <span class="org-comment">% Heights for the Cube [m]</span>
|
<pre class="src src-matlab"> Hcs = 1e<span class="org-type">-</span>3<span class="org-type">*</span>[250<span class="org-type">:</span>20<span class="org-type">:</span>350]; <span class="org-comment">% Heights for the Cube [m]</span>
|
||||||
Ks = zeros(6, 6, length(Hcs));
|
Ks = zeros(6, 6, length(Hcs));
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1141,7 +1141,7 @@ Ks = zeros(6, 6, length(Hcs));
|
|||||||
The height of the Stewart platform is fixed:
|
The height of the Stewart platform is fixed:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 100e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1149,8 +1149,8 @@ The height of the Stewart platform is fixed:
|
|||||||
The frames \(\{A\}\) and \(\{B\}\) are positioned at the Stewart platform center as well as the cube’s center:
|
The frames \(\{A\}\) and \(\{B\}\) are positioned at the Stewart platform center as well as the cube’s center:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">MO_B = <span class="org-type">-</span>50e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
<pre class="src src-matlab"> MO_B = <span class="org-type">-</span>50e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1168,14 +1168,14 @@ We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varyi
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org701701b" class="outline-3">
|
<div id="outline-container-org948a425" class="outline-3">
|
||||||
<h3 id="org701701b"><span class="section-number-3">3.2</span> Conclusion</h3>
|
<h3 id="org948a425"><span class="section-number-3">3.2</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-3-2">
|
<div class="outline-text-3" id="text-3-2">
|
||||||
<p>
|
<p>
|
||||||
We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size.
|
We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="important" id="org93b8347">
|
<div class="important" id="org60cc507">
|
||||||
<p>
|
<p>
|
||||||
In order to maximize the rotational stiffness of the Stewart platform, the size of the cube should be the highest possible.
|
In order to maximize the rotational stiffness of the Stewart platform, the size of the cube should be the highest possible.
|
||||||
</p>
|
</p>
|
||||||
@ -1192,7 +1192,7 @@ In order to maximize the rotational stiffness of the Stewart platform, the size
|
|||||||
<a id="org3507b2b"></a>
|
<a id="org3507b2b"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="org265afc7">
|
<div class="note" id="org5934a9c">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_coupling_cartesianl.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_coupling_cartesianl.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -1256,8 +1256,8 @@ Let’s create a Cubic Stewart Platform where the <b>Center of Mass of the m
|
|||||||
We define the size of the Stewart platform and the position of frames \(\{A\}\) and \(\{B\}\).
|
We define the size of the Stewart platform and the position of frames \(\{A\}\) and \(\{B\}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 200e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 200e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = <span class="org-type">-</span>10e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = <span class="org-type">-</span>10e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1265,20 +1265,20 @@ MO_B = <span class="org-type">-</span>10e<span class="org-type">-</span>3; <spa
|
|||||||
Now, we set the cube’s parameters such that the center of the cube is coincident with \(\{A\}\) and \(\{B\}\).
|
Now, we set the cube’s parameters such that the center of the cube is coincident with \(\{A\}\) and \(\{B\}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Hc = 2.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
<pre class="src src-matlab"> Hc = 2.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
||||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 25e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 25e<span class="org-type">-</span>3);
|
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 25e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 25e<span class="org-type">-</span>3);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C'</span>, 1e1<span class="org-type">*</span>ones(6,1));
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C'</span>, 1e1<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1286,7 +1286,7 @@ stewart = initializeStewartPose(stewart);
|
|||||||
Now we set the geometry and mass of the mobile platform such that its center of mass is coincident with \(\{A\}\) and \(\{B\}\).
|
Now we set the geometry and mass of the mobile platform such that its center of mass is coincident with \(\{A\}\) and \(\{B\}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_F.Fa)), ...
|
<pre class="src src-matlab"> stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_F.Fa)), ...
|
||||||
<span class="org-string">'Mpm'</span>, 10, ...
|
<span class="org-string">'Mpm'</span>, 10, ...
|
||||||
<span class="org-string">'Mph'</span>, 20e<span class="org-type">-</span>3, ...
|
<span class="org-string">'Mph'</span>, 20e<span class="org-type">-</span>3, ...
|
||||||
<span class="org-string">'Mpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_M.Mb)));
|
<span class="org-string">'Mpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_M.Mb)));
|
||||||
@ -1297,8 +1297,8 @@ Now we set the geometry and mass of the mobile platform such that its center of
|
|||||||
And we set small mass for the struts.
|
And we set small mass for the struts.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeCylindricalStruts(stewart, <span class="org-string">'Fsm'</span>, 1e<span class="org-type">-</span>3, <span class="org-string">'Msm'</span>, 1e<span class="org-type">-</span>3);
|
<pre class="src src-matlab"> stewart = initializeCylindricalStruts(stewart, <span class="org-string">'Fsm'</span>, 1e<span class="org-type">-</span>3, <span class="org-string">'Msm'</span>, 1e<span class="org-type">-</span>3);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1306,9 +1306,9 @@ stewart = initializeInertialSensor(stewart);
|
|||||||
No flexibility below the Stewart platform and no payload.
|
No flexibility below the Stewart platform and no payload.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1327,24 +1327,24 @@ The obtain geometry is shown in figure <a href="#orgb6b060a">10</a>.
|
|||||||
We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to the displacement of each strut \(d \bm{\mathcal{L}}\).
|
We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to the displacement of each strut \(d \bm{\mathcal{L}}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
<pre class="src src-matlab"> open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1352,10 +1352,10 @@ G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">
|
|||||||
Now, thanks to the Jacobian (Figure <a href="#org2137f5a">9</a>), we compute the transfer function from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\).
|
Now, thanks to the Jacobian (Figure <a href="#org2137f5a">9</a>), we compute the transfer function from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gc = inv(stewart.kinematics.J)<span class="org-type">*</span>G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>);
|
<pre class="src src-matlab"> Gc = inv(stewart.kinematics.J)<span class="org-type">*</span>G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>);
|
||||||
Gc = inv(stewart.kinematics.J)<span class="org-type">*</span>G<span class="org-type">*</span>stewart.kinematics.J;
|
Gc = inv(stewart.kinematics.J)<span class="org-type">*</span>G<span class="org-type">*</span>stewart.kinematics.J;
|
||||||
Gc.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
|
Gc.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
|
||||||
Gc.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
|
Gc.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1381,7 +1381,7 @@ It is interesting to note here that the system shown in Figure <a href="#org9d84
|
|||||||
<p><span class="figure-number">Figure 12: </span>Alternative way to decouple the system</p>
|
<p><span class="figure-number">Figure 12: </span>Alternative way to decouple the system</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="important" id="orgd31482e">
|
<div class="important" id="org489ed3b">
|
||||||
<p>
|
<p>
|
||||||
The dynamics is well decoupled at all frequencies.
|
The dynamics is well decoupled at all frequencies.
|
||||||
</p>
|
</p>
|
||||||
@ -1413,8 +1413,8 @@ This is because the Mass, Damping and Stiffness matrices are all diagonal.
|
|||||||
Let’s create a Stewart platform with a cubic architecture where the cube’s center is at the center of the Stewart platform.
|
Let’s create a Stewart platform with a cubic architecture where the cube’s center is at the center of the Stewart platform.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 200e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 200e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = <span class="org-type">-</span>100e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = <span class="org-type">-</span>100e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1422,20 +1422,20 @@ MO_B = <span class="org-type">-</span>100e<span class="org-type">-</span>3; <sp
|
|||||||
Now, we set the cube’s parameters such that the center of the cube is coincident with \(\{A\}\) and \(\{B\}\).
|
Now, we set the cube’s parameters such that the center of the cube is coincident with \(\{A\}\) and \(\{B\}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Hc = 2.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
<pre class="src src-matlab"> Hc = 2.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
||||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 25e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 25e<span class="org-type">-</span>3);
|
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 25e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 25e<span class="org-type">-</span>3);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C'</span>, 1e1<span class="org-type">*</span>ones(6,1));
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C'</span>, 1e1<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1443,7 +1443,7 @@ stewart = initializeStewartPose(stewart);
|
|||||||
However, the Center of Mass of the mobile platform is <b>not</b> located at the cube’s center.
|
However, the Center of Mass of the mobile platform is <b>not</b> located at the cube’s center.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_F.Fa)), ...
|
<pre class="src src-matlab"> stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_F.Fa)), ...
|
||||||
<span class="org-string">'Mpm'</span>, 10, ...
|
<span class="org-string">'Mpm'</span>, 10, ...
|
||||||
<span class="org-string">'Mph'</span>, 20e<span class="org-type">-</span>3, ...
|
<span class="org-string">'Mph'</span>, 20e<span class="org-type">-</span>3, ...
|
||||||
<span class="org-string">'Mpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_M.Mb)));
|
<span class="org-string">'Mpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_M.Mb)));
|
||||||
@ -1454,8 +1454,8 @@ However, the Center of Mass of the mobile platform is <b>not</b> located at the
|
|||||||
And we set small mass for the struts.
|
And we set small mass for the struts.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeCylindricalStruts(stewart, <span class="org-string">'Fsm'</span>, 1e<span class="org-type">-</span>3, <span class="org-string">'Msm'</span>, 1e<span class="org-type">-</span>3);
|
<pre class="src src-matlab"> stewart = initializeCylindricalStruts(stewart, <span class="org-string">'Fsm'</span>, 1e<span class="org-type">-</span>3, <span class="org-string">'Msm'</span>, 1e<span class="org-type">-</span>3);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1463,9 +1463,9 @@ stewart = initializeInertialSensor(stewart);
|
|||||||
No flexibility below the Stewart platform and no payload.
|
No flexibility below the Stewart platform and no payload.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1483,24 +1483,24 @@ The obtain geometry is shown in figure <a href="#orgc57dcd2">13</a>.
|
|||||||
We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to the displacement of each strut \(d \bm{\mathcal{L}}\).
|
We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to the displacement of each strut \(d \bm{\mathcal{L}}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
<pre class="src src-matlab"> open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1508,9 +1508,9 @@ G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">
|
|||||||
And we use the Jacobian to compute the transfer function from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\).
|
And we use the Jacobian to compute the transfer function from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gc = inv(stewart.kinematics.J)<span class="org-type">*</span>G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>);
|
<pre class="src src-matlab"> Gc = inv(stewart.kinematics.J)<span class="org-type">*</span>G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>);
|
||||||
Gc.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
|
Gc.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
|
||||||
Gc.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
|
Gc.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1525,7 +1525,7 @@ The obtain dynamics \(\bm{G}_{c}(s) = \bm{J}^{-T} \bm{G}(s) \bm{J}^{-1}\) is sho
|
|||||||
<p><span class="figure-number">Figure 14: </span>Obtained Dynamics from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\) (<a href="./figs/stewart_conf_coupling_mass_matrix.png">png</a>, <a href="./figs/stewart_conf_coupling_mass_matrix.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 14: </span>Obtained Dynamics from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\) (<a href="./figs/stewart_conf_coupling_mass_matrix.png">png</a>, <a href="./figs/stewart_conf_coupling_mass_matrix.pdf">pdf</a>)</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="important" id="orgc60cb20">
|
<div class="important" id="org798e5c6">
|
||||||
<p>
|
<p>
|
||||||
The system is decoupled at low frequency (the Stiffness matrix being diagonal), but it is <b>not</b> decoupled at all frequencies.
|
The system is decoupled at low frequency (the Stiffness matrix being diagonal), but it is <b>not</b> decoupled at all frequencies.
|
||||||
</p>
|
</p>
|
||||||
@ -1538,10 +1538,10 @@ This was expected as the mass matrix is not diagonal (the Center of Mass of the
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgf407e4d" class="outline-3">
|
<div id="outline-container-org7d50eae" class="outline-3">
|
||||||
<h3 id="orgf407e4d"><span class="section-number-3">4.3</span> Conclusion</h3>
|
<h3 id="org7d50eae"><span class="section-number-3">4.3</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-4-3">
|
<div class="outline-text-3" id="text-4-3">
|
||||||
<div class="important" id="org982344b">
|
<div class="important" id="org9b1be89">
|
||||||
<p>
|
<p>
|
||||||
Some conclusions can be drawn from the above analysis:
|
Some conclusions can be drawn from the above analysis:
|
||||||
</p>
|
</p>
|
||||||
@ -1562,7 +1562,7 @@ Some conclusions can be drawn from the above analysis:
|
|||||||
<a id="org7b3ed31"></a>
|
<a id="org7b3ed31"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="org96fba24">
|
<div class="note" id="org7a9b096">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_coupling_strutsl.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_coupling_strutsl.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -1593,28 +1593,28 @@ Let’s generate a Cubic architecture where the cube’s center and the
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 200e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 200e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = <span class="org-type">-</span>10e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = <span class="org-type">-</span>10e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
Hc = 2.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
Hc = 2.5<span class="org-type">*</span>H; <span class="org-comment">% Size of the useful part of the cube [m]</span>
|
||||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
||||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 25e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 25e<span class="org-type">-</span>3);
|
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 25e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 25e<span class="org-type">-</span>3);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C'</span>, 1e1<span class="org-type">*</span>ones(6,1));
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C'</span>, 1e1<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_F.Fa)), ...
|
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_F.Fa)), ...
|
||||||
<span class="org-string">'Mpm'</span>, 10, ...
|
<span class="org-string">'Mpm'</span>, 10, ...
|
||||||
<span class="org-string">'Mph'</span>, 20e<span class="org-type">-</span>3, ...
|
<span class="org-string">'Mph'</span>, 20e<span class="org-type">-</span>3, ...
|
||||||
<span class="org-string">'Mpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_M.Mb)));
|
<span class="org-string">'Mpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_M.Mb)));
|
||||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'Fsm'</span>, 1e<span class="org-type">-</span>3, <span class="org-string">'Msm'</span>, 1e<span class="org-type">-</span>3);
|
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'Fsm'</span>, 1e<span class="org-type">-</span>3, <span class="org-string">'Msm'</span>, 1e<span class="org-type">-</span>3);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1622,15 +1622,15 @@ stewart = initializeInertialSensor(stewart);
|
|||||||
No flexibility below the Stewart platform and no payload.
|
No flexibility below the Stewart platform and no payload.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1669,26 +1669,26 @@ Now we generate a Stewart platform which is not cubic but with approximately the
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">H = 200e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
<pre class="src src-matlab"> H = 200e<span class="org-type">-</span>3; <span class="org-comment">% height of the Stewart platform [m]</span>
|
||||||
MO_B = <span class="org-type">-</span>10e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
MO_B = <span class="org-type">-</span>10e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, H, <span class="org-string">'MO_B'</span>, MO_B);
|
||||||
stewart = generateGeneralConfiguration(stewart, <span class="org-string">'FR'</span>, 250e<span class="org-type">-</span>3, <span class="org-string">'MR'</span>, 150e<span class="org-type">-</span>3);
|
stewart = generateGeneralConfiguration(stewart, <span class="org-string">'FR'</span>, 250e<span class="org-type">-</span>3, <span class="org-string">'MR'</span>, 150e<span class="org-type">-</span>3);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C'</span>, 1e1<span class="org-type">*</span>ones(6,1));
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C'</span>, 1e1<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_F.Fa)), ...
|
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_F.Fa)), ...
|
||||||
<span class="org-string">'Mpm'</span>, 10, ...
|
<span class="org-string">'Mpm'</span>, 10, ...
|
||||||
<span class="org-string">'Mph'</span>, 20e<span class="org-type">-</span>3, ...
|
<span class="org-string">'Mph'</span>, 20e<span class="org-type">-</span>3, ...
|
||||||
<span class="org-string">'Mpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_M.Mb)));
|
<span class="org-string">'Mpr'</span>, 1.2<span class="org-type">*</span>max(vecnorm(stewart.platform_M.Mb)));
|
||||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'Fsm'</span>, 1e<span class="org-type">-</span>3, <span class="org-string">'Msm'</span>, 1e<span class="org-type">-</span>3);
|
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'Fsm'</span>, 1e<span class="org-type">-</span>3, <span class="org-string">'Msm'</span>, 1e<span class="org-type">-</span>3);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1696,9 +1696,9 @@ stewart = initializeInertialSensor(stewart);
|
|||||||
No flexibility below the Stewart platform and no payload.
|
No flexibility below the Stewart platform and no payload.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1729,10 +1729,10 @@ And we identify the dynamics from the actuator forces \(\tau_{i}\) to the relati
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org0348380" class="outline-3">
|
<div id="outline-container-orgeb8ae82" class="outline-3">
|
||||||
<h3 id="org0348380"><span class="section-number-3">5.3</span> Conclusion</h3>
|
<h3 id="orgeb8ae82"><span class="section-number-3">5.3</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-5-3">
|
<div class="outline-text-3" id="text-5-3">
|
||||||
<div class="important" id="orgd92f0ac">
|
<div class="important" id="org74729c6">
|
||||||
<p>
|
<p>
|
||||||
The Cubic architecture seems to not have any significant effect on the coupling between actuator and sensors of each strut and thus provides no advantages for decentralized control.
|
The Cubic architecture seems to not have any significant effect on the coupling between actuator and sensors of each strut and thus provides no advantages for decentralized control.
|
||||||
</p>
|
</p>
|
||||||
@ -1766,24 +1766,24 @@ This Matlab function is accessible <a href="../src/generateCubicConfiguration.m"
|
|||||||
<h4 id="org2cafc68">Function description</h4>
|
<h4 id="org2cafc68">Function description</h4>
|
||||||
<div class="outline-text-4" id="text-org2cafc68">
|
<div class="outline-text-4" id="text-org2cafc68">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">generateCubicConfiguration</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">generateCubicConfiguration</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% generateCubicConfiguration - Generate a Cubic Configuration</span>
|
<span class="org-comment">% generateCubicConfiguration - Generate a Cubic Configuration</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [stewart] = generateCubicConfiguration(stewart, args)</span>
|
<span class="org-comment">% Syntax: [stewart] = generateCubicConfiguration(stewart, args)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - stewart - A structure with the following fields</span>
|
<span class="org-comment">% - stewart - A structure with the following fields</span>
|
||||||
<span class="org-comment">% - geometry.H [1x1] - Total height of the platform [m]</span>
|
<span class="org-comment">% - geometry.H [1x1] - Total height of the platform [m]</span>
|
||||||
<span class="org-comment">% - args - Can have the following fields:</span>
|
<span class="org-comment">% - args - Can have the following fields:</span>
|
||||||
<span class="org-comment">% - Hc [1x1] - Height of the "useful" part of the cube [m]</span>
|
<span class="org-comment">% - Hc [1x1] - Height of the "useful" part of the cube [m]</span>
|
||||||
<span class="org-comment">% - FOc [1x1] - Height of the center of the cube with respect to {F} [m]</span>
|
<span class="org-comment">% - FOc [1x1] - Height of the center of the cube with respect to {F} [m]</span>
|
||||||
<span class="org-comment">% - FHa [1x1] - Height of the plane joining the points ai with respect to the frame {F} [m]</span>
|
<span class="org-comment">% - FHa [1x1] - Height of the plane joining the points ai with respect to the frame {F} [m]</span>
|
||||||
<span class="org-comment">% - MHb [1x1] - Height of the plane joining the points bi with respect to the frame {M} [m]</span>
|
<span class="org-comment">% - MHb [1x1] - Height of the plane joining the points bi with respect to the frame {M} [m]</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Outputs:</span>
|
<span class="org-comment">% Outputs:</span>
|
||||||
<span class="org-comment">% - stewart - updated Stewart structure with the added fields:</span>
|
<span class="org-comment">% - stewart - updated Stewart structure with the added fields:</span>
|
||||||
<span class="org-comment">% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}</span>
|
<span class="org-comment">% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}</span>
|
||||||
<span class="org-comment">% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}</span>
|
<span class="org-comment">% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1805,13 +1805,13 @@ This Matlab function is accessible <a href="../src/generateCubicConfiguration.m"
|
|||||||
<h4 id="org4fd2c96">Optional Parameters</h4>
|
<h4 id="org4fd2c96">Optional Parameters</h4>
|
||||||
<div class="outline-text-4" id="text-org4fd2c96">
|
<div class="outline-text-4" id="text-org4fd2c96">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">stewart</span>
|
<span class="org-variable-name">stewart</span>
|
||||||
<span class="org-variable-name">args</span>.Hc (1,1) double {mustBeNumeric, mustBePositive} = 60e<span class="org-type">-</span>3
|
<span class="org-variable-name">args</span>.Hc (1,1) double {mustBeNumeric, mustBePositive} = 60e<span class="org-type">-</span>3
|
||||||
<span class="org-variable-name">args</span>.FOc (1,1) double {mustBeNumeric} = 50e<span class="org-type">-</span>3
|
<span class="org-variable-name">args</span>.FOc (1,1) double {mustBeNumeric} = 50e<span class="org-type">-</span>3
|
||||||
<span class="org-variable-name">args</span>.FHa (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e<span class="org-type">-</span>3
|
<span class="org-variable-name">args</span>.FHa (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e<span class="org-type">-</span>3
|
||||||
<span class="org-variable-name">args</span>.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e<span class="org-type">-</span>3
|
<span class="org-variable-name">args</span>.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e<span class="org-type">-</span>3
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1821,8 +1821,8 @@ This Matlab function is accessible <a href="../src/generateCubicConfiguration.m"
|
|||||||
<h4 id="orgac26a8b">Check the <code>stewart</code> structure elements</h4>
|
<h4 id="orgac26a8b">Check the <code>stewart</code> structure elements</h4>
|
||||||
<div class="outline-text-4" id="text-orgac26a8b">
|
<div class="outline-text-4" id="text-orgac26a8b">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">assert(isfield(stewart.geometry, <span class="org-string">'H'</span>), <span class="org-string">'stewart.geometry should have attribute H'</span>)
|
<pre class="src src-matlab"> assert(isfield(stewart.geometry, <span class="org-string">'H'</span>), <span class="org-string">'stewart.geometry should have attribute H'</span>)
|
||||||
H = stewart.geometry.H;
|
H = stewart.geometry.H;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1837,18 +1837,18 @@ We define the useful points of the cube with respect to the Cube’s center.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">sx = [ 2; <span class="org-type">-</span>1; <span class="org-type">-</span>1];
|
<pre class="src src-matlab"> sx = [ 2; <span class="org-type">-</span>1; <span class="org-type">-</span>1];
|
||||||
sy = [ 0; 1; <span class="org-type">-</span>1];
|
sy = [ 0; 1; <span class="org-type">-</span>1];
|
||||||
sz = [ 1; 1; 1];
|
sz = [ 1; 1; 1];
|
||||||
|
|
||||||
R = [sx, sy, sz]<span class="org-type">./</span>vecnorm([sx, sy, sz]);
|
R = [sx, sy, sz]<span class="org-type">./</span>vecnorm([sx, sy, sz]);
|
||||||
|
|
||||||
L = args.Hc<span class="org-type">*</span>sqrt(3);
|
L = args.Hc<span class="org-type">*</span>sqrt(3);
|
||||||
|
|
||||||
Cc = R<span class="org-type">'*</span>[[0;0;L],[L;0;L],[L;0;0],[L;L;0],[0;L;0],[0;L;L]] <span class="org-type">-</span> [0;0;1.5<span class="org-type">*</span>args.Hc];
|
Cc = R<span class="org-type">'*</span>[[0;0;L],[L;0;L],[L;0;0],[L;L;0],[0;L;0],[0;L;L]] <span class="org-type">-</span> [0;0;1.5<span class="org-type">*</span>args.Hc];
|
||||||
|
|
||||||
CCf = [Cc(<span class="org-type">:</span>,1), Cc(<span class="org-type">:</span>,3), Cc(<span class="org-type">:</span>,3), Cc(<span class="org-type">:</span>,5), Cc(<span class="org-type">:</span>,5), Cc(<span class="org-type">:</span>,1)]; <span class="org-comment">% CCf(:,i) corresponds to the bottom cube's vertice corresponding to the i'th leg</span>
|
CCf = [Cc(<span class="org-type">:</span>,1), Cc(<span class="org-type">:</span>,3), Cc(<span class="org-type">:</span>,3), Cc(<span class="org-type">:</span>,5), Cc(<span class="org-type">:</span>,5), Cc(<span class="org-type">:</span>,1)]; <span class="org-comment">% CCf(:,i) corresponds to the bottom cube's vertice corresponding to the i'th leg</span>
|
||||||
CCm = [Cc(<span class="org-type">:</span>,2), Cc(<span class="org-type">:</span>,2), Cc(<span class="org-type">:</span>,4), Cc(<span class="org-type">:</span>,4), Cc(<span class="org-type">:</span>,6), Cc(<span class="org-type">:</span>,6)]; <span class="org-comment">% CCm(:,i) corresponds to the top cube's vertice corresponding to the i'th leg</span>
|
CCm = [Cc(<span class="org-type">:</span>,2), Cc(<span class="org-type">:</span>,2), Cc(<span class="org-type">:</span>,4), Cc(<span class="org-type">:</span>,4), Cc(<span class="org-type">:</span>,6), Cc(<span class="org-type">:</span>,6)]; <span class="org-comment">% CCm(:,i) corresponds to the top cube's vertice corresponding to the i'th leg</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1861,7 +1861,7 @@ CCm = [Cc(<span class="org-type">:</span>,2), Cc(<span class="org-type">:</span>
|
|||||||
We can compute the vector of each leg \({}^{C}\hat{\bm{s}}_{i}\) (unit vector from \({}^{C}C_{f}\) to \({}^{C}C_{m}\)).
|
We can compute the vector of each leg \({}^{C}\hat{\bm{s}}_{i}\) (unit vector from \({}^{C}C_{f}\) to \({}^{C}C_{m}\)).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">CSi = (CCm <span class="org-type">-</span> CCf)<span class="org-type">./</span>vecnorm(CCm <span class="org-type">-</span> CCf);
|
<pre class="src src-matlab"> CSi = (CCm <span class="org-type">-</span> CCf)<span class="org-type">./</span>vecnorm(CCm <span class="org-type">-</span> CCf);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1869,8 +1869,8 @@ We can compute the vector of each leg \({}^{C}\hat{\bm{s}}_{i}\) (unit vector fr
|
|||||||
We now which to compute the position of the joints \(a_{i}\) and \(b_{i}\).
|
We now which to compute the position of the joints \(a_{i}\) and \(b_{i}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Fa = CCf <span class="org-type">+</span> [0; 0; args.FOc] <span class="org-type">+</span> ((args.FHa<span class="org-type">-</span>(args.FOc<span class="org-type">-</span>args.Hc<span class="org-type">/</span>2))<span class="org-type">./</span>CSi(3,<span class="org-type">:</span>))<span class="org-type">.*</span>CSi;
|
<pre class="src src-matlab"> Fa = CCf <span class="org-type">+</span> [0; 0; args.FOc] <span class="org-type">+</span> ((args.FHa<span class="org-type">-</span>(args.FOc<span class="org-type">-</span>args.Hc<span class="org-type">/</span>2))<span class="org-type">./</span>CSi(3,<span class="org-type">:</span>))<span class="org-type">.*</span>CSi;
|
||||||
Mb = CCf <span class="org-type">+</span> [0; 0; args.FOc<span class="org-type">-</span>H] <span class="org-type">+</span> ((H<span class="org-type">-</span>args.MHb<span class="org-type">-</span>(args.FOc<span class="org-type">-</span>args.Hc<span class="org-type">/</span>2))<span class="org-type">./</span>CSi(3,<span class="org-type">:</span>))<span class="org-type">.*</span>CSi;
|
Mb = CCf <span class="org-type">+</span> [0; 0; args.FOc<span class="org-type">-</span>H] <span class="org-type">+</span> ((H<span class="org-type">-</span>args.MHb<span class="org-type">-</span>(args.FOc<span class="org-type">-</span>args.Hc<span class="org-type">/</span>2))<span class="org-type">./</span>CSi(3,<span class="org-type">:</span>))<span class="org-type">.*</span>CSi;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1880,8 +1880,8 @@ Mb = CCf <span class="org-type">+</span> [0; 0; args.FOc<span class="org-type">-
|
|||||||
<h4 id="org153763b">Populate the <code>stewart</code> structure</h4>
|
<h4 id="org153763b">Populate the <code>stewart</code> structure</h4>
|
||||||
<div class="outline-text-4" id="text-org153763b">
|
<div class="outline-text-4" id="text-org153763b">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart.platform_F.Fa = Fa;
|
<pre class="src src-matlab"> stewart.platform_F.Fa = Fa;
|
||||||
stewart.platform_M.Mb = Mb;
|
stewart.platform_M.Mb = Mb;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1905,7 +1905,7 @@ stewart.platform_M.Mb = Mb;
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -3,7 +3,7 @@
|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:52 -->
|
<!-- 2021-01-08 ven. 15:30 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Stewart Platform - Dynamics Study</title>
|
<title>Stewart Platform - Dynamics Study</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -43,13 +43,13 @@
|
|||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgc730bef">1.1. Comparison with fixed support</a></li>
|
<li><a href="#orgc730bef">1.1. Comparison with fixed support</a></li>
|
||||||
<li><a href="#orgefde538">1.2. Comparison with a flexible support</a></li>
|
<li><a href="#orgefde538">1.2. Comparison with a flexible support</a></li>
|
||||||
<li><a href="#orga9eb2fd">1.3. Conclusion</a></li>
|
<li><a href="#org53765b8">1.3. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#orgb6a1ef7">2. Comparison of the static transfer function and the Compliance matrix</a>
|
<li><a href="#orgb6a1ef7">2. Comparison of the static transfer function and the Compliance matrix</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org3f1c253">2.1. Analysis</a></li>
|
<li><a href="#org3f1c253">2.1. Analysis</a></li>
|
||||||
<li><a href="#orge261263">2.2. Conclusion</a></li>
|
<li><a href="#orga9eb2fd">2.2. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
</ul>
|
</ul>
|
||||||
@ -71,17 +71,17 @@ In this section, we wish to compare the effect of forces/torques applied by the
|
|||||||
Let’s generate a Stewart platform.
|
Let’s generate a Stewart platform.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -90,9 +90,9 @@ We don’t put any flexibility below the Stewart platform such that <b>its b
|
|||||||
We also don’t put any payload on top of the Stewart platform.
|
We also don’t put any payload on top of the Stewart platform.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -100,22 +100,22 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
The transfer function from actuator forces \(\bm{\tau}\) to the relative displacement of the mobile platform \(\mathcal{\bm{X}}\) is extracted.
|
The transfer function from actuator forces \(\bm{\tau}\) to the relative displacement of the mobile platform \(\mathcal{\bm{X}}\) is extracted.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -123,8 +123,8 @@ G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">
|
|||||||
Using the Jacobian matrix, we compute the transfer function from force/torques applied by the actuators on the frame \(\{B\}\) fixed to the mobile platform:
|
Using the Jacobian matrix, we compute the transfer function from force/torques applied by the actuators on the frame \(\{B\}\) fixed to the mobile platform:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gc = minreal(G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>));
|
<pre class="src src-matlab"> Gc = minreal(G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>));
|
||||||
Gc.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
Gc.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -132,15 +132,15 @@ Gc.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">
|
|||||||
We also extract the transfer function from external forces \(\bm{\mathcal{F}}_{\text{ext}}\) on the frame \(\{B\}\) fixed to the mobile platform to the relative displacement \(\mathcal{\bm{X}}\) of \(\{B\}\) with respect to frame \(\{A\}\):
|
We also extract the transfer function from external forces \(\bm{\mathcal{F}}_{\text{ext}}\) on the frame \(\{B\}\) fixed to the mobile platform to the relative displacement \(\mathcal{\bm{X}}\) of \(\{B\}\) with respect to frame \(\{A\}\):
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'F_ext'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% External forces/torques applied on {B}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'F_ext'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% External forces/torques applied on {B}</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
Gd = linearize(mdl, io, options);
|
Gd = linearize(mdl, io, options);
|
||||||
Gd.InputName = {<span class="org-string">'Fex'</span>, <span class="org-string">'Fey'</span>, <span class="org-string">'Fez'</span>, <span class="org-string">'Mex'</span>, <span class="org-string">'Mey'</span>, <span class="org-string">'Mez'</span>};
|
Gd.InputName = {<span class="org-string">'Fex'</span>, <span class="org-string">'Fey'</span>, <span class="org-string">'Fez'</span>, <span class="org-string">'Mex'</span>, <span class="org-string">'Mey'</span>, <span class="org-string">'Mez'</span>};
|
||||||
Gd.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
Gd.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -175,7 +175,7 @@ This can be understood from figure <a href="#orgd6db375">2</a> where \(\mathcal{
|
|||||||
We now add a flexible support under the Stewart platform.
|
We now add a flexible support under the Stewart platform.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'flexible'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'flexible'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -183,28 +183,28 @@ We now add a flexible support under the Stewart platform.
|
|||||||
And we perform again the identification.
|
And we perform again the identification.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
|
|
||||||
Gc = minreal(G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>));
|
Gc = minreal(G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>));
|
||||||
Gc.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
Gc.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'F_ext'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% External forces/torques applied on {B}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'F_ext'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% External forces/torques applied on {B}</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
Gd = linearize(mdl, io, options);
|
Gd = linearize(mdl, io, options);
|
||||||
Gd.InputName = {<span class="org-string">'Fex'</span>, <span class="org-string">'Fey'</span>, <span class="org-string">'Fez'</span>, <span class="org-string">'Mex'</span>, <span class="org-string">'Mey'</span>, <span class="org-string">'Mez'</span>};
|
Gd.InputName = {<span class="org-string">'Fex'</span>, <span class="org-string">'Fey'</span>, <span class="org-string">'Fez'</span>, <span class="org-string">'Mex'</span>, <span class="org-string">'Mey'</span>, <span class="org-string">'Mez'</span>};
|
||||||
Gd.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
Gd.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -235,10 +235,10 @@ And thus \(\mathcal{F}_{x}\) and \(\mathcal{F}_{x,\text{ext}}\) have clearly <b>
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="outline-container-orga9eb2fd" class="outline-3">
|
<div id="outline-container-org53765b8" class="outline-3">
|
||||||
<h3 id="orga9eb2fd"><span class="section-number-3">1.3</span> Conclusion</h3>
|
<h3 id="org53765b8"><span class="section-number-3">1.3</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-1-3">
|
<div class="outline-text-3" id="text-1-3">
|
||||||
<div class="important" id="org4878fef">
|
<div class="important" id="org35e4b5f">
|
||||||
<p>
|
<p>
|
||||||
The transfer function from forces/torques applied by the actuators on the payload \(\bm{\mathcal{F}} = \bm{J}^T \bm{\tau}\) to the pose of the mobile platform \(\bm{\mathcal{X}}\) is the same as the transfer function from external forces/torques to \(\bm{\mathcal{X}}\) as long as the Stewart platform’s base is fixed.
|
The transfer function from forces/torques applied by the actuators on the payload \(\bm{\mathcal{F}} = \bm{J}^T \bm{\tau}\) to the pose of the mobile platform \(\bm{\mathcal{X}}\) is the same as the transfer function from external forces/torques to \(\bm{\mathcal{X}}\) as long as the Stewart platform’s base is fixed.
|
||||||
</p>
|
</p>
|
||||||
@ -263,17 +263,17 @@ In this section, we see how the Compliance matrix of the Stewart platform is lin
|
|||||||
Initialization of the Stewart platform.
|
Initialization of the Stewart platform.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -281,9 +281,9 @@ stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</spa
|
|||||||
No flexibility below the Stewart platform and no payload.
|
No flexibility below the Stewart platform and no payload.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -291,28 +291,28 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
Estimation of the transfer function from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\):
|
Estimation of the transfer function from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\):
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gc = minreal(G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>));
|
<pre class="src src-matlab"> Gc = minreal(G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>));
|
||||||
Gc.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
Gc.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -470,10 +470,10 @@ And now at the Compliance matrix.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orge261263" class="outline-3">
|
<div id="outline-container-orga9eb2fd" class="outline-3">
|
||||||
<h3 id="orge261263"><span class="section-number-3">2.2</span> Conclusion</h3>
|
<h3 id="orga9eb2fd"><span class="section-number-3">2.2</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-2-2">
|
<div class="outline-text-3" id="text-2-2">
|
||||||
<div class="important" id="org2428297">
|
<div class="important" id="orgcecc007">
|
||||||
<p>
|
<p>
|
||||||
The low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\) corresponds to the compliance matrix of the Stewart platform.
|
The low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\) corresponds to the compliance matrix of the Stewart platform.
|
||||||
</p>
|
</p>
|
||||||
@ -485,7 +485,7 @@ The low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathc
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -3,7 +3,7 @@
|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:52 -->
|
<!-- 2021-01-08 ven. 15:29 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Stewart Platform with Flexible Elements</title>
|
<title>Stewart Platform with Flexible Elements</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -24,48 +24,48 @@
|
|||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgc309c7b">1. Simscape Model</a>
|
<li><a href="#orgc309c7b">1. Simscape Model</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org0e00e94">1.1. Flexible APA</a></li>
|
<li><a href="#orgae23ac5">1.1. Flexible APA</a></li>
|
||||||
<li><a href="#orgf337fe9">1.2. Flexible Joint</a></li>
|
<li><a href="#orgf337fe9">1.2. Flexible Joint</a></li>
|
||||||
<li><a href="#orgc239ed1">1.3. Identification</a></li>
|
<li><a href="#orga8d83ce">1.3. Identification</a></li>
|
||||||
<li><a href="#org59e4972">1.4. No Flexible Elements</a></li>
|
<li><a href="#org59e4972">1.4. No Flexible Elements</a></li>
|
||||||
<li><a href="#orgb06052a">1.5. Flexible joints</a></li>
|
<li><a href="#orgb06052a">1.5. Flexible joints</a></li>
|
||||||
<li><a href="#org4cccff6">1.6. Flexible APA</a></li>
|
<li><a href="#org0e00e94">1.6. Flexible APA</a></li>
|
||||||
<li><a href="#org4f41f14">1.7. Flexible Joints and APA</a></li>
|
<li><a href="#org4f41f14">1.7. Flexible Joints and APA</a></li>
|
||||||
<li><a href="#orga39e477">1.8. Save</a></li>
|
<li><a href="#orga39e477">1.8. Save</a></li>
|
||||||
<li><a href="#org1e66228">1.9. Direct Velocity Feedback</a></li>
|
<li><a href="#org1e66228">1.9. Direct Velocity Feedback</a></li>
|
||||||
<li><a href="#orgef60bbc">1.10. Integral Force Feedback</a></li>
|
<li><a href="#orgef60bbc">1.10. Integral Force Feedback</a></li>
|
||||||
<li><a href="#org50fdd32">1.11. Procedure to include flexible elements into Simscape</a></li>
|
<li><a href="#org50fdd32">1.11. Procedure to include flexible elements into Simscape</a></li>
|
||||||
<li><a href="#org55fe34f">1.12. Conclusion</a></li>
|
<li><a href="#org52c4099">1.12. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org2d65f84">2. Control with flexible elements</a>
|
<li><a href="#org2d65f84">2. Control with flexible elements</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org7f0d75c">2.1. Flexible APA and Flexible Joint</a></li>
|
<li><a href="#org7f0d75c">2.1. Flexible APA and Flexible Joint</a></li>
|
||||||
<li><a href="#org5f84aea">2.2. Identification</a></li>
|
<li><a href="#orgc239ed1">2.2. Identification</a></li>
|
||||||
<li><a href="#org5ae25be">2.3. Decentralized Direct Velocity Feedback</a></li>
|
<li><a href="#org5ae25be">2.3. Decentralized Direct Velocity Feedback</a></li>
|
||||||
<li><a href="#org3d014d0">2.4. HAC</a></li>
|
<li><a href="#org3d014d0">2.4. HAC</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org2b937bc">3. Flexible Joint Specifications</a>
|
<li><a href="#org2b937bc">3. Flexible Joint Specifications</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org775a387">3.1. Stewart Platform Initialization</a></li>
|
<li><a href="#org166293c">3.1. Stewart Platform Initialization</a></li>
|
||||||
<li><a href="#orgc430963">3.2. Effect of the Bending Stiffness</a></li>
|
<li><a href="#orgc430963">3.2. Effect of the Bending Stiffness</a></li>
|
||||||
<li><a href="#orgb29824b">3.3. Effect of the Torsion Stiffness</a></li>
|
<li><a href="#orgb29824b">3.3. Effect of the Torsion Stiffness</a></li>
|
||||||
<li><a href="#org6d029b0">3.4. Effect of the Axial Stiffness</a></li>
|
<li><a href="#org6d029b0">3.4. Effect of the Axial Stiffness</a></li>
|
||||||
<li><a href="#org5177329">3.5. Effect of the Radial (Shear) Stiffness</a></li>
|
<li><a href="#org5177329">3.5. Effect of the Radial (Shear) Stiffness</a></li>
|
||||||
<li><a href="#orge0f8240">3.6. Comparison of perfect joint and worst specified joint</a></li>
|
<li><a href="#orgd67ef9e">3.6. Comparison of perfect joint and worst specified joint</a></li>
|
||||||
<li><a href="#org79b6e2d">3.7. Conclusion</a></li>
|
<li><a href="#org55fe34f">3.7. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org8798d60">4. Flexible Joint Specifications with the APA300ML</a>
|
<li><a href="#org8798d60">4. Flexible Joint Specifications with the APA300ML</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org6d56b33">4.1. Stewart Platform Initialization</a></li>
|
<li><a href="#org6fc554b">4.1. Stewart Platform Initialization</a></li>
|
||||||
<li><a href="#orgdc3d576">4.2. Comparison of perfect joint and worst specified joint</a></li>
|
<li><a href="#orge0f8240">4.2. Comparison of perfect joint and worst specified joint</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#orgbae1ad3">5. Relative Motion Sensors</a>
|
<li><a href="#orgbae1ad3">5. Relative Motion Sensors</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org74f7ec9">5.1. Stewart Platform Initialization</a></li>
|
<li><a href="#org775a387">5.1. Stewart Platform Initialization</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#orgb454975">6. Struts with Encoders</a>
|
<li><a href="#orgb454975">6. Struts with Encoders</a>
|
||||||
@ -82,11 +82,11 @@
|
|||||||
<h2 id="orgc309c7b"><span class="section-number-2">1</span> Simscape Model</h2>
|
<h2 id="orgc309c7b"><span class="section-number-2">1</span> Simscape Model</h2>
|
||||||
<div class="outline-text-2" id="text-1">
|
<div class="outline-text-2" id="text-1">
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org0e00e94" class="outline-3">
|
<div id="outline-container-orgae23ac5" class="outline-3">
|
||||||
<h3 id="org0e00e94"><span class="section-number-3">1.1</span> Flexible APA</h3>
|
<h3 id="orgae23ac5"><span class="section-number-3">1.1</span> Flexible APA</h3>
|
||||||
<div class="outline-text-3" id="text-1-1">
|
<div class="outline-text-3" id="text-1-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -209,7 +209,7 @@
|
|||||||
<h3 id="orgf337fe9"><span class="section-number-3">1.2</span> Flexible Joint</h3>
|
<h3 id="orgf337fe9"><span class="section-number-3">1.2</span> Flexible Joint</h3>
|
||||||
<div class="outline-text-3" id="text-1-2">
|
<div class="outline-text-3" id="text-1-2">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">flex_joint = load(<span class="org-string">'./mat/flexor_025.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
<pre class="src src-matlab"> flex_joint = load(<span class="org-string">'./mat/flexor_025.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -325,37 +325,37 @@
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgc239ed1" class="outline-3">
|
<div id="outline-container-orga8d83ce" class="outline-3">
|
||||||
<h3 id="orgc239ed1"><span class="section-number-3">1.3</span> Identification</h3>
|
<h3 id="orga8d83ce"><span class="section-number-3">1.3</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-1-3">
|
<div class="outline-text-3" id="text-1-3">
|
||||||
<p>
|
<p>
|
||||||
And we identify the dynamics from force actuators to force sensors.
|
And we identify the dynamics from force actuators to force sensors.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Taum'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Taum'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors [N]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -365,12 +365,12 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="org59e4972"><span class="section-number-3">1.4</span> No Flexible Elements</h3>
|
<h3 id="org59e4972"><span class="section-number-3">1.4</span> No Flexible Elements</h3>
|
||||||
<div class="outline-text-3" id="text-1-4">
|
<div class="outline-text-3" id="text-1-4">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
||||||
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||||
@ -380,21 +380,21 @@ stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</sp
|
|||||||
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
|
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -411,32 +411,32 @@ G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
Gj = linearize(mdl, io, options);
|
Gj = linearize(mdl, io, options);
|
||||||
Gj.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Gj.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Gj.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
Gj.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org4cccff6" class="outline-3">
|
<div id="outline-container-org0e00e94" class="outline-3">
|
||||||
<h3 id="org4cccff6"><span class="section-number-3">1.6</span> Flexible APA</h3>
|
<h3 id="org0e00e94"><span class="section-number-3">1.6</span> Flexible APA</h3>
|
||||||
<div class="outline-text-3" id="text-1-6">
|
<div class="outline-text-3" id="text-1-6">
|
||||||
|
|
||||||
<div id="org6abb282" class="figure">
|
<div id="org6abb282" class="figure">
|
||||||
@ -446,12 +446,12 @@ Gj.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string"
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
||||||
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||||
@ -461,19 +461,19 @@ stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</sp
|
|||||||
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
Ga = <span class="org-type">-</span>linearize(mdl, io, options);
|
Ga = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||||
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Ga.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
Ga.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -490,24 +490,24 @@ Ga.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string"
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gf = <span class="org-type">-</span>linearize(mdl, io, options);
|
<pre class="src src-matlab"> Gf = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||||
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -517,7 +517,7 @@ Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string"
|
|||||||
<h3 id="orga39e477"><span class="section-number-3">1.8</span> Save</h3>
|
<h3 id="orga39e477"><span class="section-number-3">1.8</span> Save</h3>
|
||||||
<div class="outline-text-3" id="text-1-8">
|
<div class="outline-text-3" id="text-1-8">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">save(<span class="org-string">'./mat/flexible_stewart_platform.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'Gj'</span>, <span class="org-string">'Ga'</span>, <span class="org-string">'Gf'</span>);
|
<pre class="src src-matlab"> save(<span class="org-string">'./mat/flexible_stewart_platform.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'Gj'</span>, <span class="org-string">'Ga'</span>, <span class="org-string">'Gf'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -566,10 +566,10 @@ In order to model a flexible element with only few mass-spring-damper elements:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org55fe34f" class="outline-3">
|
<div id="outline-container-org52c4099" class="outline-3">
|
||||||
<h3 id="org55fe34f"><span class="section-number-3">1.12</span> Conclusion</h3>
|
<h3 id="org52c4099"><span class="section-number-3">1.12</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-1-12">
|
<div class="outline-text-3" id="text-1-12">
|
||||||
<div class="important" id="orgba069e0">
|
<div class="important" id="org7acf160">
|
||||||
<p>
|
<p>
|
||||||
The results seems to indicate that the model is well represented with only few degrees of freedom.
|
The results seems to indicate that the model is well represented with only few degrees of freedom.
|
||||||
This permit to have a relatively sane number of states for the model.
|
This permit to have a relatively sane number of states for the model.
|
||||||
@ -588,66 +588,66 @@ This permit to have a relatively sane number of states for the model.
|
|||||||
<h3 id="org7f0d75c"><span class="section-number-3">2.1</span> Flexible APA and Flexible Joint</h3>
|
<h3 id="org7f0d75c"><span class="section-number-3">2.1</span> Flexible APA and Flexible Joint</h3>
|
||||||
<div class="outline-text-3" id="text-2-1">
|
<div class="outline-text-3" id="text-2-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
flex_joint = load(<span class="org-string">'./mat/flexor_ID16.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
flex_joint = load(<span class="org-string">'./mat/flexor_ID16.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org5f84aea" class="outline-3">
|
<div id="outline-container-orgc239ed1" class="outline-3">
|
||||||
<h3 id="org5f84aea"><span class="section-number-3">2.2</span> Identification</h3>
|
<h3 id="orgc239ed1"><span class="section-number-3">2.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-2-2">
|
<div class="outline-text-3" id="text-2-2">
|
||||||
<p>
|
<p>
|
||||||
And we identify the dynamics from force actuators to force sensors.
|
And we identify the dynamics from force actuators to force sensors.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">G = <span class="org-type">-</span>linearize(mdl, io, options);
|
<pre class="src src-matlab"> G = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -660,12 +660,12 @@ G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">
|
|||||||
Controller Design
|
Controller Design
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Kl = <span class="org-type">-</span>1e5<span class="org-type">*</span>s<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>2e2)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>5e2) <span class="org-type">*</span> eye(6);
|
<pre class="src src-matlab"> Kl = <span class="org-type">-</span>1e5<span class="org-type">*</span>s<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>2e2)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>5e2) <span class="org-type">*</span> eye(6);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">isstable(feedback(G(1<span class="org-type">:</span>6,1<span class="org-type">:</span>6)<span class="org-type">*</span>Kl, eye(6), <span class="org-type">-</span>1))
|
<pre class="src src-matlab"> isstable(feedback(G(1<span class="org-type">:</span>6,1<span class="org-type">:</span>6)<span class="org-type">*</span>Kl, eye(6), <span class="org-type">-</span>1))
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -679,37 +679,37 @@ Controller Design
|
|||||||
<h3 id="org3d014d0"><span class="section-number-3">2.4</span> HAC</h3>
|
<h3 id="org3d014d0"><span class="section-number-3">2.4</span> HAC</h3>
|
||||||
<div class="outline-text-3" id="text-2-4">
|
<div class="outline-text-3" id="text-2-4">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Kx = tf(zeros(6));
|
<pre class="src src-matlab"> Kx = tf(zeros(6));
|
||||||
|
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-hac-dvf'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-hac-dvf'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'input'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'input'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
|
G.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gl = <span class="org-type">-</span>stewart.kinematics.J<span class="org-type">*</span>G;
|
<pre class="src src-matlab"> Gl = <span class="org-type">-</span>stewart.kinematics.J<span class="org-type">*</span>G;
|
||||||
Gl.OutputName = {<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>};
|
Gl.OutputName = {<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300;
|
<pre class="src src-matlab"> wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300;
|
||||||
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gl, wc)))) <span class="org-type">*</span> wc<span class="org-type">/</span>s <span class="org-type">*</span> 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>3<span class="org-type">/</span>wc);
|
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gl, wc)))) <span class="org-type">*</span> wc<span class="org-type">/</span>s <span class="org-type">*</span> 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>3<span class="org-type">/</span>wc);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -720,39 +720,39 @@ Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gl, wc)))) <span cl
|
|||||||
<h2 id="org2b937bc"><span class="section-number-2">3</span> Flexible Joint Specifications</h2>
|
<h2 id="org2b937bc"><span class="section-number-2">3</span> Flexible Joint Specifications</h2>
|
||||||
<div class="outline-text-2" id="text-3">
|
<div class="outline-text-2" id="text-3">
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org775a387" class="outline-3">
|
<div id="outline-container-org166293c" class="outline-3">
|
||||||
<h3 id="org775a387"><span class="section-number-3">3.1</span> Stewart Platform Initialization</h3>
|
<h3 id="org166293c"><span class="section-number-3">3.1</span> Stewart Platform Initialization</h3>
|
||||||
<div class="outline-text-3" id="text-3-1">
|
<div class="outline-text-3" id="text-3-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 43e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C1'</span>, 10<span class="org-type">*</span>ones(6,1));
|
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 43e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C1'</span>, 10<span class="org-type">*</span>ones(6,1));
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
|
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
<pre class="src src-matlab"> open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -762,7 +762,7 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="orgc430963"><span class="section-number-3">3.2</span> Effect of the Bending Stiffness</h3>
|
<h3 id="orgc430963"><span class="section-number-3">3.2</span> Effect of the Bending Stiffness</h3>
|
||||||
<div class="outline-text-3" id="text-3-2">
|
<div class="outline-text-3" id="text-3-2">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Kfs = [1, 10, 100, 1000]; <span class="org-comment">% [Nm/rad]</span>
|
<pre class="src src-matlab"> Kfs = [1, 10, 100, 1000]; <span class="org-comment">% [Nm/rad]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -772,7 +772,7 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="orgb29824b"><span class="section-number-3">3.3</span> Effect of the Torsion Stiffness</h3>
|
<h3 id="orgb29824b"><span class="section-number-3">3.3</span> Effect of the Torsion Stiffness</h3>
|
||||||
<div class="outline-text-3" id="text-3-3">
|
<div class="outline-text-3" id="text-3-3">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Kts = [10, 100, 500, 1000]; <span class="org-comment">% [Nm/rad]</span>
|
<pre class="src src-matlab"> Kts = [10, 100, 500, 1000]; <span class="org-comment">% [Nm/rad]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -782,7 +782,7 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="org6d029b0"><span class="section-number-3">3.4</span> Effect of the Axial Stiffness</h3>
|
<h3 id="org6d029b0"><span class="section-number-3">3.4</span> Effect of the Axial Stiffness</h3>
|
||||||
<div class="outline-text-3" id="text-3-4">
|
<div class="outline-text-3" id="text-3-4">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Kas = [1e6, 1e7, 1e8, 5e8, 1e9]; <span class="org-comment">% [N/m]</span>
|
<pre class="src src-matlab"> Kas = [1e6, 1e7, 1e8, 5e8, 1e9]; <span class="org-comment">% [N/m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -792,17 +792,17 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="org5177329"><span class="section-number-3">3.5</span> Effect of the Radial (Shear) Stiffness</h3>
|
<h3 id="org5177329"><span class="section-number-3">3.5</span> Effect of the Radial (Shear) Stiffness</h3>
|
||||||
<div class="outline-text-3" id="text-3-5">
|
<div class="outline-text-3" id="text-3-5">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Krs = [1e4, 1e5, 1e6, 1e7]; <span class="org-comment">% [N/m]</span>
|
<pre class="src src-matlab"> Krs = [1e4, 1e5, 1e6, 1e7]; <span class="org-comment">% [N/m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orge0f8240" class="outline-3">
|
<div id="outline-container-orgd67ef9e" class="outline-3">
|
||||||
<h3 id="orge0f8240"><span class="section-number-3">3.6</span> Comparison of perfect joint and worst specified joint</h3>
|
<h3 id="orgd67ef9e"><span class="section-number-3">3.6</span> Comparison of perfect joint and worst specified joint</h3>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org79b6e2d" class="outline-3">
|
<div id="outline-container-org55fe34f" class="outline-3">
|
||||||
<h3 id="org79b6e2d"><span class="section-number-3">3.7</span> Conclusion</h3>
|
<h3 id="org55fe34f"><span class="section-number-3">3.7</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-3-7">
|
<div class="outline-text-3" id="text-3-7">
|
||||||
<p>
|
<p>
|
||||||
Qualitatively:
|
Qualitatively:
|
||||||
@ -891,78 +891,78 @@ Quantitatively:
|
|||||||
<h2 id="org8798d60"><span class="section-number-2">4</span> Flexible Joint Specifications with the APA300ML</h2>
|
<h2 id="org8798d60"><span class="section-number-2">4</span> Flexible Joint Specifications with the APA300ML</h2>
|
||||||
<div class="outline-text-2" id="text-4">
|
<div class="outline-text-2" id="text-4">
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org6d56b33" class="outline-3">
|
<div id="outline-container-org6fc554b" class="outline-3">
|
||||||
<h3 id="org6d56b33"><span class="section-number-3">4.1</span> Stewart Platform Initialization</h3>
|
<h3 id="org6fc554b"><span class="section-number-3">4.1</span> Stewart Platform Initialization</h3>
|
||||||
<div class="outline-text-3" id="text-4-1">
|
<div class="outline-text-3" id="text-4-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
|
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
<pre class="src src-matlab"> open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgdc3d576" class="outline-3">
|
<div id="outline-container-orge0f8240" class="outline-3">
|
||||||
<h3 id="orgdc3d576"><span class="section-number-3">4.2</span> Comparison of perfect joint and worst specified joint</h3>
|
<h3 id="orge0f8240"><span class="section-number-3">4.2</span> Comparison of perfect joint and worst specified joint</h3>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-orgbae1ad3" class="outline-2">
|
<div id="outline-container-orgbae1ad3" class="outline-2">
|
||||||
<h2 id="orgbae1ad3"><span class="section-number-2">5</span> Relative Motion Sensors</h2>
|
<h2 id="orgbae1ad3"><span class="section-number-2">5</span> Relative Motion Sensors</h2>
|
||||||
<div class="outline-text-2" id="text-5">
|
<div class="outline-text-2" id="text-5">
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org74f7ec9" class="outline-3">
|
<div id="outline-container-org775a387" class="outline-3">
|
||||||
<h3 id="org74f7ec9"><span class="section-number-3">5.1</span> Stewart Platform Initialization</h3>
|
<h3 id="org775a387"><span class="section-number-3">5.1</span> Stewart Platform Initialization</h3>
|
||||||
<div class="outline-text-3" id="text-5-1">
|
<div class="outline-text-3" id="text-5-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
||||||
<span class="org-comment">% stewart = initializeFlexibleStrutDynamics(stewart, 'H', 0.03, 'K', apa.K, 'M', apa.M, 'n_xyz', apa.n_xyz, 'xi', 0.1, 'step_file', 'mat/APA300ML.STEP');</span>
|
<span class="org-comment">% stewart = initializeFlexibleStrutDynamics(stewart, 'H', 0.03, 'K', apa.K, 'M', apa.M, 'n_xyz', apa.n_xyz, 'xi', 0.1, 'step_file', 'mat/APA300ML.STEP');</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">flex_joint = load(<span class="org-string">'./mat/flexor_025.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
<pre class="src src-matlab"> flex_joint = load(<span class="org-string">'./mat/flexor_025.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
||||||
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||||
@ -976,33 +976,33 @@ stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</sp
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeCylindricalPlatforms(stewart);
|
<pre class="src src-matlab"> stewart = initializeCylindricalPlatforms(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeCylindricalStruts(stewart);
|
<pre class="src src-matlab"> stewart = initializeCylindricalStruts(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = computeJacobian(stewart);
|
<pre class="src src-matlab"> stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
|
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1017,7 +1017,7 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="org6bde940"><span class="section-number-3">6.1</span> Flexible Strut</h3>
|
<h3 id="org6bde940"><span class="section-number-3">6.1</span> Flexible Strut</h3>
|
||||||
<div class="outline-text-3" id="text-6-1">
|
<div class="outline-text-3" id="text-6-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/strut_encoder.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/strut_encoder.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1148,13 +1148,13 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="org4b369e6"><span class="section-number-3">6.2</span> Stewart Platform</h3>
|
<h3 id="org4b369e6"><span class="section-number-3">6.2</span> Stewart Platform</h3>
|
||||||
<div class="outline-text-3" id="text-6-2">
|
<div class="outline-text-3" id="text-6-2">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 95e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 220e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 95e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 220e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart, <span class="org-string">'FH'</span>, 22.5e<span class="org-type">-</span>3, <span class="org-string">'FR'</span>, 114e<span class="org-type">-</span>3, <span class="org-string">'FTh'</span>, [ <span class="org-type">-</span>11, 11, 120<span class="org-type">-</span>11, 120<span class="org-type">+</span>11, 240<span class="org-type">-</span>11, 240<span class="org-type">+</span>11]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180), ...
|
stewart = generateGeneralConfiguration(stewart, <span class="org-string">'FH'</span>, 22.5e<span class="org-type">-</span>3, <span class="org-string">'FR'</span>, 114e<span class="org-type">-</span>3, <span class="org-string">'FTh'</span>, [ <span class="org-type">-</span>11, 11, 120<span class="org-type">-</span>11, 120<span class="org-type">+</span>11, 240<span class="org-type">-</span>11, 240<span class="org-type">+</span>11]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180), ...
|
||||||
<span class="org-string">'MH'</span>, 22.5e<span class="org-type">-</span>3, <span class="org-string">'MR'</span>, 110e<span class="org-type">-</span>3, <span class="org-string">'MTh'</span>, [<span class="org-type">-</span>60<span class="org-type">+</span>15, 60<span class="org-type">-</span>15, 60<span class="org-type">+</span>15, 180<span class="org-type">-</span>15, 180<span class="org-type">+</span>15, <span class="org-type">-</span>60<span class="org-type">-</span>15]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180));
|
<span class="org-string">'MH'</span>, 22.5e<span class="org-type">-</span>3, <span class="org-string">'MR'</span>, 110e<span class="org-type">-</span>3, <span class="org-string">'MTh'</span>, [<span class="org-type">-</span>60<span class="org-type">+</span>15, 60<span class="org-type">-</span>15, 60<span class="org-type">+</span>15, 180<span class="org-type">-</span>15, 180<span class="org-type">+</span>15, <span class="org-type">-</span>60<span class="org-type">-</span>15]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180));
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
|
|
||||||
stewart = initializeFlexibleStrutAndJointDynamics(stewart, <span class="org-string">'H'</span>, (apa.int_xyz(1,3) <span class="org-type">-</span> apa.int_xyz(2,3)), ...
|
stewart = initializeFlexibleStrutAndJointDynamics(stewart, <span class="org-string">'H'</span>, (apa.int_xyz(1,3) <span class="org-type">-</span> apa.int_xyz(2,3)), ...
|
||||||
<span class="org-string">'K'</span>, apa.K, ...
|
<span class="org-string">'K'</span>, apa.K, ...
|
||||||
<span class="org-string">'M'</span>, apa.M, ...
|
<span class="org-string">'M'</span>, apa.M, ...
|
||||||
<span class="org-string">'n_xyz'</span>, apa.n_xyz, ...
|
<span class="org-string">'n_xyz'</span>, apa.n_xyz, ...
|
||||||
@ -1162,45 +1162,45 @@ stewart = initializeFlexibleStrutAndJointDynamics(stewart, <span class="org-stri
|
|||||||
<span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, ...
|
<span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, ...
|
||||||
<span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
<span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||||
|
|
||||||
stewart = initializeSolidPlatforms(stewart);
|
stewart = initializeSolidPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||||
ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 1);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 1);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Lm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Lm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors [N]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, ...
|
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, ...
|
||||||
<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>};
|
<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
@ -1216,7 +1216,7 @@ G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
<p class="date">Created: 2021-01-08 ven. 15:29</p>
|
||||||
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|
</div>
|
||||||
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|
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|
||||||
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|
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|
||||||
|
|||||||
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|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
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|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:52 -->
|
<!-- 2021-01-08 ven. 15:29 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Identification of the Stewart Platform using Simscape</title>
|
<title>Identification of the Stewart Platform using Simscape</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -50,13 +50,13 @@
|
|||||||
</li>
|
</li>
|
||||||
<li><a href="#orgfeed9a3">2. Transmissibility Analysis</a>
|
<li><a href="#orgfeed9a3">2. Transmissibility Analysis</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org5ba3096">2.1. Initialize the Stewart platform</a></li>
|
<li><a href="#org7c6996a">2.1. Initialize the Stewart platform</a></li>
|
||||||
<li><a href="#org279dcc8">2.2. Transmissibility</a></li>
|
<li><a href="#org279dcc8">2.2. Transmissibility</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org3ad92e9">3. Compliance Analysis</a>
|
<li><a href="#org3ad92e9">3. Compliance Analysis</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgc957431">3.1. Initialize the Stewart platform</a></li>
|
<li><a href="#org5ba3096">3.1. Initialize the Stewart platform</a></li>
|
||||||
<li><a href="#org26cb46a">3.2. Compliance</a></li>
|
<li><a href="#org26cb46a">3.2. Compliance</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
@ -64,18 +64,18 @@
|
|||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org25ca725">4.1. Compute the Transmissibility</a>
|
<li><a href="#org25ca725">4.1. Compute the Transmissibility</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgafb57d0">Function description</a></li>
|
<li><a href="#orgeae7abf">Function description</a></li>
|
||||||
<li><a href="#orga00af61">Optional Parameters</a></li>
|
<li><a href="#orge4c0895">Optional Parameters</a></li>
|
||||||
<li><a href="#org17a8811">Identification of the Transmissibility Matrix</a></li>
|
<li><a href="#org17a8811">Identification of the Transmissibility Matrix</a></li>
|
||||||
<li><a href="#orgbc9a383">Computation of the Frobenius norm</a></li>
|
<li><a href="#orgfd96322">Computation of the Frobenius norm</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#orgb6e05b3">4.2. Compute the Compliance</a>
|
<li><a href="#orgb6e05b3">4.2. Compute the Compliance</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org210c0ca">Function description</a></li>
|
<li><a href="#orgafb57d0">Function description</a></li>
|
||||||
<li><a href="#org24feeb1">Optional Parameters</a></li>
|
<li><a href="#orga00af61">Optional Parameters</a></li>
|
||||||
<li><a href="#org2c35042">Identification of the Compliance Matrix</a></li>
|
<li><a href="#org2c35042">Identification of the Compliance Matrix</a></li>
|
||||||
<li><a href="#orgb002200">Computation of the Frobenius norm</a></li>
|
<li><a href="#orgbc9a383">Computation of the Frobenius norm</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
</ul>
|
</ul>
|
||||||
@ -105,24 +105,24 @@ In this document, we discuss the various methods to identify the behavior of the
|
|||||||
<h3 id="org40f9c57"><span class="section-number-3">1.1</span> Initialize the Stewart Platform</h3>
|
<h3 id="org40f9c57"><span class="section-number-3">1.1</span> Initialize the Stewart Platform</h3>
|
||||||
<div class="outline-text-3" id="text-1-1">
|
<div class="outline-text-3" id="text-1-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -132,23 +132,23 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="orgd9529ee"><span class="section-number-3">1.2</span> Identification</h3>
|
<h3 id="orgd9529ee"><span class="section-number-3">1.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-1-2">
|
<div class="outline-text-3" id="text-1-2">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 2, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Velocity of {B} w.r.t. {A}</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 2, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Velocity of {B} w.r.t. {A}</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io);
|
||||||
<span class="org-comment">% G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};</span>
|
<span class="org-comment">% G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};</span>
|
||||||
<span class="org-comment">% G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};</span>
|
<span class="org-comment">% G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -156,7 +156,7 @@ G = linearize(mdl, io);
|
|||||||
Let’s check the size of <code>G</code>:
|
Let’s check the size of <code>G</code>:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">size(G)
|
<pre class="src src-matlab"> size(G)
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -173,7 +173,7 @@ ans =
|
|||||||
We expect to have only 12 states (corresponding to the 6dof of the mobile platform).
|
We expect to have only 12 states (corresponding to the 6dof of the mobile platform).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gm = minreal(G);
|
<pre class="src src-matlab"> Gm = minreal(G);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -196,7 +196,7 @@ And indeed, we obtain 12 states.
|
|||||||
We can perform the following transformation using the <code>ss2ss</code> command.
|
We can perform the following transformation using the <code>ss2ss</code> command.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gt = ss2ss(Gm, Gm.C);
|
<pre class="src src-matlab"> Gt = ss2ss(Gm, Gm.C);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -212,14 +212,14 @@ The measurements are the 6 displacement and 6 velocities of mobile platform with
|
|||||||
We could perform the transformation by hand:
|
We could perform the transformation by hand:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">At = Gm.C<span class="org-type">*</span>Gm.A<span class="org-type">*</span>pinv(Gm.C);
|
<pre class="src src-matlab"> At = Gm.C<span class="org-type">*</span>Gm.A<span class="org-type">*</span>pinv(Gm.C);
|
||||||
|
|
||||||
Bt = Gm.C<span class="org-type">*</span>Gm.B;
|
Bt = Gm.C<span class="org-type">*</span>Gm.B;
|
||||||
|
|
||||||
Ct = eye(12);
|
Ct = eye(12);
|
||||||
Dt = zeros(12, 6);
|
Dt = zeros(12, 6);
|
||||||
|
|
||||||
Gt = ss(At, Bt, Ct, Dt);
|
Gt = ss(At, Bt, Ct, Dt);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -229,7 +229,7 @@ Gt = ss(At, Bt, Ct, Dt);
|
|||||||
<h3 id="org11e3698"><span class="section-number-3">1.4</span> Analysis</h3>
|
<h3 id="org11e3698"><span class="section-number-3">1.4</span> Analysis</h3>
|
||||||
<div class="outline-text-3" id="text-1-4">
|
<div class="outline-text-3" id="text-1-4">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">[V,D] = eig(Gt.A);
|
<pre class="src src-matlab"> [V,D] = eig(Gt.A);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -306,28 +306,28 @@ To visualize the i’th mode, we may excite the system using the inputs \(U_
|
|||||||
Let’s first sort the modes and just take the modes corresponding to a eigenvalue with a positive imaginary part.
|
Let’s first sort the modes and just take the modes corresponding to a eigenvalue with a positive imaginary part.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ws = imag(diag(D));
|
<pre class="src src-matlab"> ws = imag(diag(D));
|
||||||
[ws,I] = sort(ws)
|
[ws,I] = sort(ws)
|
||||||
ws = ws(7<span class="org-type">:</span>end); I = I(7<span class="org-type">:</span>end);
|
ws = ws(7<span class="org-type">:</span>end); I = I(7<span class="org-type">:</span>end);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(ws)</span>
|
<pre class="src src-matlab"> <span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(ws)</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">i_mode = I(<span class="org-constant">i</span>); <span class="org-comment">% the argument is the i'th mode</span>
|
<pre class="src src-matlab"> i_mode = I(<span class="org-constant">i</span>); <span class="org-comment">% the argument is the i'th mode</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">lambda_i = D(i_mode, i_mode);
|
<pre class="src src-matlab"> lambda_i = D(i_mode, i_mode);
|
||||||
xi_i = V(<span class="org-type">:</span>,i_mode);
|
xi_i = V(<span class="org-type">:</span>,i_mode);
|
||||||
|
|
||||||
a_i = real(lambda_i);
|
a_i = real(lambda_i);
|
||||||
b_i = imag(lambda_i);
|
b_i = imag(lambda_i);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -335,13 +335,13 @@ b_i = imag(lambda_i);
|
|||||||
Let do 10 periods of the mode.
|
Let do 10 periods of the mode.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">t = linspace(0, 10<span class="org-type">/</span>(imag(lambda_i)<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>), 1000);
|
<pre class="src src-matlab"> t = linspace(0, 10<span class="org-type">/</span>(imag(lambda_i)<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>), 1000);
|
||||||
U_i = pinv(Gt.B) <span class="org-type">*</span> real(xi_i <span class="org-type">*</span> lambda_i <span class="org-type">*</span> (cos(b_i <span class="org-type">*</span> t) <span class="org-type">+</span> 1<span class="org-constant">i</span><span class="org-type">*</span>sin(b_i <span class="org-type">*</span> t)));
|
U_i = pinv(Gt.B) <span class="org-type">*</span> real(xi_i <span class="org-type">*</span> lambda_i <span class="org-type">*</span> (cos(b_i <span class="org-type">*</span> t) <span class="org-type">+</span> 1<span class="org-constant">i</span><span class="org-type">*</span>sin(b_i <span class="org-type">*</span> t)));
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">U = timeseries(U_i, t);
|
<pre class="src src-matlab"> U = timeseries(U_i, t);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -349,9 +349,9 @@ U_i = pinv(Gt.B) <span class="org-type">*</span> real(xi_i <span class="org-type
|
|||||||
Simulation:
|
Simulation:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
<pre class="src src-matlab"> load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
||||||
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, num2str(t(<span class="org-variable-name">end</span>)));
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, num2str(t(<span class="org-variable-name">end</span>)));
|
||||||
<span class="org-matlab-simulink-keyword">sim</span>(mdl);
|
<span class="org-matlab-simulink-keyword">sim</span>(mdl);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -359,7 +359,7 @@ Simulation:
|
|||||||
Save the movie of the mode shape.
|
Save the movie of the mode shape.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">smwritevideo(mdl, sprintf(<span class="org-string">'figs/mode%i'</span>, <span class="org-constant">i</span>), ...
|
<pre class="src src-matlab"> smwritevideo(mdl, sprintf(<span class="org-string">'figs/mode%i'</span>, <span class="org-constant">i</span>), ...
|
||||||
<span class="org-string">'PlaybackSpeedRatio'</span>, 1<span class="org-type">/</span>(b_i<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>), ...
|
<span class="org-string">'PlaybackSpeedRatio'</span>, 1<span class="org-type">/</span>(b_i<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>), ...
|
||||||
<span class="org-string">'FrameRate'</span>, 30, ...
|
<span class="org-string">'FrameRate'</span>, 30, ...
|
||||||
<span class="org-string">'FrameSize'</span>, [800, 400]);
|
<span class="org-string">'FrameSize'</span>, [800, 400]);
|
||||||
@ -367,7 +367,7 @@ Save the movie of the mode shape.
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">end</span>
|
<pre class="src src-matlab"> <span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -402,21 +402,21 @@ Save the movie of the mode shape.
|
|||||||
<a id="org5213401"></a>
|
<a id="org5213401"></a>
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org5ba3096" class="outline-3">
|
<div id="outline-container-org7c6996a" class="outline-3">
|
||||||
<h3 id="org5ba3096"><span class="section-number-3">2.1</span> Initialize the Stewart platform</h3>
|
<h3 id="org7c6996a"><span class="section-number-3">2.1</span> Initialize the Stewart platform</h3>
|
||||||
<div class="outline-text-3" id="text-2-1">
|
<div class="outline-text-3" id="text-2-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
|
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -424,9 +424,9 @@ stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</spa
|
|||||||
We set the rotation point of the ground to be at the same point at frames \(\{A\}\) and \(\{B\}\).
|
We set the rotation point of the ground to be at the same point at frames \(\{A\}\) and \(\{B\}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -436,30 +436,30 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="org279dcc8"><span class="section-number-3">2.2</span> Transmissibility</h3>
|
<h3 id="org279dcc8"><span class="section-number-3">2.2</span> Transmissibility</h3>
|
||||||
<div class="outline-text-3" id="text-2-2">
|
<div class="outline-text-3" id="text-2-2">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances/D_w'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Base Motion [m, rad]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances/D_w'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Base Motion [m, rad]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Absolute Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion [m, rad]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Absolute Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion [m, rad]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
T = linearize(mdl, io, options);
|
T = linearize(mdl, io, options);
|
||||||
T.InputName = {<span class="org-string">'Wdx'</span>, <span class="org-string">'Wdy'</span>, <span class="org-string">'Wdz'</span>, <span class="org-string">'Wrx'</span>, <span class="org-string">'Wry'</span>, <span class="org-string">'Wrz'</span>};
|
T.InputName = {<span class="org-string">'Wdx'</span>, <span class="org-string">'Wdy'</span>, <span class="org-string">'Wdz'</span>, <span class="org-string">'Wrx'</span>, <span class="org-string">'Wry'</span>, <span class="org-string">'Wrz'</span>};
|
||||||
T.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
T.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">freqs = logspace(1, 4, 1000);
|
<pre class="src src-matlab"> freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
<span class="org-type">figure</span>;
|
<span class="org-type">figure</span>;
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</span>
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
||||||
subplot(6, 6, (ix<span class="org-type">-</span>1)<span class="org-type">*</span>6 <span class="org-type">+</span> iy);
|
subplot(6, 6, (ix<span class="org-type">-</span>1)<span class="org-type">*</span>6 <span class="org-type">+</span> iy);
|
||||||
hold on;
|
hold on;
|
||||||
@ -474,7 +474,7 @@ T.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">
|
|||||||
yticklabels({});
|
yticklabels({});
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -487,13 +487,13 @@ From (<a href="#citeproc_bib_item_1">Preumont et al. 2007</a>), one can use the
|
|||||||
\end{align*}
|
\end{align*}
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">freqs = logspace(1, 4, 1000);
|
<pre class="src src-matlab"> freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
T_norm = zeros(length(freqs), 1);
|
T_norm = zeros(length(freqs), 1);
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(freqs)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(freqs)</span>
|
||||||
T_norm(<span class="org-constant">i</span>) = sqrt(trace(freqresp(T, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">*</span>freqresp(T, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">'</span>));
|
T_norm(<span class="org-constant">i</span>) = sqrt(trace(freqresp(T, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">*</span>freqresp(T, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">'</span>));
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -503,14 +503,14 @@ And we normalize by a factor \(\sqrt{6}\) to obtain a performance metric compara
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Gamma = T_norm<span class="org-type">/</span>sqrt(6);
|
<pre class="src src-matlab"> Gamma = T_norm<span class="org-type">/</span>sqrt(6);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
<pre class="src src-matlab"> <span class="org-type">figure</span>;
|
||||||
plot(freqs, Gamma)
|
plot(freqs, Gamma)
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -524,21 +524,21 @@ plot(freqs, Gamma)
|
|||||||
<a id="org39baa25"></a>
|
<a id="org39baa25"></a>
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-orgc957431" class="outline-3">
|
<div id="outline-container-org5ba3096" class="outline-3">
|
||||||
<h3 id="orgc957431"><span class="section-number-3">3.1</span> Initialize the Stewart platform</h3>
|
<h3 id="org5ba3096"><span class="section-number-3">3.1</span> Initialize the Stewart platform</h3>
|
||||||
<div class="outline-text-3" id="text-3-1">
|
<div class="outline-text-3" id="text-3-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
|
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -546,9 +546,9 @@ stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</spa
|
|||||||
We set the rotation point of the ground to be at the same point at frames \(\{A\}\) and \(\{B\}\).
|
We set the rotation point of the ground to be at the same point at frames \(\{A\}\) and \(\{B\}\).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -558,30 +558,30 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
|
|||||||
<h3 id="org26cb46a"><span class="section-number-3">3.2</span> Compliance</h3>
|
<h3 id="org26cb46a"><span class="section-number-3">3.2</span> Compliance</h3>
|
||||||
<div class="outline-text-3" id="text-3-2">
|
<div class="outline-text-3" id="text-3-2">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances/F_ext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Base Motion [m, rad]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances/F_ext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Base Motion [m, rad]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Absolute Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion [m, rad]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Absolute Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion [m, rad]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
C = linearize(mdl, io, options);
|
C = linearize(mdl, io, options);
|
||||||
C.InputName = {<span class="org-string">'Fdx'</span>, <span class="org-string">'Fdy'</span>, <span class="org-string">'Fdz'</span>, <span class="org-string">'Mdx'</span>, <span class="org-string">'Mdy'</span>, <span class="org-string">'Mdz'</span>};
|
C.InputName = {<span class="org-string">'Fdx'</span>, <span class="org-string">'Fdy'</span>, <span class="org-string">'Fdz'</span>, <span class="org-string">'Mdx'</span>, <span class="org-string">'Mdy'</span>, <span class="org-string">'Mdz'</span>};
|
||||||
C.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
C.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">freqs = logspace(1, 4, 1000);
|
<pre class="src src-matlab"> freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
<span class="org-type">figure</span>;
|
<span class="org-type">figure</span>;
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</span>
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
||||||
subplot(6, 6, (ix<span class="org-type">-</span>1)<span class="org-type">*</span>6 <span class="org-type">+</span> iy);
|
subplot(6, 6, (ix<span class="org-type">-</span>1)<span class="org-type">*</span>6 <span class="org-type">+</span> iy);
|
||||||
hold on;
|
hold on;
|
||||||
@ -596,7 +596,7 @@ C.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">
|
|||||||
yticklabels({});
|
yticklabels({});
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -605,20 +605,20 @@ We can try to use the Frobenius norm to obtain a scalar value representing the 6
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">freqs = logspace(1, 4, 1000);
|
<pre class="src src-matlab"> freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
C_norm = zeros(length(freqs), 1);
|
C_norm = zeros(length(freqs), 1);
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(freqs)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(freqs)</span>
|
||||||
C_norm(<span class="org-constant">i</span>) = sqrt(trace(freqresp(C, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">*</span>freqresp(C, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">'</span>));
|
C_norm(<span class="org-constant">i</span>) = sqrt(trace(freqresp(C, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">*</span>freqresp(C, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">'</span>));
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
<pre class="src src-matlab"> <span class="org-type">figure</span>;
|
||||||
plot(freqs, C_norm)
|
plot(freqs, C_norm)
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -637,42 +637,42 @@ plot(freqs, C_norm)
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgafb57d0" class="outline-4">
|
<div id="outline-container-orgeae7abf" class="outline-4">
|
||||||
<h4 id="orgafb57d0">Function description</h4>
|
<h4 id="orgeae7abf">Function description</h4>
|
||||||
<div class="outline-text-4" id="text-orgafb57d0">
|
<div class="outline-text-4" id="text-orgeae7abf">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[T, T_norm, freqs]</span> = <span class="org-function-name">computeTransmissibility</span>(<span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[T, T_norm, freqs]</span> = <span class="org-function-name">computeTransmissibility</span>(<span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% computeTransmissibility -</span>
|
<span class="org-comment">% computeTransmissibility -</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [T, T_norm, freqs] = computeTransmissibility(args)</span>
|
<span class="org-comment">% Syntax: [T, T_norm, freqs] = computeTransmissibility(args)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - args - Structure with the following fields:</span>
|
<span class="org-comment">% - args - Structure with the following fields:</span>
|
||||||
<span class="org-comment">% - plots [true/false] - Should plot the transmissilibty matrix and its Frobenius norm</span>
|
<span class="org-comment">% - plots [true/false] - Should plot the transmissilibty matrix and its Frobenius norm</span>
|
||||||
<span class="org-comment">% - freqs [] - Frequency vector to estimate the Frobenius norm</span>
|
<span class="org-comment">% - freqs [] - Frequency vector to estimate the Frobenius norm</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Outputs:</span>
|
<span class="org-comment">% Outputs:</span>
|
||||||
<span class="org-comment">% - T [6x6 ss] - Transmissibility matrix</span>
|
<span class="org-comment">% - T [6x6 ss] - Transmissibility matrix</span>
|
||||||
<span class="org-comment">% - T_norm [length(freqs)x1] - Frobenius norm of the Transmissibility matrix</span>
|
<span class="org-comment">% - T_norm [length(freqs)x1] - Frobenius norm of the Transmissibility matrix</span>
|
||||||
<span class="org-comment">% - freqs [length(freqs)x1] - Frequency vector in [Hz]</span>
|
<span class="org-comment">% - freqs [length(freqs)x1] - Frequency vector in [Hz]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orga00af61" class="outline-4">
|
<div id="outline-container-orge4c0895" class="outline-4">
|
||||||
<h4 id="orga00af61">Optional Parameters</h4>
|
<h4 id="orge4c0895">Optional Parameters</h4>
|
||||||
<div class="outline-text-4" id="text-orga00af61">
|
<div class="outline-text-4" id="text-orge4c0895">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">args</span>.plots logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
<span class="org-variable-name">args</span>.plots logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
||||||
<span class="org-variable-name">args</span>.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
<span class="org-variable-name">args</span>.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">freqs = args.freqs;
|
<pre class="src src-matlab"> freqs = args.freqs;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -682,22 +682,22 @@ plot(freqs, C_norm)
|
|||||||
<h4 id="org17a8811">Identification of the Transmissibility Matrix</h4>
|
<h4 id="org17a8811">Identification of the Transmissibility Matrix</h4>
|
||||||
<div class="outline-text-4" id="text-org17a8811">
|
<div class="outline-text-4" id="text-org17a8811">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances/D_w'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Base Motion [m, rad]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances/D_w'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Base Motion [m, rad]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Absolute Motion Sensor'</span>], 1, <span class="org-string">'output'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion [m, rad]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Absolute Motion Sensor'</span>], 1, <span class="org-string">'output'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion [m, rad]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
T = linearize(mdl, io, options);
|
T = linearize(mdl, io, options);
|
||||||
T.InputName = {<span class="org-string">'Wdx'</span>, <span class="org-string">'Wdy'</span>, <span class="org-string">'Wdz'</span>, <span class="org-string">'Wrx'</span>, <span class="org-string">'Wry'</span>, <span class="org-string">'Wrz'</span>};
|
T.InputName = {<span class="org-string">'Wdx'</span>, <span class="org-string">'Wdy'</span>, <span class="org-string">'Wdz'</span>, <span class="org-string">'Wrx'</span>, <span class="org-string">'Wry'</span>, <span class="org-string">'Wrz'</span>};
|
||||||
T.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
T.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -705,9 +705,9 @@ T.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">
|
|||||||
If wanted, the 6x6 transmissibility matrix is plotted.
|
If wanted, the 6x6 transmissibility matrix is plotted.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">p_handle = zeros(6<span class="org-type">*</span>6,1);
|
<pre class="src src-matlab"> p_handle = zeros(6<span class="org-type">*</span>6,1);
|
||||||
|
|
||||||
<span class="org-keyword">if</span> args.plots
|
<span class="org-keyword">if</span> args.plots
|
||||||
fig = <span class="org-type">figure</span>;
|
fig = <span class="org-type">figure</span>;
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</span>
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
||||||
@ -733,37 +733,37 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
|||||||
han.YLabel.Visible = <span class="org-string">'on'</span>;
|
han.YLabel.Visible = <span class="org-string">'on'</span>;
|
||||||
xlabel(han, <span class="org-string">'Frequency [Hz]'</span>);
|
xlabel(han, <span class="org-string">'Frequency [Hz]'</span>);
|
||||||
ylabel(han, <span class="org-string">'Transmissibility [m/m]'</span>);
|
ylabel(han, <span class="org-string">'Transmissibility [m/m]'</span>);
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgbc9a383" class="outline-4">
|
<div id="outline-container-orgfd96322" class="outline-4">
|
||||||
<h4 id="orgbc9a383">Computation of the Frobenius norm</h4>
|
<h4 id="orgfd96322">Computation of the Frobenius norm</h4>
|
||||||
<div class="outline-text-4" id="text-orgbc9a383">
|
<div class="outline-text-4" id="text-orgfd96322">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">T_norm = zeros(length(freqs), 1);
|
<pre class="src src-matlab"> T_norm = zeros(length(freqs), 1);
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(freqs)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(freqs)</span>
|
||||||
T_norm(<span class="org-constant">i</span>) = sqrt(trace(freqresp(T, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">*</span>freqresp(T, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">'</span>));
|
T_norm(<span class="org-constant">i</span>) = sqrt(trace(freqresp(T, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">*</span>freqresp(T, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">'</span>));
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">T_norm = T_norm<span class="org-type">/</span>sqrt(6);
|
<pre class="src src-matlab"> T_norm = T_norm<span class="org-type">/</span>sqrt(6);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">if</span> args.plots
|
<pre class="src src-matlab"> <span class="org-keyword">if</span> args.plots
|
||||||
<span class="org-type">figure</span>;
|
<span class="org-type">figure</span>;
|
||||||
plot(freqs, T_norm)
|
plot(freqs, T_norm)
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>);
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>);
|
||||||
ylabel(<span class="org-string">'Transmissibility - Frobenius Norm'</span>);
|
ylabel(<span class="org-string">'Transmissibility - Frobenius Norm'</span>);
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -778,42 +778,42 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org210c0ca" class="outline-4">
|
<div id="outline-container-orgafb57d0" class="outline-4">
|
||||||
<h4 id="org210c0ca">Function description</h4>
|
<h4 id="orgafb57d0">Function description</h4>
|
||||||
<div class="outline-text-4" id="text-org210c0ca">
|
<div class="outline-text-4" id="text-orgafb57d0">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[C, C_norm, freqs]</span> = <span class="org-function-name">computeCompliance</span>(<span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[C, C_norm, freqs]</span> = <span class="org-function-name">computeCompliance</span>(<span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% computeCompliance -</span>
|
<span class="org-comment">% computeCompliance -</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [C, C_norm, freqs] = computeCompliance(args)</span>
|
<span class="org-comment">% Syntax: [C, C_norm, freqs] = computeCompliance(args)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - args - Structure with the following fields:</span>
|
<span class="org-comment">% - args - Structure with the following fields:</span>
|
||||||
<span class="org-comment">% - plots [true/false] - Should plot the transmissilibty matrix and its Frobenius norm</span>
|
<span class="org-comment">% - plots [true/false] - Should plot the transmissilibty matrix and its Frobenius norm</span>
|
||||||
<span class="org-comment">% - freqs [] - Frequency vector to estimate the Frobenius norm</span>
|
<span class="org-comment">% - freqs [] - Frequency vector to estimate the Frobenius norm</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Outputs:</span>
|
<span class="org-comment">% Outputs:</span>
|
||||||
<span class="org-comment">% - C [6x6 ss] - Compliance matrix</span>
|
<span class="org-comment">% - C [6x6 ss] - Compliance matrix</span>
|
||||||
<span class="org-comment">% - C_norm [length(freqs)x1] - Frobenius norm of the Compliance matrix</span>
|
<span class="org-comment">% - C_norm [length(freqs)x1] - Frobenius norm of the Compliance matrix</span>
|
||||||
<span class="org-comment">% - freqs [length(freqs)x1] - Frequency vector in [Hz]</span>
|
<span class="org-comment">% - freqs [length(freqs)x1] - Frequency vector in [Hz]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org24feeb1" class="outline-4">
|
<div id="outline-container-orga00af61" class="outline-4">
|
||||||
<h4 id="org24feeb1">Optional Parameters</h4>
|
<h4 id="orga00af61">Optional Parameters</h4>
|
||||||
<div class="outline-text-4" id="text-org24feeb1">
|
<div class="outline-text-4" id="text-orga00af61">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">args</span>.plots logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
<span class="org-variable-name">args</span>.plots logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
||||||
<span class="org-variable-name">args</span>.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
<span class="org-variable-name">args</span>.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">freqs = args.freqs;
|
<pre class="src src-matlab"> freqs = args.freqs;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -823,22 +823,22 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
|||||||
<h4 id="org2c35042">Identification of the Compliance Matrix</h4>
|
<h4 id="org2c35042">Identification of the Compliance Matrix</h4>
|
||||||
<div class="outline-text-4" id="text-org2c35042">
|
<div class="outline-text-4" id="text-org2c35042">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances/F_ext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% External forces [N, N*m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances/F_ext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% External forces [N, N*m]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Absolute Motion Sensor'</span>], 1, <span class="org-string">'output'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion [m, rad]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Absolute Motion Sensor'</span>], 1, <span class="org-string">'output'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion [m, rad]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
C = linearize(mdl, io, options);
|
C = linearize(mdl, io, options);
|
||||||
C.InputName = {<span class="org-string">'Fdx'</span>, <span class="org-string">'Fdy'</span>, <span class="org-string">'Fdz'</span>, <span class="org-string">'Mdx'</span>, <span class="org-string">'Mdy'</span>, <span class="org-string">'Mdz'</span>};
|
C.InputName = {<span class="org-string">'Fdx'</span>, <span class="org-string">'Fdy'</span>, <span class="org-string">'Fdz'</span>, <span class="org-string">'Mdx'</span>, <span class="org-string">'Mdy'</span>, <span class="org-string">'Mdz'</span>};
|
||||||
C.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
C.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -846,9 +846,9 @@ C.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">
|
|||||||
If wanted, the 6x6 transmissibility matrix is plotted.
|
If wanted, the 6x6 transmissibility matrix is plotted.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">p_handle = zeros(6<span class="org-type">*</span>6,1);
|
<pre class="src src-matlab"> p_handle = zeros(6<span class="org-type">*</span>6,1);
|
||||||
|
|
||||||
<span class="org-keyword">if</span> args.plots
|
<span class="org-keyword">if</span> args.plots
|
||||||
fig = <span class="org-type">figure</span>;
|
fig = <span class="org-type">figure</span>;
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</span>
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
||||||
@ -873,34 +873,34 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
|||||||
han.YLabel.Visible = <span class="org-string">'on'</span>;
|
han.YLabel.Visible = <span class="org-string">'on'</span>;
|
||||||
xlabel(han, <span class="org-string">'Frequency [Hz]'</span>);
|
xlabel(han, <span class="org-string">'Frequency [Hz]'</span>);
|
||||||
ylabel(han, <span class="org-string">'Compliance [m/N, rad/(N*m)]'</span>);
|
ylabel(han, <span class="org-string">'Compliance [m/N, rad/(N*m)]'</span>);
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgb002200" class="outline-4">
|
<div id="outline-container-orgbc9a383" class="outline-4">
|
||||||
<h4 id="orgb002200">Computation of the Frobenius norm</h4>
|
<h4 id="orgbc9a383">Computation of the Frobenius norm</h4>
|
||||||
<div class="outline-text-4" id="text-orgb002200">
|
<div class="outline-text-4" id="text-orgbc9a383">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">freqs = args.freqs;
|
<pre class="src src-matlab"> freqs = args.freqs;
|
||||||
|
|
||||||
C_norm = zeros(length(freqs), 1);
|
C_norm = zeros(length(freqs), 1);
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(freqs)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(freqs)</span>
|
||||||
C_norm(<span class="org-constant">i</span>) = sqrt(trace(freqresp(C, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">*</span>freqresp(C, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">'</span>));
|
C_norm(<span class="org-constant">i</span>) = sqrt(trace(freqresp(C, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">*</span>freqresp(C, freqs(<span class="org-constant">i</span>), <span class="org-string">'Hz'</span>)<span class="org-type">'</span>));
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">if</span> args.plots
|
<pre class="src src-matlab"> <span class="org-keyword">if</span> args.plots
|
||||||
<span class="org-type">figure</span>;
|
<span class="org-type">figure</span>;
|
||||||
plot(freqs, C_norm)
|
plot(freqs, C_norm)
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>);
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>);
|
||||||
ylabel(<span class="org-string">'Compliance - Frobenius Norm'</span>);
|
ylabel(<span class="org-string">'Compliance - Frobenius Norm'</span>);
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -915,7 +915,7 @@ C_norm = zeros(length(freqs), 1);
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
<p class="date">Created: 2021-01-08 ven. 15:29</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
7
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4
docs/js/jquery.min.js
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@ -0,0 +1 @@
|
|||||||
|
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85
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$(function() {
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$('.note').before("<p class='admonition-title note'>Note</p>");
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$('.warning').before("<p class='admonition-title warning'>Warning</p>");
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$(document).on('click', ".wy-menu-vertical .current ul li a", function() {
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// add TOC button
|
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var toggleSidebar = $('<div id="toggle-sidebar"><a href="#table-of-contents"><h2>Table of Contents</h2></a></div>');
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$('#content').prepend(toggleSidebar);
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|
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// add close button when sidebar showed in mobile screen
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var closeBtn = $('<a class="close-sidebar" href="#">Close</a>');
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var tocTitle = $('#table-of-contents').find('h2');
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tocTitle.append(closeBtn);
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});
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window.SphinxRtdTheme = (function (jquery) {
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var stickyNav = (function () {
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win,
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stickyNavCssClass = 'stickynav',
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applyStickNav = function () {
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navBar = jquery('nav.wy-nav-side:first');
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win = jquery(window);
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};
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jquery(init);
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return {
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enable : enable
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}());
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StickyNav : stickyNav
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};
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}($));
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@ -3,7 +3,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:52 -->
|
<!-- 2021-01-08 ven. 15:17 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Kinematic Study of the Stewart Platform</title>
|
<title>Kinematic Study of the Stewart Platform</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -60,14 +60,14 @@
|
|||||||
</li>
|
</li>
|
||||||
<li><a href="#orgbb09f83">4. Estimation of the range validity of the approximate inverse kinematics</a>
|
<li><a href="#orgbb09f83">4. Estimation of the range validity of the approximate inverse kinematics</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orga79cde2">4.1. Stewart architecture definition</a></li>
|
<li><a href="#org78ce060">4.1. Stewart architecture definition</a></li>
|
||||||
<li><a href="#org34777fa">4.2. Comparison for “pure” translations</a></li>
|
<li><a href="#org34777fa">4.2. Comparison for “pure” translations</a></li>
|
||||||
<li><a href="#org76d9fc1">4.3. Conclusion</a></li>
|
<li><a href="#org76d9fc1">4.3. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org091e857">5. Estimated required actuator stroke from specified platform mobility</a>
|
<li><a href="#org091e857">5. Estimated required actuator stroke from specified platform mobility</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org7b16d1f">5.1. Stewart architecture definition</a></li>
|
<li><a href="#org34f6e0e">5.1. Stewart architecture definition</a></li>
|
||||||
<li><a href="#org82ba572">5.2. Wanted translations and rotations</a></li>
|
<li><a href="#org82ba572">5.2. Wanted translations and rotations</a></li>
|
||||||
<li><a href="#org5897eab">5.3. Needed stroke for “pure” rotations or translations</a></li>
|
<li><a href="#org5897eab">5.3. Needed stroke for “pure” rotations or translations</a></li>
|
||||||
<li><a href="#org1674055">5.4. Needed stroke for “combined” rotations or translations</a></li>
|
<li><a href="#org1674055">5.4. Needed stroke for “combined” rotations or translations</a></li>
|
||||||
@ -75,7 +75,7 @@
|
|||||||
</li>
|
</li>
|
||||||
<li><a href="#orgb685a81">6. Estimated platform mobility from specified actuator stroke</a>
|
<li><a href="#orgb685a81">6. Estimated platform mobility from specified actuator stroke</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org555f3a5">6.1. Stewart architecture definition</a></li>
|
<li><a href="#orga79cde2">6.1. Stewart architecture definition</a></li>
|
||||||
<li><a href="#orga6e12fe">6.2. Pure translations</a></li>
|
<li><a href="#orga6e12fe">6.2. Pure translations</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
@ -96,8 +96,8 @@
|
|||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org7a0813a">8.1. <code>computeJacobian</code>: Compute the Jacobian Matrix</a>
|
<li><a href="#org7a0813a">8.1. <code>computeJacobian</code>: Compute the Jacobian Matrix</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org8a3d2ba">Function description</a></li>
|
<li><a href="#org7f0fcca">Function description</a></li>
|
||||||
<li><a href="#org5f6ad77">Check the <code>stewart</code> structure elements</a></li>
|
<li><a href="#orgf06bd47">Check the <code>stewart</code> structure elements</a></li>
|
||||||
<li><a href="#org01f1158">Compute Jacobian Matrix</a></li>
|
<li><a href="#org01f1158">Compute Jacobian Matrix</a></li>
|
||||||
<li><a href="#org91d652d">Compute Stiffness Matrix</a></li>
|
<li><a href="#org91d652d">Compute Stiffness Matrix</a></li>
|
||||||
<li><a href="#org323b34e">Compute Compliance Matrix</a></li>
|
<li><a href="#org323b34e">Compute Compliance Matrix</a></li>
|
||||||
@ -107,17 +107,17 @@
|
|||||||
<li><a href="#org710c2c8">8.2. <code>inverseKinematics</code>: Compute Inverse Kinematics</a>
|
<li><a href="#org710c2c8">8.2. <code>inverseKinematics</code>: Compute Inverse Kinematics</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orge7e6266">Theory</a></li>
|
<li><a href="#orge7e6266">Theory</a></li>
|
||||||
<li><a href="#org6586e8a">Function description</a></li>
|
<li><a href="#org39a0af1">Function description</a></li>
|
||||||
<li><a href="#orgf078a15">Optional Parameters</a></li>
|
<li><a href="#orgcb9b73a">Optional Parameters</a></li>
|
||||||
<li><a href="#org4151034">Check the <code>stewart</code> structure elements</a></li>
|
<li><a href="#org31e89c1">Check the <code>stewart</code> structure elements</a></li>
|
||||||
<li><a href="#org7189e65">Compute</a></li>
|
<li><a href="#org7189e65">Compute</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#orgdc218cd">8.3. <code>forwardKinematicsApprox</code>: Compute the Approximate Forward Kinematics</a>
|
<li><a href="#orgdc218cd">8.3. <code>forwardKinematicsApprox</code>: Compute the Approximate Forward Kinematics</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org9b19ae7">Function description</a></li>
|
<li><a href="#org8a3d2ba">Function description</a></li>
|
||||||
<li><a href="#orgdf60206">Optional Parameters</a></li>
|
<li><a href="#orgf078a15">Optional Parameters</a></li>
|
||||||
<li><a href="#org2c19f08">Check the <code>stewart</code> structure elements</a></li>
|
<li><a href="#org5f6ad77">Check the <code>stewart</code> structure elements</a></li>
|
||||||
<li><a href="#orga496714">Computation</a></li>
|
<li><a href="#orga496714">Computation</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
@ -442,7 +442,7 @@ The function <code>forwardKinematicsApprox</code> (described <a href="#orgb960ae
|
|||||||
<a id="org5f8c5ea"></a>
|
<a id="org5f8c5ea"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="org9501cc6">
|
<div class="note" id="org919aba4">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_approximation_validity.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_approximation_validity.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -464,23 +464,23 @@ This will also gives us the range for which the approximate forward kinematic is
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orga79cde2" class="outline-3">
|
<div id="outline-container-org78ce060" class="outline-3">
|
||||||
<h3 id="orga79cde2"><span class="section-number-3">4.1</span> Stewart architecture definition</h3>
|
<h3 id="org78ce060"><span class="section-number-3">4.1</span> Stewart architecture definition</h3>
|
||||||
<div class="outline-text-3" id="text-4-1">
|
<div class="outline-text-3" id="text-4-1">
|
||||||
<p>
|
<p>
|
||||||
We first define some general Stewart architecture.
|
We first define some general Stewart architecture.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart);
|
stewart = initializeJointDynamics(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -499,16 +499,16 @@ The estimate required strut stroke for both the approximate and exact solutions
|
|||||||
The relative strut length displacement is shown in Figure <a href="#orgb451b90">2</a>.
|
The relative strut length displacement is shown in Figure <a href="#orgb451b90">2</a>.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Xrs = logspace(<span class="org-type">-</span>6, <span class="org-type">-</span>1, 100); <span class="org-comment">% Wanted X translation of the mobile platform [m]</span>
|
<pre class="src src-matlab"> Xrs = logspace(<span class="org-type">-</span>6, <span class="org-type">-</span>1, 100); <span class="org-comment">% Wanted X translation of the mobile platform [m]</span>
|
||||||
|
|
||||||
Ls_approx = zeros(6, length(Xrs));
|
Ls_approx = zeros(6, length(Xrs));
|
||||||
Ls_exact = zeros(6, length(Xrs));
|
Ls_exact = zeros(6, length(Xrs));
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(Xrs)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(Xrs)</span>
|
||||||
Xr = Xrs(<span class="org-constant">i</span>);
|
Xr = Xrs(<span class="org-constant">i</span>);
|
||||||
L_approx(<span class="org-type">:</span>, <span class="org-constant">i</span>) = stewart.kinematics.J<span class="org-type">*</span>[Xr; 0; 0; 0; 0; 0;];
|
L_approx(<span class="org-type">:</span>, <span class="org-constant">i</span>) = stewart.kinematics.J<span class="org-type">*</span>[Xr; 0; 0; 0; 0; 0;];
|
||||||
[<span class="org-type">~</span>, L_exact(<span class="org-type">:</span>, <span class="org-constant">i</span>)] = inverseKinematics(stewart, <span class="org-string">'AP'</span>, [Xr; 0; 0]);
|
[<span class="org-type">~</span>, L_exact(<span class="org-type">:</span>, <span class="org-constant">i</span>)] = inverseKinematics(stewart, <span class="org-string">'AP'</span>, [Xr; 0; 0]);
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -531,7 +531,7 @@ Ls_exact = zeros(6, length(Xrs));
|
|||||||
<div id="outline-container-org76d9fc1" class="outline-3">
|
<div id="outline-container-org76d9fc1" class="outline-3">
|
||||||
<h3 id="org76d9fc1"><span class="section-number-3">4.3</span> Conclusion</h3>
|
<h3 id="org76d9fc1"><span class="section-number-3">4.3</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-4-3">
|
<div class="outline-text-3" id="text-4-3">
|
||||||
<div class="important" id="orgfe0578a">
|
<div class="important" id="org3d5a817">
|
||||||
<p>
|
<p>
|
||||||
For small wanted displacements (up to \(\approx 1\%\) of the size of the Hexapod), the approximate inverse kinematic solution using the Jacobian matrix is quite correct.
|
For small wanted displacements (up to \(\approx 1\%\) of the size of the Hexapod), the approximate inverse kinematic solution using the Jacobian matrix is quite correct.
|
||||||
</p>
|
</p>
|
||||||
@ -548,7 +548,7 @@ For small wanted displacements (up to \(\approx 1\%\) of the size of the Hexapod
|
|||||||
<a id="orgb1464b6"></a>
|
<a id="orgb1464b6"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="org4fab0bc">
|
<div class="note" id="org7858fd4">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_required_actuator_stroke.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_required_actuator_stroke.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -565,23 +565,23 @@ This is what is analyzed in this section.
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org7b16d1f" class="outline-3">
|
<div id="outline-container-org34f6e0e" class="outline-3">
|
||||||
<h3 id="org7b16d1f"><span class="section-number-3">5.1</span> Stewart architecture definition</h3>
|
<h3 id="org34f6e0e"><span class="section-number-3">5.1</span> Stewart architecture definition</h3>
|
||||||
<div class="outline-text-3" id="text-5-1">
|
<div class="outline-text-3" id="text-5-1">
|
||||||
<p>
|
<p>
|
||||||
Let’s first define the Stewart platform architecture that we want to study.
|
Let’s first define the Stewart platform architecture that we want to study.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart);
|
stewart = initializeJointDynamics(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -594,12 +594,12 @@ stewart = computeJacobian(stewart);
|
|||||||
Let’s now define the wanted extreme translations and rotations.
|
Let’s now define the wanted extreme translations and rotations.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Tx_max = 50e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
<pre class="src src-matlab"> Tx_max = 50e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Ty_max = 50e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
Ty_max = 50e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Tz_max = 50e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
Tz_max = 50e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Rx_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
Rx_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
||||||
Ry_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
Ry_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
||||||
Rz_max = 0; <span class="org-comment">% Rotation [rad]</span>
|
Rz_max = 0; <span class="org-comment">% Rotation [rad]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -614,12 +614,12 @@ We do that using either the Inverse Kinematic solution or the Jacobian matrix as
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">LTx = stewart.kinematics.J<span class="org-type">*</span>[Tx_max 0 0 0 0 0]<span class="org-type">'</span>;
|
<pre class="src src-matlab"> LTx = stewart.kinematics.J<span class="org-type">*</span>[Tx_max 0 0 0 0 0]<span class="org-type">'</span>;
|
||||||
LTy = stewart.kinematics.J<span class="org-type">*</span>[0 Ty_max 0 0 0 0]<span class="org-type">'</span>;
|
LTy = stewart.kinematics.J<span class="org-type">*</span>[0 Ty_max 0 0 0 0]<span class="org-type">'</span>;
|
||||||
LTz = stewart.kinematics.J<span class="org-type">*</span>[0 0 Tz_max 0 0 0]<span class="org-type">'</span>;
|
LTz = stewart.kinematics.J<span class="org-type">*</span>[0 0 Tz_max 0 0 0]<span class="org-type">'</span>;
|
||||||
LRx = stewart.kinematics.J<span class="org-type">*</span>[0 0 0 Rx_max 0 0]<span class="org-type">'</span>;
|
LRx = stewart.kinematics.J<span class="org-type">*</span>[0 0 0 Rx_max 0 0]<span class="org-type">'</span>;
|
||||||
LRy = stewart.kinematics.J<span class="org-type">*</span>[0 0 0 0 Ry_max 0]<span class="org-type">'</span>;
|
LRy = stewart.kinematics.J<span class="org-type">*</span>[0 0 0 0 Ry_max 0]<span class="org-type">'</span>;
|
||||||
LRz = stewart.kinematics.J<span class="org-type">*</span>[0 0 0 0 0 Rz_max]<span class="org-type">'</span>;
|
LRz = stewart.kinematics.J<span class="org-type">*</span>[0 0 0 0 0 Rz_max]<span class="org-type">'</span>;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -652,7 +652,7 @@ To do so, we may estimate the required actuator stroke for all possible combinat
|
|||||||
Let’s first generate all the possible combination of maximum translation and rotations.
|
Let’s first generate all the possible combination of maximum translation and rotations.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Ps = [2<span class="org-type">*</span>(dec2bin(0<span class="org-type">:</span>5<span class="org-type">^</span>2<span class="org-type">-</span>1,5)<span class="org-type">-</span><span class="org-string">'0'</span>)<span class="org-type">-</span>1, zeros(5<span class="org-type">^</span>2, 1)]<span class="org-type">.*</span>[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
<pre class="src src-matlab"> Ps = [2<span class="org-type">*</span>(dec2bin(0<span class="org-type">:</span>5<span class="org-type">^</span>2<span class="org-type">-</span>1,5)<span class="org-type">-</span><span class="org-string">'0'</span>)<span class="org-type">-</span>1, zeros(5<span class="org-type">^</span>2, 1)]<span class="org-type">.*</span>[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -914,10 +914,10 @@ Let’s first generate all the possible combination of maximum translation a
|
|||||||
For all possible combination, we compute the required actuator stroke using the inverse kinematic solution.
|
For all possible combination, we compute the required actuator stroke using the inverse kinematic solution.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">L_min = 0;
|
<pre class="src src-matlab"> L_min = 0;
|
||||||
L_max = 0;
|
L_max = 0;
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:size(Ps,1)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:size(Ps,1)</span>
|
||||||
Rx = [1 0 0;
|
Rx = [1 0 0;
|
||||||
0 cos(Ps(<span class="org-constant">i</span>, 4)) <span class="org-type">-</span>sin(Ps(<span class="org-constant">i</span>, 4));
|
0 cos(Ps(<span class="org-constant">i</span>, 4)) <span class="org-type">-</span>sin(Ps(<span class="org-constant">i</span>, 4));
|
||||||
0 sin(Ps(<span class="org-constant">i</span>, 4)) cos(Ps(<span class="org-constant">i</span>, 4))];
|
0 sin(Ps(<span class="org-constant">i</span>, 4)) cos(Ps(<span class="org-constant">i</span>, 4))];
|
||||||
@ -939,7 +939,7 @@ L_max = 0;
|
|||||||
<span class="org-keyword">if</span> max(Ls) <span class="org-type">></span> L_max
|
<span class="org-keyword">if</span> max(Ls) <span class="org-type">></span> L_max
|
||||||
L_max = max(Ls)
|
L_max = max(Ls)
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -965,7 +965,7 @@ This is probably a much realistic estimation of the required actuator stroke.
|
|||||||
<a id="orge61164c"></a>
|
<a id="orge61164c"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="orgc9ecb6b">
|
<div class="note" id="orge5bfdd7">
|
||||||
<p>
|
<p>
|
||||||
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_mobility.m">here</a>.
|
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_mobility.m">here</a>.
|
||||||
</p>
|
</p>
|
||||||
@ -985,23 +985,23 @@ However, for small displacements, we can use the Jacobian as an approximate solu
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org555f3a5" class="outline-3">
|
<div id="outline-container-orga79cde2" class="outline-3">
|
||||||
<h3 id="org555f3a5"><span class="section-number-3">6.1</span> Stewart architecture definition</h3>
|
<h3 id="orga79cde2"><span class="section-number-3">6.1</span> Stewart architecture definition</h3>
|
||||||
<div class="outline-text-3" id="text-6-1">
|
<div class="outline-text-3" id="text-6-1">
|
||||||
<p>
|
<p>
|
||||||
Let’s first define the Stewart platform architecture that we want to study.
|
Let’s first define the Stewart platform architecture that we want to study.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart);
|
stewart = initializeJointDynamics(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1009,8 +1009,8 @@ stewart = computeJacobian(stewart);
|
|||||||
Let’s now define the actuator stroke.
|
Let’s now define the actuator stroke.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">L_min = <span class="org-type">-</span>50e<span class="org-type">-</span>6; <span class="org-comment">% [m]</span>
|
<pre class="src src-matlab"> L_min = <span class="org-type">-</span>50e<span class="org-type">-</span>6; <span class="org-comment">% [m]</span>
|
||||||
L_max = 50e<span class="org-type">-</span>6; <span class="org-comment">% [m]</span>
|
L_max = 50e<span class="org-type">-</span>6; <span class="org-comment">% [m]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1038,11 +1038,11 @@ To obtain the mobility “volume” attainable by the Stewart platform w
|
|||||||
For each possible value of \((\theta, \phi)\), we compute the maximum radius \(r\) attainable with the constraint that the stroke of each actuator should be between <code>L_min</code> and <code>L_max</code>.
|
For each possible value of \((\theta, \phi)\), we compute the maximum radius \(r\) attainable with the constraint that the stroke of each actuator should be between <code>L_min</code> and <code>L_max</code>.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">thetas = linspace(0, <span class="org-constant">pi</span>, 50);
|
<pre class="src src-matlab"> thetas = linspace(0, <span class="org-constant">pi</span>, 50);
|
||||||
phis = linspace(0, 2<span class="org-type">*</span><span class="org-constant">pi</span>, 50);
|
phis = linspace(0, 2<span class="org-type">*</span><span class="org-constant">pi</span>, 50);
|
||||||
rs = zeros(length(thetas), length(phis));
|
rs = zeros(length(thetas), length(phis));
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(thetas)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(thetas)</span>
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">j</span></span> = <span class="org-constant">1:length(phis)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">j</span></span> = <span class="org-constant">1:length(phis)</span>
|
||||||
Tx = sin(thetas(<span class="org-constant">i</span>))<span class="org-type">*</span>cos(phis(<span class="org-constant">j</span>));
|
Tx = sin(thetas(<span class="org-constant">i</span>))<span class="org-type">*</span>cos(phis(<span class="org-constant">j</span>));
|
||||||
Ty = sin(thetas(<span class="org-constant">i</span>))<span class="org-type">*</span>sin(phis(<span class="org-constant">j</span>));
|
Ty = sin(thetas(<span class="org-constant">i</span>))<span class="org-type">*</span>sin(phis(<span class="org-constant">j</span>));
|
||||||
@ -1052,7 +1052,7 @@ rs = zeros(length(thetas), length(phis));
|
|||||||
|
|
||||||
rs(<span class="org-constant">i</span>, <span class="org-constant">j</span>) = max([dL(dL<span class="org-type"><</span>0)<span class="org-type">*</span>L_min; dL(dL<span class="org-type">></span>0)<span class="org-type">*</span>L_max]);
|
rs(<span class="org-constant">i</span>, <span class="org-constant">j</span>) = max([dL(dL<span class="org-type"><</span>0)<span class="org-type">*</span>L_min; dL(dL<span class="org-type">></span>0)<span class="org-type">*</span>L_max]);
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1109,37 +1109,37 @@ We can also approximate the mobility by a sphere with a radius equal to the mini
|
|||||||
Let’s first define the Stewart Platform Geometry.
|
Let’s first define the Stewart Platform Geometry.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 150e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 150e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart, <span class="org-string">'AP'</span>, [0; 0; 0]);
|
stewart = computeJointsPose(stewart, <span class="org-string">'AP'</span>, [0; 0; 0]);
|
||||||
|
|
||||||
As_init = stewart.geometry.As;
|
As_init = stewart.geometry.As;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Tx_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
<pre class="src src-matlab"> Tx_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Ty_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
Ty_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Tz_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
Tz_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Rx_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
Rx_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
||||||
Ry_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
Ry_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
||||||
Rz_max = 0; <span class="org-comment">% Rotation [rad]</span>
|
Rz_max = 0; <span class="org-comment">% Rotation [rad]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Ps = [2<span class="org-type">*</span>(dec2bin(0<span class="org-type">:</span>5<span class="org-type">^</span>2<span class="org-type">-</span>1,5)<span class="org-type">-</span><span class="org-string">'0'</span>)<span class="org-type">-</span>1, zeros(5<span class="org-type">^</span>2, 1)]<span class="org-type">.*</span>[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
<pre class="src src-matlab"> Ps = [2<span class="org-type">*</span>(dec2bin(0<span class="org-type">:</span>5<span class="org-type">^</span>2<span class="org-type">-</span>1,5)<span class="org-type">-</span><span class="org-string">'0'</span>)<span class="org-type">-</span>1, zeros(5<span class="org-type">^</span>2, 1)]<span class="org-type">.*</span>[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">flex_ang = zeros(size(Ps, 1), 6);
|
<pre class="src src-matlab"> flex_ang = zeros(size(Ps, 1), 6);
|
||||||
Rxs = zeros(size(Ps, 1), 6)
|
Rxs = zeros(size(Ps, 1), 6)
|
||||||
Rys = zeros(size(Ps, 1), 6)
|
Rys = zeros(size(Ps, 1), 6)
|
||||||
Rzs = zeros(size(Ps, 1), 6)
|
Rzs = zeros(size(Ps, 1), 6)
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">Ps_i</span> = <span class="org-constant">1:size(Ps, 1)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">Ps_i</span> = <span class="org-constant">1:size(Ps, 1)</span>
|
||||||
Rx = [1 0 0;
|
Rx = [1 0 0;
|
||||||
0 cos(Ps(Ps_i, 4)) <span class="org-type">-</span>sin(Ps(Ps_i, 4));
|
0 cos(Ps(Ps_i, 4)) <span class="org-type">-</span>sin(Ps(Ps_i, 4));
|
||||||
0 sin(Ps(Ps_i, 4)) cos(Ps(Ps_i, 4))];
|
0 sin(Ps(Ps_i, 4)) cos(Ps(Ps_i, 4))];
|
||||||
@ -1165,7 +1165,7 @@ Rzs = zeros(size(Ps, 1), 6)
|
|||||||
Rxs(Ps_i, l_i) = atan2(<span class="org-type">-</span>MRf(2,3)<span class="org-type">/</span>cos(Rys(Ps_i, l_i)), MRf(3,3)<span class="org-type">/</span>cos(Rys(Ps_i, l_i)));
|
Rxs(Ps_i, l_i) = atan2(<span class="org-type">-</span>MRf(2,3)<span class="org-type">/</span>cos(Rys(Ps_i, l_i)), MRf(3,3)<span class="org-type">/</span>cos(Rys(Ps_i, l_i)));
|
||||||
Rzs(Ps_i, l_i) = atan2(<span class="org-type">-</span>MRf(1,2)<span class="org-type">/</span>cos(Rys(Ps_i, l_i)), MRf(1,1)<span class="org-type">/</span>cos(Rys(Ps_i, l_i)));
|
Rzs(Ps_i, l_i) = atan2(<span class="org-type">-</span>MRf(1,2)<span class="org-type">/</span>cos(Rys(Ps_i, l_i)), MRf(1,1)<span class="org-type">/</span>cos(Rys(Ps_i, l_i)));
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1173,7 +1173,7 @@ Rzs = zeros(size(Ps, 1), 6)
|
|||||||
And the maximum bending of the flexible joints is: (in [mrad])
|
And the maximum bending of the flexible joints is: (in [mrad])
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">1e3<span class="org-type">*</span>max(max(abs(flex_ang)))
|
<pre class="src src-matlab"> 1e3<span class="org-type">*</span>max(max(abs(flex_ang)))
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1183,7 +1183,7 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
|||||||
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">1e3<span class="org-type">*</span>max(max(sqrt(Rxs<span class="org-type">.^</span>2 <span class="org-type">+</span> Rys<span class="org-type">.^</span>2)))
|
<pre class="src src-matlab"> 1e3<span class="org-type">*</span>max(max(sqrt(Rxs<span class="org-type">.^</span>2 <span class="org-type">+</span> Rys<span class="org-type">.^</span>2)))
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1193,7 +1193,7 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
|||||||
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">1e3<span class="org-type">*</span>max(max(Rzs))
|
<pre class="src src-matlab"> 1e3<span class="org-type">*</span>max(max(Rzs))
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1211,31 +1211,31 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
|||||||
<h4 id="org656927f"><span class="section-number-4">7.2.1</span> Model Init</h4>
|
<h4 id="org656927f"><span class="section-number-4">7.2.1</span> Model Init</h4>
|
||||||
<div class="outline-text-4" id="text-7-2-1">
|
<div class="outline-text-4" id="text-7-2-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
<pre class="src src-matlab"> open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
|
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
disturbances = initializeDisturbances();
|
disturbances = initializeDisturbances();
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1245,29 +1245,29 @@ references = initializeReferences(stewart);
|
|||||||
<h4 id="orgc18819c"><span class="section-number-4">7.2.2</span> Controller design to be close to the wanted displacement</h4>
|
<h4 id="orgc18819c"><span class="section-number-4">7.2.2</span> Controller design to be close to the wanted displacement</h4>
|
||||||
<div class="outline-text-4" id="text-7-2-2">
|
<div class="outline-text-4" id="text-7-2-2">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io);
|
||||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||||
G.OutputName = {<span class="org-string">'L1'</span>, <span class="org-string">'L2'</span>, <span class="org-string">'L3'</span>, <span class="org-string">'L4'</span>, <span class="org-string">'L5'</span>, <span class="org-string">'L6'</span>};
|
G.OutputName = {<span class="org-string">'L1'</span>, <span class="org-string">'L2'</span>, <span class="org-string">'L3'</span>, <span class="org-string">'L4'</span>, <span class="org-string">'L5'</span>, <span class="org-string">'L6'</span>};
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>30;
|
<pre class="src src-matlab"> wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>30;
|
||||||
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span class="org-type">*</span> wc<span class="org-type">/</span>s <span class="org-type">*</span> 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>3<span class="org-type">/</span>wc);
|
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span class="org-type">*</span> wc<span class="org-type">/</span>s <span class="org-type">*</span> 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>3<span class="org-type">/</span>wc);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
|
<pre class="src src-matlab"> controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1277,25 +1277,25 @@ Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span cla
|
|||||||
<h4 id="orgd125932"><span class="section-number-4">7.2.3</span> Simulations</h4>
|
<h4 id="orgd125932"><span class="section-number-4">7.2.3</span> Simulations</h4>
|
||||||
<div class="outline-text-4" id="text-7-2-3">
|
<div class="outline-text-4" id="text-7-2-3">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Tx_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
<pre class="src src-matlab"> Tx_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Ty_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
Ty_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Tz_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
Tz_max = 60e<span class="org-type">-</span>6; <span class="org-comment">% Translation [m]</span>
|
||||||
Rx_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
Rx_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
||||||
Ry_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
Ry_max = 30e<span class="org-type">-</span>6; <span class="org-comment">% Rotation [rad]</span>
|
||||||
Rz_max = 0; <span class="org-comment">% Rotation [rad]</span>
|
Rz_max = 0; <span class="org-comment">% Rotation [rad]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Ps = [2<span class="org-type">*</span>(dec2bin(0<span class="org-type">:</span>5<span class="org-type">^</span>2<span class="org-type">-</span>1,5)<span class="org-type">-</span><span class="org-string">'0'</span>)<span class="org-type">-</span>1, zeros(5<span class="org-type">^</span>2, 1)]<span class="org-type">.*</span>[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
<pre class="src src-matlab"> Ps = [2<span class="org-type">*</span>(dec2bin(0<span class="org-type">:</span>5<span class="org-type">^</span>2<span class="org-type">-</span>1,5)<span class="org-type">-</span><span class="org-string">'0'</span>)<span class="org-type">-</span>1, zeros(5<span class="org-type">^</span>2, 1)]<span class="org-type">.*</span>[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">cl_perf = zeros(size(Ps, 1), 1); <span class="org-comment">% Closed loop performance [percentage]</span>
|
<pre class="src src-matlab"> cl_perf = zeros(size(Ps, 1), 1); <span class="org-comment">% Closed loop performance [percentage]</span>
|
||||||
Rs = zeros(size(Ps, 1), 5); <span class="org-comment">% Max Flexor angles for the 6 legs [mrad]</span>
|
Rs = zeros(size(Ps, 1), 5); <span class="org-comment">% Max Flexor angles for the 6 legs [mrad]</span>
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name">Ps_i</span> = <span class="org-constant">1:size(Ps, 1)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name">Ps_i</span> = <span class="org-constant">1:size(Ps, 1)</span>
|
||||||
fprintf(<span class="org-string">'Experiment %i over %i'</span>, Ps_i, size(Ps, 1));
|
fprintf(<span class="org-string">'Experiment %i over %i'</span>, Ps_i, size(Ps, 1));
|
||||||
|
|
||||||
references = initializeReferences(stewart, <span class="org-string">'t'</span>, 0, <span class="org-string">'r'</span>, Ps(Ps_i, <span class="org-type">:</span>)<span class="org-type">'</span>);
|
references = initializeReferences(stewart, <span class="org-string">'t'</span>, 0, <span class="org-string">'r'</span>, Ps(Ps_i, <span class="org-type">:</span>)<span class="org-type">'</span>);
|
||||||
@ -1304,7 +1304,7 @@ Rs = zeros(size(Ps, 1), 5); <span class="org-comment">% Max Flexor angles for th
|
|||||||
|
|
||||||
cl_perf(Ps_i) = 100<span class="org-type">*</span>max(abs((simout.y.dLm.Data(end, <span class="org-type">:</span>) <span class="org-type">-</span> references.rL.Data(<span class="org-type">:</span>,1,1)<span class="org-type">'</span>)<span class="org-type">./</span>simout.y.dLm.Data(end, <span class="org-type">:</span>)));
|
cl_perf(Ps_i) = 100<span class="org-type">*</span>max(abs((simout.y.dLm.Data(end, <span class="org-type">:</span>) <span class="org-type">-</span> references.rL.Data(<span class="org-type">:</span>,1,1)<span class="org-type">'</span>)<span class="org-type">./</span>simout.y.dLm.Data(end, <span class="org-type">:</span>)));
|
||||||
Rs(Ps_i, <span class="org-type">:</span>) = [max(abs(1e3<span class="org-type">*</span>simout.y.Rf.Data(end, 1<span class="org-type">:</span>2<span class="org-type">:</span>end))), max(abs(1e3<span class="org-type">*</span>simout.y.Rf.Data(end, 2<span class="org-type">:</span>2<span class="org-type">:</span>end))), max(abs(1e3<span class="org-type">*</span>simout.y.Rm.Data(end, 1<span class="org-type">:</span>3<span class="org-type">:</span>end))), max(abs(1e3<span class="org-type">*</span>simout.y.Rm.Data(end, 2<span class="org-type">:</span>3<span class="org-type">:</span>end))), max(abs(1e3<span class="org-type">*</span>simout.y.Rm.Data(end, 3<span class="org-type">:</span>3<span class="org-type">:</span>end)))]<span class="org-type">'</span>;
|
Rs(Ps_i, <span class="org-type">:</span>) = [max(abs(1e3<span class="org-type">*</span>simout.y.Rf.Data(end, 1<span class="org-type">:</span>2<span class="org-type">:</span>end))), max(abs(1e3<span class="org-type">*</span>simout.y.Rf.Data(end, 2<span class="org-type">:</span>2<span class="org-type">:</span>end))), max(abs(1e3<span class="org-type">*</span>simout.y.Rm.Data(end, 1<span class="org-type">:</span>3<span class="org-type">:</span>end))), max(abs(1e3<span class="org-type">*</span>simout.y.Rm.Data(end, 2<span class="org-type">:</span>3<span class="org-type">:</span>end))), max(abs(1e3<span class="org-type">*</span>simout.y.Rm.Data(end, 3<span class="org-type">:</span>3<span class="org-type">:</span>end)))]<span class="org-type">'</span>;
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1312,7 +1312,7 @@ Rs = zeros(size(Ps, 1), 5); <span class="org-comment">% Max Flexor angles for th
|
|||||||
Verify that the simulations are all correct:
|
Verify that the simulations are all correct:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">max(cl_perf)
|
<pre class="src src-matlab"> max(cl_perf)
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1390,43 +1390,43 @@ This Matlab function is accessible <a href="../src/computeJacobian.m">here</a>.
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org8a3d2ba" class="outline-4">
|
<div id="outline-container-org7f0fcca" class="outline-4">
|
||||||
<h4 id="org8a3d2ba">Function description</h4>
|
<h4 id="org7f0fcca">Function description</h4>
|
||||||
<div class="outline-text-4" id="text-org8a3d2ba">
|
<div class="outline-text-4" id="text-org7f0fcca">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">computeJacobian</span>(<span class="org-variable-name">stewart</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">computeJacobian</span>(<span class="org-variable-name">stewart</span>)
|
||||||
<span class="org-comment">% computeJacobian -</span>
|
<span class="org-comment">% computeJacobian -</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [stewart] = computeJacobian(stewart)</span>
|
<span class="org-comment">% Syntax: [stewart] = computeJacobian(stewart)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - stewart - With at least the following fields:</span>
|
<span class="org-comment">% - stewart - With at least the following fields:</span>
|
||||||
<span class="org-comment">% - geometry.As [3x6] - The 6 unit vectors for each strut expressed in {A}</span>
|
<span class="org-comment">% - geometry.As [3x6] - The 6 unit vectors for each strut expressed in {A}</span>
|
||||||
<span class="org-comment">% - geometry.Ab [3x6] - The 6 position of the joints bi expressed in {A}</span>
|
<span class="org-comment">% - geometry.Ab [3x6] - The 6 position of the joints bi expressed in {A}</span>
|
||||||
<span class="org-comment">% - actuators.K [6x1] - Total stiffness of the actuators</span>
|
<span class="org-comment">% - actuators.K [6x1] - Total stiffness of the actuators</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Outputs:</span>
|
<span class="org-comment">% Outputs:</span>
|
||||||
<span class="org-comment">% - stewart - With the 3 added field:</span>
|
<span class="org-comment">% - stewart - With the 3 added field:</span>
|
||||||
<span class="org-comment">% - kinematics.J [6x6] - The Jacobian Matrix</span>
|
<span class="org-comment">% - kinematics.J [6x6] - The Jacobian Matrix</span>
|
||||||
<span class="org-comment">% - kinematics.K [6x6] - The Stiffness Matrix</span>
|
<span class="org-comment">% - kinematics.K [6x6] - The Stiffness Matrix</span>
|
||||||
<span class="org-comment">% - kinematics.C [6x6] - The Compliance Matrix</span>
|
<span class="org-comment">% - kinematics.C [6x6] - The Compliance Matrix</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org5f6ad77" class="outline-4">
|
<div id="outline-container-orgf06bd47" class="outline-4">
|
||||||
<h4 id="org5f6ad77">Check the <code>stewart</code> structure elements</h4>
|
<h4 id="orgf06bd47">Check the <code>stewart</code> structure elements</h4>
|
||||||
<div class="outline-text-4" id="text-org5f6ad77">
|
<div class="outline-text-4" id="text-orgf06bd47">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">assert(isfield(stewart.geometry, <span class="org-string">'As'</span>), <span class="org-string">'stewart.geometry should have attribute As'</span>)
|
<pre class="src src-matlab"> assert(isfield(stewart.geometry, <span class="org-string">'As'</span>), <span class="org-string">'stewart.geometry should have attribute As'</span>)
|
||||||
As = stewart.geometry.As;
|
As = stewart.geometry.As;
|
||||||
|
|
||||||
assert(isfield(stewart.geometry, <span class="org-string">'Ab'</span>), <span class="org-string">'stewart.geometry should have attribute Ab'</span>)
|
assert(isfield(stewart.geometry, <span class="org-string">'Ab'</span>), <span class="org-string">'stewart.geometry should have attribute Ab'</span>)
|
||||||
Ab = stewart.geometry.Ab;
|
Ab = stewart.geometry.Ab;
|
||||||
|
|
||||||
assert(isfield(stewart.actuators, <span class="org-string">'K'</span>), <span class="org-string">'stewart.actuators should have attribute K'</span>)
|
assert(isfield(stewart.actuators, <span class="org-string">'K'</span>), <span class="org-string">'stewart.actuators should have attribute K'</span>)
|
||||||
Ki = stewart.actuators.K;
|
Ki = stewart.actuators.K;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1437,7 +1437,7 @@ Ki = stewart.actuators.K;
|
|||||||
<h4 id="org01f1158">Compute Jacobian Matrix</h4>
|
<h4 id="org01f1158">Compute Jacobian Matrix</h4>
|
||||||
<div class="outline-text-4" id="text-org01f1158">
|
<div class="outline-text-4" id="text-org01f1158">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">J = [As<span class="org-type">'</span> , cross(Ab, As)<span class="org-type">'</span>];
|
<pre class="src src-matlab"> J = [As<span class="org-type">'</span> , cross(Ab, As)<span class="org-type">'</span>];
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1447,7 +1447,7 @@ Ki = stewart.actuators.K;
|
|||||||
<h4 id="org91d652d">Compute Stiffness Matrix</h4>
|
<h4 id="org91d652d">Compute Stiffness Matrix</h4>
|
||||||
<div class="outline-text-4" id="text-org91d652d">
|
<div class="outline-text-4" id="text-org91d652d">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">K = J<span class="org-type">'*</span>diag(Ki)<span class="org-type">*</span>J;
|
<pre class="src src-matlab"> K = J<span class="org-type">'*</span>diag(Ki)<span class="org-type">*</span>J;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1457,7 +1457,7 @@ Ki = stewart.actuators.K;
|
|||||||
<h4 id="org323b34e">Compute Compliance Matrix</h4>
|
<h4 id="org323b34e">Compute Compliance Matrix</h4>
|
||||||
<div class="outline-text-4" id="text-org323b34e">
|
<div class="outline-text-4" id="text-org323b34e">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">C = inv(K);
|
<pre class="src src-matlab"> C = inv(K);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1467,9 +1467,9 @@ Ki = stewart.actuators.K;
|
|||||||
<h4 id="orgebce485">Populate the <code>stewart</code> structure</h4>
|
<h4 id="orgebce485">Populate the <code>stewart</code> structure</h4>
|
||||||
<div class="outline-text-4" id="text-orgebce485">
|
<div class="outline-text-4" id="text-orgebce485">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart.kinematics.J = J;
|
<pre class="src src-matlab"> stewart.kinematics.J = J;
|
||||||
stewart.kinematics.K = K;
|
stewart.kinematics.K = K;
|
||||||
stewart.kinematics.C = C;
|
stewart.kinematics.C = C;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1525,58 +1525,58 @@ Otherwise, when the limbs’ lengths derived yield complex numbers, then the
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org6586e8a" class="outline-4">
|
<div id="outline-container-org39a0af1" class="outline-4">
|
||||||
<h4 id="org6586e8a">Function description</h4>
|
<h4 id="org39a0af1">Function description</h4>
|
||||||
<div class="outline-text-4" id="text-org6586e8a">
|
<div class="outline-text-4" id="text-org39a0af1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[Li, dLi]</span> = <span class="org-function-name">inverseKinematics</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[Li, dLi]</span> = <span class="org-function-name">inverseKinematics</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% inverseKinematics - Compute the needed length of each strut to have the wanted position and orientation of {B} with respect to {A}</span>
|
<span class="org-comment">% inverseKinematics - Compute the needed length of each strut to have the wanted position and orientation of {B} with respect to {A}</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [stewart] = inverseKinematics(stewart)</span>
|
<span class="org-comment">% Syntax: [stewart] = inverseKinematics(stewart)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - stewart - A structure with the following fields</span>
|
<span class="org-comment">% - stewart - A structure with the following fields</span>
|
||||||
<span class="org-comment">% - geometry.Aa [3x6] - The positions ai expressed in {A}</span>
|
<span class="org-comment">% - geometry.Aa [3x6] - The positions ai expressed in {A}</span>
|
||||||
<span class="org-comment">% - geometry.Bb [3x6] - The positions bi expressed in {B}</span>
|
<span class="org-comment">% - geometry.Bb [3x6] - The positions bi expressed in {B}</span>
|
||||||
<span class="org-comment">% - geometry.l [6x1] - Length of each strut</span>
|
<span class="org-comment">% - geometry.l [6x1] - Length of each strut</span>
|
||||||
<span class="org-comment">% - args - Can have the following fields:</span>
|
<span class="org-comment">% - args - Can have the following fields:</span>
|
||||||
<span class="org-comment">% - AP [3x1] - The wanted position of {B} with respect to {A}</span>
|
<span class="org-comment">% - AP [3x1] - The wanted position of {B} with respect to {A}</span>
|
||||||
<span class="org-comment">% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}</span>
|
<span class="org-comment">% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Outputs:</span>
|
<span class="org-comment">% Outputs:</span>
|
||||||
<span class="org-comment">% - Li [6x1] - The 6 needed length of the struts in [m] to have the wanted pose of {B} w.r.t. {A}</span>
|
<span class="org-comment">% - Li [6x1] - The 6 needed length of the struts in [m] to have the wanted pose of {B} w.r.t. {A}</span>
|
||||||
<span class="org-comment">% - dLi [6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}</span>
|
<span class="org-comment">% - dLi [6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgf078a15" class="outline-4">
|
<div id="outline-container-orgcb9b73a" class="outline-4">
|
||||||
<h4 id="orgf078a15">Optional Parameters</h4>
|
<h4 id="orgcb9b73a">Optional Parameters</h4>
|
||||||
<div class="outline-text-4" id="text-orgf078a15">
|
<div class="outline-text-4" id="text-orgcb9b73a">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">stewart</span>
|
<span class="org-variable-name">stewart</span>
|
||||||
<span class="org-variable-name">args</span>.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
<span class="org-variable-name">args</span>.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||||
<span class="org-variable-name">args</span>.ARB (3,3) double {mustBeNumeric} = eye(3)
|
<span class="org-variable-name">args</span>.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org4151034" class="outline-4">
|
<div id="outline-container-org31e89c1" class="outline-4">
|
||||||
<h4 id="org4151034">Check the <code>stewart</code> structure elements</h4>
|
<h4 id="org31e89c1">Check the <code>stewart</code> structure elements</h4>
|
||||||
<div class="outline-text-4" id="text-org4151034">
|
<div class="outline-text-4" id="text-org31e89c1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">assert(isfield(stewart.geometry, <span class="org-string">'Aa'</span>), <span class="org-string">'stewart.geometry should have attribute Aa'</span>)
|
<pre class="src src-matlab"> assert(isfield(stewart.geometry, <span class="org-string">'Aa'</span>), <span class="org-string">'stewart.geometry should have attribute Aa'</span>)
|
||||||
Aa = stewart.geometry.Aa;
|
Aa = stewart.geometry.Aa;
|
||||||
|
|
||||||
assert(isfield(stewart.geometry, <span class="org-string">'Bb'</span>), <span class="org-string">'stewart.geometry should have attribute Bb'</span>)
|
assert(isfield(stewart.geometry, <span class="org-string">'Bb'</span>), <span class="org-string">'stewart.geometry should have attribute Bb'</span>)
|
||||||
Bb = stewart.geometry.Bb;
|
Bb = stewart.geometry.Bb;
|
||||||
|
|
||||||
assert(isfield(stewart.geometry, <span class="org-string">'l'</span>), <span class="org-string">'stewart.geometry should have attribute l'</span>)
|
assert(isfield(stewart.geometry, <span class="org-string">'l'</span>), <span class="org-string">'stewart.geometry should have attribute l'</span>)
|
||||||
l = stewart.geometry.l;
|
l = stewart.geometry.l;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1587,12 +1587,12 @@ l = stewart.geometry.l;
|
|||||||
<h4 id="org7189e65">Compute</h4>
|
<h4 id="org7189e65">Compute</h4>
|
||||||
<div class="outline-text-4" id="text-org7189e65">
|
<div class="outline-text-4" id="text-org7189e65">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Li = sqrt(args.AP<span class="org-type">'*</span>args.AP <span class="org-type">+</span> diag(Bb<span class="org-type">'*</span>Bb) <span class="org-type">+</span> diag(Aa<span class="org-type">'*</span>Aa) <span class="org-type">-</span> (2<span class="org-type">*</span>args.AP<span class="org-type">'*</span>Aa)<span class="org-type">'</span> <span class="org-type">+</span> (2<span class="org-type">*</span>args.AP<span class="org-type">'*</span>(args.ARB<span class="org-type">*</span>Bb))<span class="org-type">'</span> <span class="org-type">-</span> diag(2<span class="org-type">*</span>(args.ARB<span class="org-type">*</span>Bb)<span class="org-type">'*</span>Aa));
|
<pre class="src src-matlab"> Li = sqrt(args.AP<span class="org-type">'*</span>args.AP <span class="org-type">+</span> diag(Bb<span class="org-type">'*</span>Bb) <span class="org-type">+</span> diag(Aa<span class="org-type">'*</span>Aa) <span class="org-type">-</span> (2<span class="org-type">*</span>args.AP<span class="org-type">'*</span>Aa)<span class="org-type">'</span> <span class="org-type">+</span> (2<span class="org-type">*</span>args.AP<span class="org-type">'*</span>(args.ARB<span class="org-type">*</span>Bb))<span class="org-type">'</span> <span class="org-type">-</span> diag(2<span class="org-type">*</span>(args.ARB<span class="org-type">*</span>Bb)<span class="org-type">'*</span>Aa));
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">dLi = Li<span class="org-type">-</span>l;
|
<pre class="src src-matlab"> dLi = Li<span class="org-type">-</span>l;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1611,49 +1611,49 @@ This Matlab function is accessible <a href="../src/forwardKinematicsApprox.m">he
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org9b19ae7" class="outline-4">
|
<div id="outline-container-org8a3d2ba" class="outline-4">
|
||||||
<h4 id="org9b19ae7">Function description</h4>
|
<h4 id="org8a3d2ba">Function description</h4>
|
||||||
<div class="outline-text-4" id="text-org9b19ae7">
|
<div class="outline-text-4" id="text-org8a3d2ba">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[P, R]</span> = <span class="org-function-name">forwardKinematicsApprox</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[P, R]</span> = <span class="org-function-name">forwardKinematicsApprox</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% forwardKinematicsApprox - Computed the approximate pose of {B} with respect to {A} from the length of each strut and using</span>
|
<span class="org-comment">% forwardKinematicsApprox - Computed the approximate pose of {B} with respect to {A} from the length of each strut and using</span>
|
||||||
<span class="org-comment">% the Jacobian Matrix</span>
|
<span class="org-comment">% the Jacobian Matrix</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [P, R] = forwardKinematicsApprox(stewart, args)</span>
|
<span class="org-comment">% Syntax: [P, R] = forwardKinematicsApprox(stewart, args)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - stewart - A structure with the following fields</span>
|
<span class="org-comment">% - stewart - A structure with the following fields</span>
|
||||||
<span class="org-comment">% - kinematics.J [6x6] - The Jacobian Matrix</span>
|
<span class="org-comment">% - kinematics.J [6x6] - The Jacobian Matrix</span>
|
||||||
<span class="org-comment">% - args - Can have the following fields:</span>
|
<span class="org-comment">% - args - Can have the following fields:</span>
|
||||||
<span class="org-comment">% - dL [6x1] - Displacement of each strut [m]</span>
|
<span class="org-comment">% - dL [6x1] - Displacement of each strut [m]</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Outputs:</span>
|
<span class="org-comment">% Outputs:</span>
|
||||||
<span class="org-comment">% - P [3x1] - The estimated position of {B} with respect to {A}</span>
|
<span class="org-comment">% - P [3x1] - The estimated position of {B} with respect to {A}</span>
|
||||||
<span class="org-comment">% - R [3x3] - The estimated rotation matrix that gives the orientation of {B} with respect to {A}</span>
|
<span class="org-comment">% - R [3x3] - The estimated rotation matrix that gives the orientation of {B} with respect to {A}</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgdf60206" class="outline-4">
|
<div id="outline-container-orgf078a15" class="outline-4">
|
||||||
<h4 id="orgdf60206">Optional Parameters</h4>
|
<h4 id="orgf078a15">Optional Parameters</h4>
|
||||||
<div class="outline-text-4" id="text-orgdf60206">
|
<div class="outline-text-4" id="text-orgf078a15">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">stewart</span>
|
<span class="org-variable-name">stewart</span>
|
||||||
<span class="org-variable-name">args</span>.dL (6,1) double {mustBeNumeric} = zeros(6,1)
|
<span class="org-variable-name">args</span>.dL (6,1) double {mustBeNumeric} = zeros(6,1)
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org2c19f08" class="outline-4">
|
<div id="outline-container-org5f6ad77" class="outline-4">
|
||||||
<h4 id="org2c19f08">Check the <code>stewart</code> structure elements</h4>
|
<h4 id="org5f6ad77">Check the <code>stewart</code> structure elements</h4>
|
||||||
<div class="outline-text-4" id="text-org2c19f08">
|
<div class="outline-text-4" id="text-org5f6ad77">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">assert(isfield(stewart.kinematics, <span class="org-string">'J'</span>), <span class="org-string">'stewart.kinematics should have attribute J'</span>)
|
<pre class="src src-matlab"> assert(isfield(stewart.kinematics, <span class="org-string">'J'</span>), <span class="org-string">'stewart.kinematics should have attribute J'</span>)
|
||||||
J = stewart.kinematics.J;
|
J = stewart.kinematics.J;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -1668,7 +1668,7 @@ position and orientation of {B} with respect to {A} using the following formula:
|
|||||||
\[ d \bm{\mathcal{X}} = \bm{J}^{-1} d\bm{\mathcal{L}} \]
|
\[ d \bm{\mathcal{X}} = \bm{J}^{-1} d\bm{\mathcal{L}} \]
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">X = J<span class="org-type">\</span>args.dL;
|
<pre class="src src-matlab"> X = J<span class="org-type">\</span>args.dL;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1676,7 +1676,7 @@ position and orientation of {B} with respect to {A} using the following formula:
|
|||||||
The position vector corresponds to the first 3 elements.
|
The position vector corresponds to the first 3 elements.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">P = X(1<span class="org-type">:</span>3);
|
<pre class="src src-matlab"> P = X(1<span class="org-type">:</span>3);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1685,8 +1685,8 @@ The next 3 elements are the orientation of {B} with respect to {A} expressed
|
|||||||
using the screw axis.
|
using the screw axis.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">theta = norm(X(4<span class="org-type">:</span>6));
|
<pre class="src src-matlab"> theta = norm(X(4<span class="org-type">:</span>6));
|
||||||
s = X(4<span class="org-type">:</span>6)<span class="org-type">/</span>theta;
|
s = X(4<span class="org-type">:</span>6)<span class="org-type">/</span>theta;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -1694,7 +1694,7 @@ s = X(4<span class="org-type">:</span>6)<span class="org-type">/</span>theta;
|
|||||||
We then compute the corresponding rotation matrix.
|
We then compute the corresponding rotation matrix.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">R = [s(1)<span class="org-type">^</span>2<span class="org-type">*</span>(1<span class="org-type">-</span>cos(theta)) <span class="org-type">+</span> cos(theta) , s(1)<span class="org-type">*</span>s(2)<span class="org-type">*</span>(1<span class="org-type">-</span>cos(theta)) <span class="org-type">-</span> s(3)<span class="org-type">*</span>sin(theta), s(1)<span class="org-type">*</span>s(3)<span class="org-type">*</span>(1<span class="org-type">-</span>cos(theta)) <span class="org-type">+</span> s(2)<span class="org-type">*</span>sin(theta);
|
<pre class="src src-matlab"> R = [s(1)<span class="org-type">^</span>2<span class="org-type">*</span>(1<span class="org-type">-</span>cos(theta)) <span class="org-type">+</span> cos(theta) , s(1)<span class="org-type">*</span>s(2)<span class="org-type">*</span>(1<span class="org-type">-</span>cos(theta)) <span class="org-type">-</span> s(3)<span class="org-type">*</span>sin(theta), s(1)<span class="org-type">*</span>s(3)<span class="org-type">*</span>(1<span class="org-type">-</span>cos(theta)) <span class="org-type">+</span> s(2)<span class="org-type">*</span>sin(theta);
|
||||||
s<span class="org-type">(2)*s(1)*(1-cos(theta)) + s(3)*sin(theta), s(2)^2*(1-cos(theta)) + cos(theta), s(2)*s(3)*(1-cos(theta)) - s(1)*sin(theta);</span>
|
s<span class="org-type">(2)*s(1)*(1-cos(theta)) + s(3)*sin(theta), s(2)^2*(1-cos(theta)) + cos(theta), s(2)*s(3)*(1-cos(theta)) - s(1)*sin(theta);</span>
|
||||||
s<span class="org-type">(3)*s(1)*(1-cos(theta)) - s(2)*sin(theta), s(3)*s(2)*(1-cos(theta)) + s(1)*sin(theta), s(3)^2*(1-cos(theta)) + cos(theta)];</span>
|
s<span class="org-type">(3)*s(1)*(1-cos(theta)) - s(2)*sin(theta), s(3)*s(2)*(1-cos(theta)) + s(1)*sin(theta), s(3)^2*(1-cos(theta)) + cos(theta)];</span>
|
||||||
</pre>
|
</pre>
|
||||||
@ -1715,7 +1715,7 @@ We then compute the corresponding rotation matrix.
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
<p class="date">Created: 2021-01-08 ven. 15:17</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -3,7 +3,7 @@
|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:53 -->
|
<!-- 2021-01-08 ven. 15:30 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Stewart Platform - NASS</title>
|
<title>Stewart Platform - NASS</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -39,36 +39,36 @@
|
|||||||
<h3 id="org0167386"><span class="section-number-3">1.1</span> Identification of the Dynamics</h3>
|
<h3 id="org0167386"><span class="section-number-3">1.1</span> Identification of the Dynamics</h3>
|
||||||
<div class="outline-text-3" id="text-1-1">
|
<div class="outline-text-3" id="text-1-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
flex_joint = load(<span class="org-string">'./mat/flexor_ID16.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
flex_joint = load(<span class="org-string">'./mat/flexor_ID16.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 175e<span class="org-type">-</span>3);
|
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 175e<span class="org-type">-</span>3);
|
||||||
stewart = generateGeneralConfiguration(stewart, <span class="org-string">'FH'</span>, 20e<span class="org-type">-</span>3, <span class="org-string">'MH'</span>, 20e<span class="org-type">-</span>3, <span class="org-string">'FR'</span>, 228e<span class="org-type">-</span>3<span class="org-type">/</span>2, <span class="org-string">'MR'</span>, 220e<span class="org-type">-</span>3<span class="org-type">/</span>2, <span class="org-string">'FTh'</span>, [<span class="org-type">-</span>9, 9, 120<span class="org-type">-</span>9, 120<span class="org-type">+</span>9, 240<span class="org-type">-</span>9, 240<span class="org-type">+</span>9]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180), <span class="org-string">'MTh'</span>, [<span class="org-type">-</span>60<span class="org-type">+</span>15, 60<span class="org-type">-</span>15, 60<span class="org-type">+</span>15, 180<span class="org-type">-</span>15, 180<span class="org-type">+</span>15, <span class="org-type">-</span>60<span class="org-type">-</span>15]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180));
|
stewart = generateGeneralConfiguration(stewart, <span class="org-string">'FH'</span>, 20e<span class="org-type">-</span>3, <span class="org-string">'MH'</span>, 20e<span class="org-type">-</span>3, <span class="org-string">'FR'</span>, 228e<span class="org-type">-</span>3<span class="org-type">/</span>2, <span class="org-string">'MR'</span>, 220e<span class="org-type">-</span>3<span class="org-type">/</span>2, <span class="org-string">'FTh'</span>, [<span class="org-type">-</span>9, 9, 120<span class="org-type">-</span>9, 120<span class="org-type">+</span>9, 240<span class="org-type">-</span>9, 240<span class="org-type">+</span>9]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180), <span class="org-string">'MTh'</span>, [<span class="org-type">-</span>60<span class="org-type">+</span>15, 60<span class="org-type">-</span>15, 60<span class="org-type">+</span>15, 180<span class="org-type">-</span>15, 180<span class="org-type">+</span>15, <span class="org-type">-</span>60<span class="org-type">-</span>15]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180));
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||||
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 150e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 125e<span class="org-type">-</span>3);
|
stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 150e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 125e<span class="org-type">-</span>3);
|
||||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -77,7 +77,7 @@ references = initializeReferences(stewart);
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:53</p>
|
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -3,7 +3,7 @@
|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:52 -->
|
<!-- 2021-01-08 ven. 15:29 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Stewart Platform - Simscape Model</title>
|
<title>Stewart Platform - Simscape Model</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -48,16 +48,16 @@
|
|||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgf4bef70">6.1. Payload</a>
|
<li><a href="#orgf4bef70">6.1. Payload</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org920bdd0">Function description</a></li>
|
<li><a href="#org9c0e404">Function description</a></li>
|
||||||
<li><a href="#orgbc7950f">Optional Parameters</a></li>
|
<li><a href="#orgabc81c1">Optional Parameters</a></li>
|
||||||
<li><a href="#org4ef4a9f">Add Payload Type</a></li>
|
<li><a href="#org4ef4a9f">Add Payload Type</a></li>
|
||||||
<li><a href="#org3243d76">Add Stiffness, Damping and Mass properties of the Payload</a></li>
|
<li><a href="#org3243d76">Add Stiffness, Damping and Mass properties of the Payload</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#orgd9e12ef">6.2. Ground</a>
|
<li><a href="#orgd9e12ef">6.2. Ground</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgc300ecf">Function description</a></li>
|
<li><a href="#org920bdd0">Function description</a></li>
|
||||||
<li><a href="#org1ee272a">Optional Parameters</a></li>
|
<li><a href="#orgfa4bbf4">Optional Parameters</a></li>
|
||||||
<li><a href="#org2d22970">Add Ground Type</a></li>
|
<li><a href="#org2d22970">Add Ground Type</a></li>
|
||||||
<li><a href="#orgf76def4">Add Stiffness and Damping properties of the Ground</a></li>
|
<li><a href="#orgf76def4">Add Stiffness and Damping properties of the Ground</a></li>
|
||||||
<li><a href="#orgdb67a68">Rotation Point</a></li>
|
<li><a href="#orgdb67a68">Rotation Point</a></li>
|
||||||
@ -67,8 +67,8 @@
|
|||||||
</li>
|
</li>
|
||||||
<li><a href="#org6d3b61e">7. Initialize Disturbances</a>
|
<li><a href="#org6d3b61e">7. Initialize Disturbances</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgf124972">Function Declaration and Documentation</a></li>
|
<li><a href="#orgf14752d">Function Declaration and Documentation</a></li>
|
||||||
<li><a href="#org668f4bb">Optional Parameters</a></li>
|
<li><a href="#orga64679c">Optional Parameters</a></li>
|
||||||
<li><a href="#org0f7e4dd">Structure initialization</a></li>
|
<li><a href="#org0f7e4dd">Structure initialization</a></li>
|
||||||
<li><a href="#org1a28fcd">Ground Motion</a></li>
|
<li><a href="#org1a28fcd">Ground Motion</a></li>
|
||||||
<li><a href="#org90b72d6">Direct Forces</a></li>
|
<li><a href="#org90b72d6">Direct Forces</a></li>
|
||||||
@ -76,8 +76,8 @@
|
|||||||
</li>
|
</li>
|
||||||
<li><a href="#org93f2d30">8. Initialize References</a>
|
<li><a href="#org93f2d30">8. Initialize References</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org81500bb">Function Declaration and Documentation</a></li>
|
<li><a href="#orgf124972">Function Declaration and Documentation</a></li>
|
||||||
<li><a href="#org05322ee">Optional Parameters</a></li>
|
<li><a href="#orgbc7950f">Optional Parameters</a></li>
|
||||||
<li><a href="#org6f05adc">8.1. Compute the corresponding strut length</a></li>
|
<li><a href="#org6f05adc">8.1. Compute the corresponding strut length</a></li>
|
||||||
<li><a href="#orgda73a50">References</a></li>
|
<li><a href="#orgda73a50">References</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
@ -144,7 +144,7 @@ Basically, the configuration is stored in a mat file <code>conf_simscape.mat</co
|
|||||||
It is automatically loaded when the Simulink project is open. It can be loaded manually with the command:
|
It is automatically loaded when the Simulink project is open. It can be loaded manually with the command:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
<pre class="src src-matlab"> load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -152,7 +152,7 @@ It is automatically loaded when the Simulink project is open. It can be loaded m
|
|||||||
It is however possible to modify specific parameters just for one simulation using the <code>set_param</code> command:
|
It is however possible to modify specific parameters just for one simulation using the <code>set_param</code> command:
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, 1);
|
<pre class="src src-matlab"> <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, 1);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -303,50 +303,50 @@ This Matlab function is accessible <a href="../src/initializePayload.m">here</a>
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org920bdd0" class="outline-4">
|
<div id="outline-container-org9c0e404" class="outline-4">
|
||||||
<h4 id="org920bdd0">Function description</h4>
|
<h4 id="org9c0e404">Function description</h4>
|
||||||
<div class="outline-text-4" id="text-org920bdd0">
|
<div class="outline-text-4" id="text-org9c0e404">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[payload]</span> = <span class="org-function-name">initializePayload</span>(<span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[payload]</span> = <span class="org-function-name">initializePayload</span>(<span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% initializePayload - Initialize the Payload that can then be used for simulations and analysis</span>
|
<span class="org-comment">% initializePayload - Initialize the Payload that can then be used for simulations and analysis</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [payload] = initializePayload(args)</span>
|
<span class="org-comment">% Syntax: [payload] = initializePayload(args)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - args - Structure with the following fields:</span>
|
<span class="org-comment">% - args - Structure with the following fields:</span>
|
||||||
<span class="org-comment">% - type - 'none', 'rigid', 'flexible', 'cartesian'</span>
|
<span class="org-comment">% - type - 'none', 'rigid', 'flexible', 'cartesian'</span>
|
||||||
<span class="org-comment">% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]</span>
|
<span class="org-comment">% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]</span>
|
||||||
<span class="org-comment">% This also the position where K and C are defined</span>
|
<span class="org-comment">% This also the position where K and C are defined</span>
|
||||||
<span class="org-comment">% - K [6x1] - Stiffness of the Payload [N/m, N/rad]</span>
|
<span class="org-comment">% - K [6x1] - Stiffness of the Payload [N/m, N/rad]</span>
|
||||||
<span class="org-comment">% - C [6x1] - Damping of the Payload [N/(m/s), N/(rad/s)]</span>
|
<span class="org-comment">% - C [6x1] - Damping of the Payload [N/(m/s), N/(rad/s)]</span>
|
||||||
<span class="org-comment">% - m [1x1] - Mass of the Payload [kg]</span>
|
<span class="org-comment">% - m [1x1] - Mass of the Payload [kg]</span>
|
||||||
<span class="org-comment">% - I [3x3] - Inertia matrix for the Payload [kg*m2]</span>
|
<span class="org-comment">% - I [3x3] - Inertia matrix for the Payload [kg*m2]</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Outputs:</span>
|
<span class="org-comment">% Outputs:</span>
|
||||||
<span class="org-comment">% - payload - Struture with the following properties:</span>
|
<span class="org-comment">% - payload - Struture with the following properties:</span>
|
||||||
<span class="org-comment">% - type - 1 (none), 2 (rigid), 3 (flexible)</span>
|
<span class="org-comment">% - type - 1 (none), 2 (rigid), 3 (flexible)</span>
|
||||||
<span class="org-comment">% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]</span>
|
<span class="org-comment">% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]</span>
|
||||||
<span class="org-comment">% - K [6x1] - Stiffness of the Payload [N/m, N/rad]</span>
|
<span class="org-comment">% - K [6x1] - Stiffness of the Payload [N/m, N/rad]</span>
|
||||||
<span class="org-comment">% - C [6x1] - Stiffness of the Payload [N/(m/s), N/(rad/s)]</span>
|
<span class="org-comment">% - C [6x1] - Stiffness of the Payload [N/(m/s), N/(rad/s)]</span>
|
||||||
<span class="org-comment">% - m [1x1] - Mass of the Payload [kg]</span>
|
<span class="org-comment">% - m [1x1] - Mass of the Payload [kg]</span>
|
||||||
<span class="org-comment">% - I [3x3] - Inertia matrix for the Payload [kg*m2]</span>
|
<span class="org-comment">% - I [3x3] - Inertia matrix for the Payload [kg*m2]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgbc7950f" class="outline-4">
|
<div id="outline-container-orgabc81c1" class="outline-4">
|
||||||
<h4 id="orgbc7950f">Optional Parameters</h4>
|
<h4 id="orgabc81c1">Optional Parameters</h4>
|
||||||
<div class="outline-text-4" id="text-orgbc7950f">
|
<div class="outline-text-4" id="text-orgabc81c1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">args</span>.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'cartesian'</span>})} = <span class="org-string">'none'</span>
|
<span class="org-variable-name">args</span>.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'cartesian'</span>})} = <span class="org-string">'none'</span>
|
||||||
<span class="org-variable-name">args</span>.K (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e8<span class="org-type">*</span>ones(6,1)
|
<span class="org-variable-name">args</span>.K (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e8<span class="org-type">*</span>ones(6,1)
|
||||||
<span class="org-variable-name">args</span>.C (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1<span class="org-type">*</span>ones(6,1)
|
<span class="org-variable-name">args</span>.C (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1<span class="org-type">*</span>ones(6,1)
|
||||||
<span class="org-variable-name">args</span>.h (1,1) double {mustBeNumeric, mustBeNonnegative} = 100e<span class="org-type">-</span>3
|
<span class="org-variable-name">args</span>.h (1,1) double {mustBeNumeric, mustBeNonnegative} = 100e<span class="org-type">-</span>3
|
||||||
<span class="org-variable-name">args</span>.m (1,1) double {mustBeNumeric, mustBeNonnegative} = 10
|
<span class="org-variable-name">args</span>.m (1,1) double {mustBeNumeric, mustBeNonnegative} = 10
|
||||||
<span class="org-variable-name">args</span>.I (3,3) double {mustBeNumeric, mustBeNonnegative} = 1<span class="org-type">*</span>eye(3)
|
<span class="org-variable-name">args</span>.I (3,3) double {mustBeNumeric, mustBeNonnegative} = 1<span class="org-type">*</span>eye(3)
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -356,7 +356,7 @@ This Matlab function is accessible <a href="../src/initializePayload.m">here</a>
|
|||||||
<h4 id="org4ef4a9f">Add Payload Type</h4>
|
<h4 id="org4ef4a9f">Add Payload Type</h4>
|
||||||
<div class="outline-text-4" id="text-org4ef4a9f">
|
<div class="outline-text-4" id="text-org4ef4a9f">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
<pre class="src src-matlab"> <span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
||||||
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
||||||
payload.type = 1;
|
payload.type = 1;
|
||||||
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
||||||
@ -365,7 +365,7 @@ This Matlab function is accessible <a href="../src/initializePayload.m">here</a>
|
|||||||
payload.type = 3;
|
payload.type = 3;
|
||||||
<span class="org-keyword">case</span> <span class="org-string">'cartesian'</span>
|
<span class="org-keyword">case</span> <span class="org-string">'cartesian'</span>
|
||||||
payload.type = 4;
|
payload.type = 4;
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -375,12 +375,12 @@ This Matlab function is accessible <a href="../src/initializePayload.m">here</a>
|
|||||||
<h4 id="org3243d76">Add Stiffness, Damping and Mass properties of the Payload</h4>
|
<h4 id="org3243d76">Add Stiffness, Damping and Mass properties of the Payload</h4>
|
||||||
<div class="outline-text-4" id="text-org3243d76">
|
<div class="outline-text-4" id="text-org3243d76">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">payload.K = args.K;
|
<pre class="src src-matlab"> payload.K = args.K;
|
||||||
payload.C = args.C;
|
payload.C = args.C;
|
||||||
payload.m = args.m;
|
payload.m = args.m;
|
||||||
payload.I = args.I;
|
payload.I = args.I;
|
||||||
|
|
||||||
payload.h = args.h;
|
payload.h = args.h;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -399,42 +399,42 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgc300ecf" class="outline-4">
|
<div id="outline-container-org920bdd0" class="outline-4">
|
||||||
<h4 id="orgc300ecf">Function description</h4>
|
<h4 id="org920bdd0">Function description</h4>
|
||||||
<div class="outline-text-4" id="text-orgc300ecf">
|
<div class="outline-text-4" id="text-org920bdd0">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ground]</span> = <span class="org-function-name">initializeGround</span>(<span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[ground]</span> = <span class="org-function-name">initializeGround</span>(<span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% initializeGround - Initialize the Ground that can then be used for simulations and analysis</span>
|
<span class="org-comment">% initializeGround - Initialize the Ground that can then be used for simulations and analysis</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [ground] = initializeGround(args)</span>
|
<span class="org-comment">% Syntax: [ground] = initializeGround(args)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - args - Structure with the following fields:</span>
|
<span class="org-comment">% - args - Structure with the following fields:</span>
|
||||||
<span class="org-comment">% - type - 'none', 'solid', 'flexible'</span>
|
<span class="org-comment">% - type - 'none', 'solid', 'flexible'</span>
|
||||||
<span class="org-comment">% - rot_point [3x1] - Rotation point for the ground motion [m]</span>
|
<span class="org-comment">% - rot_point [3x1] - Rotation point for the ground motion [m]</span>
|
||||||
<span class="org-comment">% - K [3x1] - Translation Stiffness of the Ground [N/m]</span>
|
<span class="org-comment">% - K [3x1] - Translation Stiffness of the Ground [N/m]</span>
|
||||||
<span class="org-comment">% - C [3x1] - Translation Damping of the Ground [N/(m/s)]</span>
|
<span class="org-comment">% - C [3x1] - Translation Damping of the Ground [N/(m/s)]</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Outputs:</span>
|
<span class="org-comment">% Outputs:</span>
|
||||||
<span class="org-comment">% - ground - Struture with the following properties:</span>
|
<span class="org-comment">% - ground - Struture with the following properties:</span>
|
||||||
<span class="org-comment">% - type - 1 (none), 2 (rigid), 3 (flexible)</span>
|
<span class="org-comment">% - type - 1 (none), 2 (rigid), 3 (flexible)</span>
|
||||||
<span class="org-comment">% - K [3x1] - Translation Stiffness of the Ground [N/m]</span>
|
<span class="org-comment">% - K [3x1] - Translation Stiffness of the Ground [N/m]</span>
|
||||||
<span class="org-comment">% - C [3x1] - Translation Damping of the Ground [N/(m/s)]</span>
|
<span class="org-comment">% - C [3x1] - Translation Damping of the Ground [N/(m/s)]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org1ee272a" class="outline-4">
|
<div id="outline-container-orgfa4bbf4" class="outline-4">
|
||||||
<h4 id="org1ee272a">Optional Parameters</h4>
|
<h4 id="orgfa4bbf4">Optional Parameters</h4>
|
||||||
<div class="outline-text-4" id="text-org1ee272a">
|
<div class="outline-text-4" id="text-orgfa4bbf4">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">args</span>.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>})} = <span class="org-string">'none'</span>
|
<span class="org-variable-name">args</span>.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>})} = <span class="org-string">'none'</span>
|
||||||
<span class="org-variable-name">args</span>.rot_point (3,1) double {mustBeNumeric} = zeros(3,1)
|
<span class="org-variable-name">args</span>.rot_point (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||||
<span class="org-variable-name">args</span>.K (3,1) double {mustBeNumeric, mustBeNonnegative} = 1e8<span class="org-type">*</span>ones(3,1)
|
<span class="org-variable-name">args</span>.K (3,1) double {mustBeNumeric, mustBeNonnegative} = 1e8<span class="org-type">*</span>ones(3,1)
|
||||||
<span class="org-variable-name">args</span>.C (3,1) double {mustBeNumeric, mustBeNonnegative} = 1e1<span class="org-type">*</span>ones(3,1)
|
<span class="org-variable-name">args</span>.C (3,1) double {mustBeNumeric, mustBeNonnegative} = 1e1<span class="org-type">*</span>ones(3,1)
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -444,14 +444,14 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
|||||||
<h4 id="org2d22970">Add Ground Type</h4>
|
<h4 id="org2d22970">Add Ground Type</h4>
|
||||||
<div class="outline-text-4" id="text-org2d22970">
|
<div class="outline-text-4" id="text-org2d22970">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
<pre class="src src-matlab"> <span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
||||||
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
||||||
ground.type = 1;
|
ground.type = 1;
|
||||||
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
||||||
ground.type = 2;
|
ground.type = 2;
|
||||||
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
||||||
ground.type = 3;
|
ground.type = 3;
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -461,8 +461,8 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
|||||||
<h4 id="orgf76def4">Add Stiffness and Damping properties of the Ground</h4>
|
<h4 id="orgf76def4">Add Stiffness and Damping properties of the Ground</h4>
|
||||||
<div class="outline-text-4" id="text-orgf76def4">
|
<div class="outline-text-4" id="text-orgf76def4">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground.K = args.K;
|
<pre class="src src-matlab"> ground.K = args.K;
|
||||||
ground.C = args.C;
|
ground.C = args.C;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -472,7 +472,7 @@ ground.C = args.C;
|
|||||||
<h4 id="orgdb67a68">Rotation Point</h4>
|
<h4 id="orgdb67a68">Rotation Point</h4>
|
||||||
<div class="outline-text-4" id="text-orgdb67a68">
|
<div class="outline-text-4" id="text-orgdb67a68">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">ground.rot_point = args.rot_point;
|
<pre class="src src-matlab"> ground.rot_point = args.rot_point;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -487,33 +487,33 @@ ground.C = args.C;
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgf124972" class="outline-3">
|
<div id="outline-container-orgf14752d" class="outline-3">
|
||||||
<h3 id="orgf124972">Function Declaration and Documentation</h3>
|
<h3 id="orgf14752d">Function Declaration and Documentation</h3>
|
||||||
<div class="outline-text-3" id="text-orgf124972">
|
<div class="outline-text-3" id="text-orgf14752d">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[disturbances]</span> = <span class="org-function-name">initializeDisturbances</span>(<span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[disturbances]</span> = <span class="org-function-name">initializeDisturbances</span>(<span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% initializeDisturbances - Initialize the disturbances</span>
|
<span class="org-comment">% initializeDisturbances - Initialize the disturbances</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [disturbances] = initializeDisturbances(args)</span>
|
<span class="org-comment">% Syntax: [disturbances] = initializeDisturbances(args)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - args -</span>
|
<span class="org-comment">% - args -</span>
|
||||||
|
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org668f4bb" class="outline-3">
|
<div id="outline-container-orga64679c" class="outline-3">
|
||||||
<h3 id="org668f4bb">Optional Parameters</h3>
|
<h3 id="orga64679c">Optional Parameters</h3>
|
||||||
<div class="outline-text-3" id="text-org668f4bb">
|
<div class="outline-text-3" id="text-orga64679c">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">args</span>.Fd double {mustBeNumeric, mustBeReal} = zeros(6,1)
|
<span class="org-variable-name">args</span>.Fd double {mustBeNumeric, mustBeReal} = zeros(6,1)
|
||||||
<span class="org-variable-name">args</span>.Fd_t double {mustBeNumeric, mustBeReal} = 0
|
<span class="org-variable-name">args</span>.Fd_t double {mustBeNumeric, mustBeReal} = 0
|
||||||
<span class="org-variable-name">args</span>.Dw double {mustBeNumeric, mustBeReal} = zeros(6,1)
|
<span class="org-variable-name">args</span>.Dw double {mustBeNumeric, mustBeReal} = zeros(6,1)
|
||||||
<span class="org-variable-name">args</span>.Dw_t double {mustBeNumeric, mustBeReal} = 0
|
<span class="org-variable-name">args</span>.Dw_t double {mustBeNumeric, mustBeReal} = 0
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -524,7 +524,7 @@ ground.C = args.C;
|
|||||||
<h3 id="org0f7e4dd">Structure initialization</h3>
|
<h3 id="org0f7e4dd">Structure initialization</h3>
|
||||||
<div class="outline-text-3" id="text-org0f7e4dd">
|
<div class="outline-text-3" id="text-org0f7e4dd">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances = struct();
|
<pre class="src src-matlab"> disturbances = struct();
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -534,7 +534,7 @@ ground.C = args.C;
|
|||||||
<h3 id="org1a28fcd">Ground Motion</h3>
|
<h3 id="org1a28fcd">Ground Motion</h3>
|
||||||
<div class="outline-text-3" id="text-org1a28fcd">
|
<div class="outline-text-3" id="text-org1a28fcd">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances.Dw = timeseries([args.Dw], args.Dw_t);
|
<pre class="src src-matlab"> disturbances.Dw = timeseries([args.Dw], args.Dw_t);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -544,7 +544,7 @@ ground.C = args.C;
|
|||||||
<h3 id="org90b72d6">Direct Forces</h3>
|
<h3 id="org90b72d6">Direct Forces</h3>
|
||||||
<div class="outline-text-3" id="text-org90b72d6">
|
<div class="outline-text-3" id="text-org90b72d6">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">disturbances.Fd = timeseries([args.Fd], args.Fd_t);
|
<pre class="src src-matlab"> disturbances.Fd = timeseries([args.Fd], args.Fd_t);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -559,32 +559,32 @@ ground.C = args.C;
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org81500bb" class="outline-3">
|
<div id="outline-container-orgf124972" class="outline-3">
|
||||||
<h3 id="org81500bb">Function Declaration and Documentation</h3>
|
<h3 id="orgf124972">Function Declaration and Documentation</h3>
|
||||||
<div class="outline-text-3" id="text-org81500bb">
|
<div class="outline-text-3" id="text-orgf124972">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[references]</span> = <span class="org-function-name">initializeReferences</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
<pre class="src src-matlab"> <span class="org-keyword">function</span> <span class="org-variable-name">[references]</span> = <span class="org-function-name">initializeReferences</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
||||||
<span class="org-comment">% initializeReferences - Initialize the references</span>
|
<span class="org-comment">% initializeReferences - Initialize the references</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Syntax: [references] = initializeReferences(args)</span>
|
<span class="org-comment">% Syntax: [references] = initializeReferences(args)</span>
|
||||||
<span class="org-comment">%</span>
|
<span class="org-comment">%</span>
|
||||||
<span class="org-comment">% Inputs:</span>
|
<span class="org-comment">% Inputs:</span>
|
||||||
<span class="org-comment">% - args -</span>
|
<span class="org-comment">% - args -</span>
|
||||||
|
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org05322ee" class="outline-3">
|
<div id="outline-container-orgbc7950f" class="outline-3">
|
||||||
<h3 id="org05322ee">Optional Parameters</h3>
|
<h3 id="orgbc7950f">Optional Parameters</h3>
|
||||||
<div class="outline-text-3" id="text-org05322ee">
|
<div class="outline-text-3" id="text-orgbc7950f">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
|
<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
|
||||||
<span class="org-variable-name">stewart</span>
|
<span class="org-variable-name">stewart</span>
|
||||||
<span class="org-variable-name">args</span>.t double {mustBeNumeric, mustBeReal} = 0
|
<span class="org-variable-name">args</span>.t double {mustBeNumeric, mustBeReal} = 0
|
||||||
<span class="org-variable-name">args</span>.r double {mustBeNumeric, mustBeReal} = zeros(6, 1)
|
<span class="org-variable-name">args</span>.r double {mustBeNumeric, mustBeReal} = zeros(6, 1)
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -594,9 +594,9 @@ ground.C = args.C;
|
|||||||
<h3 id="org6f05adc"><span class="section-number-3">8.1</span> Compute the corresponding strut length</h3>
|
<h3 id="org6f05adc"><span class="section-number-3">8.1</span> Compute the corresponding strut length</h3>
|
||||||
<div class="outline-text-3" id="text-8-1">
|
<div class="outline-text-3" id="text-8-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">rL = zeros(6, length(args.t));
|
<pre class="src src-matlab"> rL = zeros(6, length(args.t));
|
||||||
|
|
||||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(args.t)</span>
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(args.t)</span>
|
||||||
R = [cos(args.r(6,<span class="org-constant">i</span>)) <span class="org-type">-</span>sin(args.r(6,<span class="org-constant">i</span>)) 0;
|
R = [cos(args.r(6,<span class="org-constant">i</span>)) <span class="org-type">-</span>sin(args.r(6,<span class="org-constant">i</span>)) 0;
|
||||||
sin(args.r(6,<span class="org-constant">i</span>)) cos(args.r(6,<span class="org-constant">i</span>)) 0;
|
sin(args.r(6,<span class="org-constant">i</span>)) cos(args.r(6,<span class="org-constant">i</span>)) 0;
|
||||||
0 0 1] <span class="org-type">*</span> ...
|
0 0 1] <span class="org-type">*</span> ...
|
||||||
@ -609,7 +609,7 @@ ground.C = args.C;
|
|||||||
|
|
||||||
[Li, dLi] = inverseKinematics(stewart, <span class="org-string">'AP'</span>, [args.r(1,<span class="org-constant">i</span>); args.r(2,<span class="org-constant">i</span>); args.r(3,<span class="org-constant">i</span>)], <span class="org-string">'ARB'</span>, R);
|
[Li, dLi] = inverseKinematics(stewart, <span class="org-string">'AP'</span>, [args.r(1,<span class="org-constant">i</span>); args.r(2,<span class="org-constant">i</span>); args.r(3,<span class="org-constant">i</span>)], <span class="org-string">'ARB'</span>, R);
|
||||||
rL(<span class="org-type">:</span>, <span class="org-constant">i</span>) = dLi;
|
rL(<span class="org-type">:</span>, <span class="org-constant">i</span>) = dLi;
|
||||||
<span class="org-keyword">end</span>
|
<span class="org-keyword">end</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -619,8 +619,8 @@ ground.C = args.C;
|
|||||||
<h3 id="orgda73a50">References</h3>
|
<h3 id="orgda73a50">References</h3>
|
||||||
<div class="outline-text-3" id="text-orgda73a50">
|
<div class="outline-text-3" id="text-orgda73a50">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">references.r = timeseries(args.r, args.t);
|
<pre class="src src-matlab"> references.r = timeseries(args.r, args.t);
|
||||||
references.rL = timeseries(rL, args.t);
|
references.rL = timeseries(rL, args.t);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -629,7 +629,7 @@ references.rL = timeseries(rL, args.t);
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
<p class="date">Created: 2021-01-08 ven. 15:29</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -3,7 +3,7 @@
|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:52 -->
|
<!-- 2021-01-08 ven. 15:30 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Simulink Project for the Stewart Simscape folder</title>
|
<title>Simulink Project for the Stewart Simscape folder</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -45,7 +45,7 @@ The project can be opened using the <code>simulinkproject</code> function:
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">simulinkproject(<span class="org-string">'../'</span>);
|
<pre class="src src-matlab"> simulinkproject(<span class="org-string">'../'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -54,19 +54,19 @@ When the project opens, a startup script is ran.
|
|||||||
The startup script is defined below and is exported to the <code>project_startup.m</code> script.
|
The startup script is defined below and is exported to the <code>project_startup.m</code> script.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">project = simulinkproject;
|
<pre class="src src-matlab"> project = simulinkproject;
|
||||||
projectRoot = project.RootFolder;
|
projectRoot = project.RootFolder;
|
||||||
|
|
||||||
myCacheFolder = fullfile(projectRoot, <span class="org-string">'.SimulinkCache'</span>);
|
myCacheFolder = fullfile(projectRoot, <span class="org-string">'.SimulinkCache'</span>);
|
||||||
myCodeFolder = fullfile(projectRoot, <span class="org-string">'.SimulinkCode'</span>);
|
myCodeFolder = fullfile(projectRoot, <span class="org-string">'.SimulinkCode'</span>);
|
||||||
|
|
||||||
Simulink.fileGenControl(<span class="org-string">'set'</span>,...
|
Simulink.fileGenControl(<span class="org-string">'set'</span>,...
|
||||||
<span class="org-string">'CacheFolder'</span>, myCacheFolder,...
|
<span class="org-string">'CacheFolder'</span>, myCacheFolder,...
|
||||||
<span class="org-string">'CodeGenFolder'</span>, myCodeFolder,...
|
<span class="org-string">'CodeGenFolder'</span>, myCodeFolder,...
|
||||||
<span class="org-string">'createDir'</span>, <span class="org-constant">true</span>);
|
<span class="org-string">'createDir'</span>, <span class="org-constant">true</span>);
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Load the Simscape Configuration</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Load the Simscape Configuration</span></span>
|
||||||
load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -74,7 +74,7 @@ load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
|||||||
When the project closes, it runs the <code>project_shutdown.m</code> script defined below.
|
When the project closes, it runs the <code>project_shutdown.m</code> script defined below.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Simulink.fileGenControl(<span class="org-string">'reset'</span>);
|
<pre class="src src-matlab"> Simulink.fileGenControl(<span class="org-string">'reset'</span>);
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -84,7 +84,7 @@ The project also permits to automatically add defined folder to the path when th
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -3,7 +3,7 @@
|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2021-01-08 ven. 15:53 -->
|
<!-- 2021-01-08 ven. 15:30 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Stewart Platform - Static Analysis</title>
|
<title>Stewart Platform - Static Analysis</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -74,7 +74,7 @@ Thus, the system is uncoupled if \(G\) and \(K\) are diagonal.
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-08 ven. 15:53</p>
|
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
File diff suppressed because it is too large
Load Diff
@ -23,9 +23,8 @@ stewart = computeJacobian(stewart);
|
|||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
||||||
|
|
||||||
ground = initializeGround('type', 'rigid', 'rot_point', stewart.platform_F.FO_A);
|
ground = initializeGround('type', 'none');
|
||||||
payload = initializePayload('type', 'none');
|
payload = initializePayload('type', 'none');
|
||||||
controller = initializeController('type', 'open-loop');
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|||||||
@ -23,14 +23,17 @@ stewart = computeJacobian(stewart);
|
|||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
||||||
|
|
||||||
ground = initializeGround('type', 'rigid', 'rot_point', stewart.platform_F.FO_A);
|
ground = initializeGround('type', 'none');
|
||||||
payload = initializePayload('type', 'none');
|
payload = initializePayload('type', 'none');
|
||||||
controller = initializeController('type', 'open-loop');
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
% And we identify the dynamics from force actuators to force sensors.
|
% And we identify the dynamics from force actuators to force sensors.
|
||||||
|
|
||||||
|
%% Options for Linearized
|
||||||
|
options = linearizeOptions;
|
||||||
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
@ -40,7 +43,7 @@ io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1;
|
|||||||
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
|
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||||||
G.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
G.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
||||||
|
|
||||||
@ -85,7 +88,7 @@ linkaxes([ax1,ax2],'x');
|
|||||||
% We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
% We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||||
|
|
||||||
stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
|
stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
|
||||||
Gf = linearize(mdl, io);
|
Gf = linearize(mdl, io, options);
|
||||||
Gf.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
Gf.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||||||
Gf.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
Gf.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
||||||
|
|
||||||
@ -94,7 +97,7 @@ Gf.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
|||||||
% We now use the amplified actuators and re-identify the dynamics
|
% We now use the amplified actuators and re-identify the dynamics
|
||||||
|
|
||||||
stewart = initializeAmplifiedStrutDynamics(stewart);
|
stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||||
Ga = linearize(mdl, io);
|
Ga = linearize(mdl, io, options);
|
||||||
Ga.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
Ga.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||||||
Ga.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
Ga.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
||||||
|
|
||||||
|
|||||||
@ -22,9 +22,8 @@ stewart = computeJacobian(stewart);
|
|||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
|
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
|
||||||
|
|
||||||
ground = initializeGround('type', 'rigid', 'rot_point', stewart.platform_F.FO_A);
|
ground = initializeGround('type', 'none');
|
||||||
payload = initializePayload('type', 'none');
|
payload = initializePayload('type', 'none');
|
||||||
controller = initializeController('type', 'open-loop');
|
|
||||||
|
|
||||||
%% Options for Linearized
|
%% Options for Linearized
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
|
|||||||
File diff suppressed because it is too large
Load Diff
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@ -40,111 +40,111 @@ In this section, we wish to compare the effect of forces/torques applied by the
|
|||||||
|
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
open('stewart_platform_model.slx')
|
open('stewart_platform_model.slx')
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Comparison with fixed support
|
** Comparison with fixed support
|
||||||
Let's generate a Stewart platform.
|
Let's generate a Stewart platform.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
We don't put any flexibility below the Stewart platform such that *its base is fixed to an inertial frame*.
|
We don't put any flexibility below the Stewart platform such that *its base is fixed to an inertial frame*.
|
||||||
We also don't put any payload on top of the Stewart platform.
|
We also don't put any payload on top of the Stewart platform.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground = initializeGround('type', 'none');
|
ground = initializeGround('type', 'none');
|
||||||
payload = initializePayload('type', 'none');
|
payload = initializePayload('type', 'none');
|
||||||
controller = initializeController('type', 'open-loop');
|
controller = initializeController('type', 'open-loop');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
The transfer function from actuator forces $\bm{\tau}$ to the relative displacement of the mobile platform $\mathcal{\bm{X}}$ is extracted.
|
The transfer function from actuator forces $\bm{\tau}$ to the relative displacement of the mobile platform $\mathcal{\bm{X}}$ is extracted.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Options for Linearized
|
%% Options for Linearized
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
||||||
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||||||
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Using the Jacobian matrix, we compute the transfer function from force/torques applied by the actuators on the frame $\{B\}$ fixed to the mobile platform:
|
Using the Jacobian matrix, we compute the transfer function from force/torques applied by the actuators on the frame $\{B\}$ fixed to the mobile platform:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Gc = minreal(G*inv(stewart.kinematics.J'));
|
Gc = minreal(G*inv(stewart.kinematics.J'));
|
||||||
Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
|
Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
We also extract the transfer function from external forces $\bm{\mathcal{F}}_{\text{ext}}$ on the frame $\{B\}$ fixed to the mobile platform to the relative displacement $\mathcal{\bm{X}}$ of $\{B\}$ with respect to frame $\{A\}$:
|
We also extract the transfer function from external forces $\bm{\mathcal{F}}_{\text{ext}}$ on the frame $\{B\}$ fixed to the mobile platform to the relative displacement $\mathcal{\bm{X}}$ of $\{B\}$ with respect to frame $\{A\}$:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'F_ext'); io_i = io_i + 1; % External forces/torques applied on {B}
|
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'F_ext'); io_i = io_i + 1; % External forces/torques applied on {B}
|
||||||
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
Gd = linearize(mdl, io, options);
|
Gd = linearize(mdl, io, options);
|
||||||
Gd.InputName = {'Fex', 'Fey', 'Fez', 'Mex', 'Mey', 'Mez'};
|
Gd.InputName = {'Fex', 'Fey', 'Fez', 'Mex', 'Mey', 'Mez'};
|
||||||
Gd.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
Gd.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
The comparison of the two transfer functions is shown in Figure [[fig:comparison_Fext_F_fixed_base]].
|
The comparison of the two transfer functions is shown in Figure [[fig:comparison_Fext_F_fixed_base]].
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
freqs = logspace(1, 4, 1000);
|
freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
figure;
|
figure;
|
||||||
|
|
||||||
ax1 = subplot(2, 1, 1);
|
ax1 = subplot(2, 1, 1);
|
||||||
hold on;
|
hold on;
|
||||||
plot(freqs, abs(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
|
plot(freqs, abs(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
|
||||||
plot(freqs, abs(squeeze(freqresp(Gd(1,1), freqs, 'Hz'))), '--');
|
plot(freqs, abs(squeeze(freqresp(Gd(1,1), freqs, 'Hz'))), '--');
|
||||||
hold off;
|
hold off;
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
ax2 = subplot(2, 1, 2);
|
ax2 = subplot(2, 1, 2);
|
||||||
hold on;
|
hold on;
|
||||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
|
||||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gd(1,1), freqs, 'Hz'))), '--');
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gd(1,1), freqs, 'Hz'))), '--');
|
||||||
hold off;
|
hold off;
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
ylim([-180, 180]);
|
ylim([-180, 180]);
|
||||||
yticks([-180, -90, 0, 90, 180]);
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
legend({'$\mathcal{X}_{x}/\mathcal{F}_{x}$', '$\mathcal{X}_{x}/\mathcal{F}_{x,ext}$'});
|
legend({'$\mathcal{X}_{x}/\mathcal{F}_{x}$', '$\mathcal{X}_{x}/\mathcal{F}_{x,ext}$'});
|
||||||
|
|
||||||
linkaxes([ax1,ax2],'x');
|
linkaxes([ax1,ax2],'x');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+header: :tangle no :exports results :results none :noweb yes
|
#+header: :tangle no :exports results :results none :noweb yes
|
||||||
@ -159,7 +159,7 @@ linkaxes([ax1,ax2],'x');
|
|||||||
This can be understood from figure [[fig:1dof_actuator_external_forces]] where $\mathcal{F}_{x}$ and $\mathcal{F}_{x,\text{ext}}$ have clearly the same effect on $\mathcal{X}_{x}$.
|
This can be understood from figure [[fig:1dof_actuator_external_forces]] where $\mathcal{F}_{x}$ and $\mathcal{F}_{x,\text{ext}}$ have clearly the same effect on $\mathcal{X}_{x}$.
|
||||||
|
|
||||||
#+begin_src latex :file 1dof_actuator_external_forces.pdf
|
#+begin_src latex :file 1dof_actuator_external_forces.pdf
|
||||||
\begin{tikzpicture}
|
\begin{tikzpicture}
|
||||||
\draw[ground] (-1, 0) -- (1, 0);
|
\draw[ground] (-1, 0) -- (1, 0);
|
||||||
|
|
||||||
\draw[spring] (-0.6, 0) -- (-0.6, 1.5) node[midway, left=0.1]{$k$};
|
\draw[spring] (-0.6, 0) -- (-0.6, 1.5) node[midway, left=0.1]{$k$};
|
||||||
@ -171,7 +171,7 @@ This can be understood from figure [[fig:1dof_actuator_external_forces]] where $
|
|||||||
\draw[->] (1.5, 2) -- ++(0, 0.5) node[right]{$\mathcal{X}_{x}$};
|
\draw[->] (1.5, 2) -- ++(0, 0.5) node[right]{$\mathcal{X}_{x}$};
|
||||||
|
|
||||||
\draw[->] (0, 2) node[]{$\bullet$} -- (0, 2.8) node[below right]{$\mathcal{F}_{x,\text{ext}}$};
|
\draw[->] (0, 2) node[]{$\bullet$} -- (0, 2.8) node[below right]{$\mathcal{F}_{x,\text{ext}}$};
|
||||||
\end{tikzpicture}
|
\end{tikzpicture}
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+name: fig:1dof_actuator_external_forces
|
#+name: fig:1dof_actuator_external_forces
|
||||||
@ -182,62 +182,62 @@ This can be understood from figure [[fig:1dof_actuator_external_forces]] where $
|
|||||||
** Comparison with a flexible support
|
** Comparison with a flexible support
|
||||||
We now add a flexible support under the Stewart platform.
|
We now add a flexible support under the Stewart platform.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground = initializeGround('type', 'flexible');
|
ground = initializeGround('type', 'flexible');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
And we perform again the identification.
|
And we perform again the identification.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
||||||
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||||||
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
|
|
||||||
Gc = minreal(G*inv(stewart.kinematics.J'));
|
Gc = minreal(G*inv(stewart.kinematics.J'));
|
||||||
Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
|
Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'F_ext'); io_i = io_i + 1; % External forces/torques applied on {B}
|
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'F_ext'); io_i = io_i + 1; % External forces/torques applied on {B}
|
||||||
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
Gd = linearize(mdl, io, options);
|
Gd = linearize(mdl, io, options);
|
||||||
Gd.InputName = {'Fex', 'Fey', 'Fez', 'Mex', 'Mey', 'Mez'};
|
Gd.InputName = {'Fex', 'Fey', 'Fez', 'Mex', 'Mey', 'Mez'};
|
||||||
Gd.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
Gd.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
The comparison between the obtained transfer functions is shown in Figure [[fig:comparison_Fext_F_flexible_base]].
|
The comparison between the obtained transfer functions is shown in Figure [[fig:comparison_Fext_F_flexible_base]].
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
freqs = logspace(1, 4, 1000);
|
freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
figure;
|
figure;
|
||||||
|
|
||||||
ax1 = subplot(2, 1, 1);
|
ax1 = subplot(2, 1, 1);
|
||||||
hold on;
|
hold on;
|
||||||
plot(freqs, abs(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
|
plot(freqs, abs(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
|
||||||
plot(freqs, abs(squeeze(freqresp(Gd(1,1), freqs, 'Hz'))), '--');
|
plot(freqs, abs(squeeze(freqresp(Gd(1,1), freqs, 'Hz'))), '--');
|
||||||
hold off;
|
hold off;
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
ax2 = subplot(2, 1, 2);
|
ax2 = subplot(2, 1, 2);
|
||||||
hold on;
|
hold on;
|
||||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
|
||||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gd(1,1), freqs, 'Hz'))), '--');
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gd(1,1), freqs, 'Hz'))), '--');
|
||||||
hold off;
|
hold off;
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
ylim([-180, 180]);
|
ylim([-180, 180]);
|
||||||
yticks([-180, -90, 0, 90, 180]);
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
legend({'$\mathcal{X}_{x}/\mathcal{F}_{x}$', '$\mathcal{X}_{x}/\mathcal{F}_{x,ext}$'});
|
legend({'$\mathcal{X}_{x}/\mathcal{F}_{x}$', '$\mathcal{X}_{x}/\mathcal{F}_{x,ext}$'});
|
||||||
|
|
||||||
linkaxes([ax1,ax2],'x');
|
linkaxes([ax1,ax2],'x');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+header: :tangle no :exports results :results none :noweb yes
|
#+header: :tangle no :exports results :results none :noweb yes
|
||||||
@ -254,7 +254,7 @@ We see that $\mathcal{F}_{x}$ applies a force both on $m$ and $m^{\prime}$ where
|
|||||||
And thus $\mathcal{F}_{x}$ and $\mathcal{F}_{x,\text{ext}}$ have clearly *not* the same effect on $\mathcal{X}_{x}$.
|
And thus $\mathcal{F}_{x}$ and $\mathcal{F}_{x,\text{ext}}$ have clearly *not* the same effect on $\mathcal{X}_{x}$.
|
||||||
|
|
||||||
#+begin_src latex :file 2dof_actuator_external_forces.pdf
|
#+begin_src latex :file 2dof_actuator_external_forces.pdf
|
||||||
\begin{tikzpicture}
|
\begin{tikzpicture}
|
||||||
\draw[ground] (-1, 0) -- (1, 0);
|
\draw[ground] (-1, 0) -- (1, 0);
|
||||||
|
|
||||||
\draw[spring] (0, 0) -- (0, 1.5) node[midway, left=0.1]{$k^{\prime}$};
|
\draw[spring] (0, 0) -- (0, 1.5) node[midway, left=0.1]{$k^{\prime}$};
|
||||||
@ -269,7 +269,7 @@ And thus $\mathcal{F}_{x}$ and $\mathcal{F}_{x,\text{ext}}$ have clearly *not* t
|
|||||||
\draw[->] (1.5, 4) -- ++(0, 0.5) node[right]{$\mathcal{X}_{x}$};
|
\draw[->] (1.5, 4) -- ++(0, 0.5) node[right]{$\mathcal{X}_{x}$};
|
||||||
|
|
||||||
\draw[->] (0, 4) node[]{$\bullet$} -- (0, 4.8) node[below right]{$\mathcal{F}_{x,\text{ext}}$};
|
\draw[->] (0, 4) node[]{$\bullet$} -- (0, 4.8) node[below right]{$\mathcal{F}_{x,\text{ext}}$};
|
||||||
\end{tikzpicture}
|
\end{tikzpicture}
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+name: fig:2dof_actuator_external_forces
|
#+name: fig:2dof_actuator_external_forces
|
||||||
@ -289,67 +289,67 @@ In this section, we see how the Compliance matrix of the Stewart platform is lin
|
|||||||
|
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
open('stewart_platform_model.slx')
|
open('stewart_platform_model.slx')
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Analysis
|
** Analysis
|
||||||
Initialization of the Stewart platform.
|
Initialization of the Stewart platform.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
No flexibility below the Stewart platform and no payload.
|
No flexibility below the Stewart platform and no payload.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground = initializeGround('type', 'none');
|
ground = initializeGround('type', 'none');
|
||||||
payload = initializePayload('type', 'none');
|
payload = initializePayload('type', 'none');
|
||||||
controller = initializeController('type', 'open-loop');
|
controller = initializeController('type', 'open-loop');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$:
|
Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Options for Linearized
|
%% Options for Linearized
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
||||||
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
G = linearize(mdl, io, options);
|
G = linearize(mdl, io, options);
|
||||||
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||||||
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Gc = minreal(G*inv(stewart.kinematics.J'));
|
Gc = minreal(G*inv(stewart.kinematics.J'));
|
||||||
Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
|
Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Let's first look at the low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$.
|
Let's first look at the low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$.
|
||||||
|
|||||||
File diff suppressed because it is too large
Load Diff
@ -46,66 +46,66 @@ In this document, we discuss the various methods to identify the behavior of the
|
|||||||
** Introduction :ignore:
|
** Introduction :ignore:
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :results none :exports none
|
#+begin_src matlab :results none :exports none
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
open('stewart_platform_model.slx')
|
open('stewart_platform_model.slx')
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Initialize the Stewart Platform
|
** Initialize the Stewart Platform
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart);
|
stewart = initializeFramesPositions(stewart);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground = initializeGround('type', 'none');
|
ground = initializeGround('type', 'none');
|
||||||
payload = initializePayload('type', 'none');
|
payload = initializePayload('type', 'none');
|
||||||
controller = initializeController('type', 'open-loop');
|
controller = initializeController('type', 'open-loop');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Identification
|
** Identification
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Options for Linearized
|
%% Options for Linearized
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
||||||
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
||||||
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 2, 'openoutput'); io_i = io_i + 1; % Velocity of {B} w.r.t. {A}
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 2, 'openoutput'); io_i = io_i + 1; % Velocity of {B} w.r.t. {A}
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io);
|
||||||
% G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};
|
% G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};
|
||||||
% G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};
|
% G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Let's check the size of =G=:
|
Let's check the size of =G=:
|
||||||
#+begin_src matlab :results replace output
|
#+begin_src matlab :results replace output
|
||||||
size(G)
|
size(G)
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -117,7 +117,7 @@ size(G)
|
|||||||
|
|
||||||
We expect to have only 12 states (corresponding to the 6dof of the mobile platform).
|
We expect to have only 12 states (corresponding to the 6dof of the mobile platform).
|
||||||
#+begin_src matlab :results replace output
|
#+begin_src matlab :results replace output
|
||||||
Gm = minreal(G);
|
Gm = minreal(G);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -129,7 +129,7 @@ And indeed, we obtain 12 states.
|
|||||||
** Coordinate transformation
|
** Coordinate transformation
|
||||||
We can perform the following transformation using the =ss2ss= command.
|
We can perform the following transformation using the =ss2ss= command.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Gt = ss2ss(Gm, Gm.C);
|
Gt = ss2ss(Gm, Gm.C);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Then, the =C= matrix of =Gt= is the unity matrix which means that the states of the state space model are equal to the measurements $\bm{Y}$.
|
Then, the =C= matrix of =Gt= is the unity matrix which means that the states of the state space model are equal to the measurements $\bm{Y}$.
|
||||||
@ -138,29 +138,29 @@ The measurements are the 6 displacement and 6 velocities of mobile platform with
|
|||||||
|
|
||||||
We could perform the transformation by hand:
|
We could perform the transformation by hand:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
At = Gm.C*Gm.A*pinv(Gm.C);
|
At = Gm.C*Gm.A*pinv(Gm.C);
|
||||||
|
|
||||||
Bt = Gm.C*Gm.B;
|
Bt = Gm.C*Gm.B;
|
||||||
|
|
||||||
Ct = eye(12);
|
Ct = eye(12);
|
||||||
Dt = zeros(12, 6);
|
Dt = zeros(12, 6);
|
||||||
|
|
||||||
Gt = ss(At, Bt, Ct, Dt);
|
Gt = ss(At, Bt, Ct, Dt);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Analysis
|
** Analysis
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
[V,D] = eig(Gt.A);
|
[V,D] = eig(Gt.A);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||||
ws = imag(diag(D))/2/pi;
|
ws = imag(diag(D))/2/pi;
|
||||||
[ws,I] = sort(ws)
|
[ws,I] = sort(ws)
|
||||||
|
|
||||||
xi = 100*real(diag(D))./imag(diag(D));
|
xi = 100*real(diag(D))./imag(diag(D));
|
||||||
xi = xi(I);
|
xi = xi(I);
|
||||||
|
|
||||||
data2orgtable([[1:length(ws(ws>0))]', ws(ws>0), xi(xi>0)], {}, {'Mode Number', 'Resonance Frequency [Hz]', 'Damping Ratio [%]'}, ' %.1f ');
|
data2orgtable([[1:length(ws(ws>0))]', ws(ws>0), xi(xi>0)], {}, {'Mode Number', 'Resonance Frequency [Hz]', 'Damping Ratio [%]'}, ' %.1f ');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -180,54 +180,54 @@ To visualize the i'th mode, we may excite the system using the inputs $U_i$ such
|
|||||||
|
|
||||||
Let's first sort the modes and just take the modes corresponding to a eigenvalue with a positive imaginary part.
|
Let's first sort the modes and just take the modes corresponding to a eigenvalue with a positive imaginary part.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ws = imag(diag(D));
|
ws = imag(diag(D));
|
||||||
[ws,I] = sort(ws)
|
[ws,I] = sort(ws)
|
||||||
ws = ws(7:end); I = I(7:end);
|
ws = ws(7:end); I = I(7:end);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
for i = 1:length(ws)
|
for i = 1:length(ws)
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
i_mode = I(i); % the argument is the i'th mode
|
i_mode = I(i); % the argument is the i'th mode
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
lambda_i = D(i_mode, i_mode);
|
lambda_i = D(i_mode, i_mode);
|
||||||
xi_i = V(:,i_mode);
|
xi_i = V(:,i_mode);
|
||||||
|
|
||||||
a_i = real(lambda_i);
|
a_i = real(lambda_i);
|
||||||
b_i = imag(lambda_i);
|
b_i = imag(lambda_i);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Let do 10 periods of the mode.
|
Let do 10 periods of the mode.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
t = linspace(0, 10/(imag(lambda_i)/2/pi), 1000);
|
t = linspace(0, 10/(imag(lambda_i)/2/pi), 1000);
|
||||||
U_i = pinv(Gt.B) * real(xi_i * lambda_i * (cos(b_i * t) + 1i*sin(b_i * t)));
|
U_i = pinv(Gt.B) * real(xi_i * lambda_i * (cos(b_i * t) + 1i*sin(b_i * t)));
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
U = timeseries(U_i, t);
|
U = timeseries(U_i, t);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Simulation:
|
Simulation:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
load('mat/conf_simscape.mat');
|
load('mat/conf_simscape.mat');
|
||||||
set_param(conf_simscape, 'StopTime', num2str(t(end)));
|
set_param(conf_simscape, 'StopTime', num2str(t(end)));
|
||||||
sim(mdl);
|
sim(mdl);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Save the movie of the mode shape.
|
Save the movie of the mode shape.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
smwritevideo(mdl, sprintf('figs/mode%i', i), ...
|
smwritevideo(mdl, sprintf('figs/mode%i', i), ...
|
||||||
'PlaybackSpeedRatio', 1/(b_i/2/pi), ...
|
'PlaybackSpeedRatio', 1/(b_i/2/pi), ...
|
||||||
'FrameRate', 30, ...
|
'FrameRate', 30, ...
|
||||||
'FrameSize', [800, 400]);
|
'FrameSize', [800, 400]);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+name: fig:mode1
|
#+name: fig:mode1
|
||||||
@ -247,68 +247,68 @@ end
|
|||||||
** Introduction :ignore:
|
** Introduction :ignore:
|
||||||
** Matlab Init :noexport:
|
** Matlab Init :noexport:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
open('stewart_platform_model.slx')
|
open('stewart_platform_model.slx')
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Initialize the Stewart platform
|
** Initialize the Stewart platform
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
|
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
We set the rotation point of the ground to be at the same point at frames $\{A\}$ and $\{B\}$.
|
We set the rotation point of the ground to be at the same point at frames $\{A\}$ and $\{B\}$.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground = initializeGround('type', 'rigid', 'rot_point', stewart.platform_F.FO_A);
|
ground = initializeGround('type', 'rigid', 'rot_point', stewart.platform_F.FO_A);
|
||||||
payload = initializePayload('type', 'rigid');
|
payload = initializePayload('type', 'rigid');
|
||||||
controller = initializeController('type', 'open-loop');
|
controller = initializeController('type', 'open-loop');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Transmissibility
|
** Transmissibility
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Options for Linearized
|
%% Options for Linearized
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Disturbances/D_w'], 1, 'openinput'); io_i = io_i + 1; % Base Motion [m, rad]
|
io(io_i) = linio([mdl, '/Disturbances/D_w'], 1, 'openinput'); io_i = io_i + 1; % Base Motion [m, rad]
|
||||||
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Absolute Motion [m, rad]
|
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Absolute Motion [m, rad]
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
T = linearize(mdl, io, options);
|
T = linearize(mdl, io, options);
|
||||||
T.InputName = {'Wdx', 'Wdy', 'Wdz', 'Wrx', 'Wry', 'Wrz'};
|
T.InputName = {'Wdx', 'Wdy', 'Wdz', 'Wrx', 'Wry', 'Wrz'};
|
||||||
T.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
T.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
freqs = logspace(1, 4, 1000);
|
freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
figure;
|
figure;
|
||||||
for ix = 1:6
|
for ix = 1:6
|
||||||
for iy = 1:6
|
for iy = 1:6
|
||||||
subplot(6, 6, (ix-1)*6 + iy);
|
subplot(6, 6, (ix-1)*6 + iy);
|
||||||
hold on;
|
hold on;
|
||||||
@ -323,7 +323,7 @@ for ix = 1:6
|
|||||||
yticklabels({});
|
yticklabels({});
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
From cite:preumont07_six_axis_singl_stage_activ, one can use the Frobenius norm of the transmissibility matrix to obtain a scalar indicator of the transmissibility performance of the system:
|
From cite:preumont07_six_axis_singl_stage_activ, one can use the Frobenius norm of the transmissibility matrix to obtain a scalar indicator of the transmissibility performance of the system:
|
||||||
@ -333,26 +333,26 @@ From cite:preumont07_six_axis_singl_stage_activ, one can use the Frobenius norm
|
|||||||
\end{align*}
|
\end{align*}
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
freqs = logspace(1, 4, 1000);
|
freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
T_norm = zeros(length(freqs), 1);
|
T_norm = zeros(length(freqs), 1);
|
||||||
|
|
||||||
for i = 1:length(freqs)
|
for i = 1:length(freqs)
|
||||||
T_norm(i) = sqrt(trace(freqresp(T, freqs(i), 'Hz')*freqresp(T, freqs(i), 'Hz')'));
|
T_norm(i) = sqrt(trace(freqresp(T, freqs(i), 'Hz')*freqresp(T, freqs(i), 'Hz')'));
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
And we normalize by a factor $\sqrt{6}$ to obtain a performance metric comparable to the transmissibility of a one-axis isolator:
|
And we normalize by a factor $\sqrt{6}$ to obtain a performance metric comparable to the transmissibility of a one-axis isolator:
|
||||||
\[ \Gamma(\omega) = \|\bm{T}(\omega)\| / \sqrt{6} \]
|
\[ \Gamma(\omega) = \|\bm{T}(\omega)\| / \sqrt{6} \]
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Gamma = T_norm/sqrt(6);
|
Gamma = T_norm/sqrt(6);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
figure;
|
figure;
|
||||||
plot(freqs, Gamma)
|
plot(freqs, Gamma)
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
* Compliance Analysis
|
* Compliance Analysis
|
||||||
@ -360,68 +360,68 @@ set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|||||||
** Introduction :ignore:
|
** Introduction :ignore:
|
||||||
** Matlab Init :noexport:
|
** Matlab Init :noexport:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
open('stewart_platform_model.slx')
|
open('stewart_platform_model.slx')
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Initialize the Stewart platform
|
** Initialize the Stewart platform
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
|
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
We set the rotation point of the ground to be at the same point at frames $\{A\}$ and $\{B\}$.
|
We set the rotation point of the ground to be at the same point at frames $\{A\}$ and $\{B\}$.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground = initializeGround('type', 'none');
|
ground = initializeGround('type', 'none');
|
||||||
payload = initializePayload('type', 'rigid');
|
payload = initializePayload('type', 'rigid');
|
||||||
controller = initializeController('type', 'open-loop');
|
controller = initializeController('type', 'open-loop');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Compliance
|
** Compliance
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Options for Linearized
|
%% Options for Linearized
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Disturbances/F_ext'], 1, 'openinput'); io_i = io_i + 1; % Base Motion [m, rad]
|
io(io_i) = linio([mdl, '/Disturbances/F_ext'], 1, 'openinput'); io_i = io_i + 1; % Base Motion [m, rad]
|
||||||
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Absolute Motion [m, rad]
|
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Absolute Motion [m, rad]
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
C = linearize(mdl, io, options);
|
C = linearize(mdl, io, options);
|
||||||
C.InputName = {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'};
|
C.InputName = {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'};
|
||||||
C.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
C.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
freqs = logspace(1, 4, 1000);
|
freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
figure;
|
figure;
|
||||||
for ix = 1:6
|
for ix = 1:6
|
||||||
for iy = 1:6
|
for iy = 1:6
|
||||||
subplot(6, 6, (ix-1)*6 + iy);
|
subplot(6, 6, (ix-1)*6 + iy);
|
||||||
hold on;
|
hold on;
|
||||||
@ -436,25 +436,25 @@ for ix = 1:6
|
|||||||
yticklabels({});
|
yticklabels({});
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
We can try to use the Frobenius norm to obtain a scalar value representing the 6-dof compliance of the Stewart platform.
|
We can try to use the Frobenius norm to obtain a scalar value representing the 6-dof compliance of the Stewart platform.
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
freqs = logspace(1, 4, 1000);
|
freqs = logspace(1, 4, 1000);
|
||||||
|
|
||||||
C_norm = zeros(length(freqs), 1);
|
C_norm = zeros(length(freqs), 1);
|
||||||
|
|
||||||
for i = 1:length(freqs)
|
for i = 1:length(freqs)
|
||||||
C_norm(i) = sqrt(trace(freqresp(C, freqs(i), 'Hz')*freqresp(C, freqs(i), 'Hz')'));
|
C_norm(i) = sqrt(trace(freqresp(C, freqs(i), 'Hz')*freqresp(C, freqs(i), 'Hz')'));
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
figure;
|
figure;
|
||||||
plot(freqs, C_norm)
|
plot(freqs, C_norm)
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
* Functions
|
* Functions
|
||||||
@ -470,20 +470,20 @@ set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [T, T_norm, freqs] = computeTransmissibility(args)
|
function [T, T_norm, freqs] = computeTransmissibility(args)
|
||||||
% computeTransmissibility -
|
% computeTransmissibility -
|
||||||
%
|
%
|
||||||
% Syntax: [T, T_norm, freqs] = computeTransmissibility(args)
|
% Syntax: [T, T_norm, freqs] = computeTransmissibility(args)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - args - Structure with the following fields:
|
% - args - Structure with the following fields:
|
||||||
% - plots [true/false] - Should plot the transmissilibty matrix and its Frobenius norm
|
% - plots [true/false] - Should plot the transmissilibty matrix and its Frobenius norm
|
||||||
% - freqs [] - Frequency vector to estimate the Frobenius norm
|
% - freqs [] - Frequency vector to estimate the Frobenius norm
|
||||||
%
|
%
|
||||||
% Outputs:
|
% Outputs:
|
||||||
% - T [6x6 ss] - Transmissibility matrix
|
% - T [6x6 ss] - Transmissibility matrix
|
||||||
% - T_norm [length(freqs)x1] - Frobenius norm of the Transmissibility matrix
|
% - T_norm [length(freqs)x1] - Frobenius norm of the Transmissibility matrix
|
||||||
% - freqs [length(freqs)x1] - Frequency vector in [Hz]
|
% - freqs [length(freqs)x1] - Frequency vector in [Hz]
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Optional Parameters
|
*** Optional Parameters
|
||||||
@ -491,14 +491,14 @@ function [T, T_norm, freqs] = computeTransmissibility(args)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
arguments
|
arguments
|
||||||
args.plots logical {mustBeNumericOrLogical} = false
|
args.plots logical {mustBeNumericOrLogical} = false
|
||||||
args.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
args.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
freqs = args.freqs;
|
freqs = args.freqs;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Identification of the Transmissibility Matrix
|
*** Identification of the Transmissibility Matrix
|
||||||
@ -506,29 +506,29 @@ freqs = args.freqs;
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Options for Linearized
|
%% Options for Linearized
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Disturbances/D_w'], 1, 'openinput'); io_i = io_i + 1; % Base Motion [m, rad]
|
io(io_i) = linio([mdl, '/Disturbances/D_w'], 1, 'openinput'); io_i = io_i + 1; % Base Motion [m, rad]
|
||||||
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'output'); io_i = io_i + 1; % Absolute Motion [m, rad]
|
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'output'); io_i = io_i + 1; % Absolute Motion [m, rad]
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
T = linearize(mdl, io, options);
|
T = linearize(mdl, io, options);
|
||||||
T.InputName = {'Wdx', 'Wdy', 'Wdz', 'Wrx', 'Wry', 'Wrz'};
|
T.InputName = {'Wdx', 'Wdy', 'Wdz', 'Wrx', 'Wry', 'Wrz'};
|
||||||
T.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
T.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
If wanted, the 6x6 transmissibility matrix is plotted.
|
If wanted, the 6x6 transmissibility matrix is plotted.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
p_handle = zeros(6*6,1);
|
p_handle = zeros(6*6,1);
|
||||||
|
|
||||||
if args.plots
|
if args.plots
|
||||||
fig = figure;
|
fig = figure;
|
||||||
for ix = 1:6
|
for ix = 1:6
|
||||||
for iy = 1:6
|
for iy = 1:6
|
||||||
@ -554,7 +554,7 @@ if args.plots
|
|||||||
han.YLabel.Visible = 'on';
|
han.YLabel.Visible = 'on';
|
||||||
xlabel(han, 'Frequency [Hz]');
|
xlabel(han, 'Frequency [Hz]');
|
||||||
ylabel(han, 'Transmissibility [m/m]');
|
ylabel(han, 'Transmissibility [m/m]');
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Computation of the Frobenius norm
|
*** Computation of the Frobenius norm
|
||||||
@ -562,25 +562,25 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
T_norm = zeros(length(freqs), 1);
|
T_norm = zeros(length(freqs), 1);
|
||||||
|
|
||||||
for i = 1:length(freqs)
|
for i = 1:length(freqs)
|
||||||
T_norm(i) = sqrt(trace(freqresp(T, freqs(i), 'Hz')*freqresp(T, freqs(i), 'Hz')'));
|
T_norm(i) = sqrt(trace(freqresp(T, freqs(i), 'Hz')*freqresp(T, freqs(i), 'Hz')'));
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
T_norm = T_norm/sqrt(6);
|
T_norm = T_norm/sqrt(6);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
if args.plots
|
if args.plots
|
||||||
figure;
|
figure;
|
||||||
plot(freqs, T_norm)
|
plot(freqs, T_norm)
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
xlabel('Frequency [Hz]');
|
xlabel('Frequency [Hz]');
|
||||||
ylabel('Transmissibility - Frobenius Norm');
|
ylabel('Transmissibility - Frobenius Norm');
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Compute the Compliance
|
** Compute the Compliance
|
||||||
@ -595,20 +595,20 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [C, C_norm, freqs] = computeCompliance(args)
|
function [C, C_norm, freqs] = computeCompliance(args)
|
||||||
% computeCompliance -
|
% computeCompliance -
|
||||||
%
|
%
|
||||||
% Syntax: [C, C_norm, freqs] = computeCompliance(args)
|
% Syntax: [C, C_norm, freqs] = computeCompliance(args)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - args - Structure with the following fields:
|
% - args - Structure with the following fields:
|
||||||
% - plots [true/false] - Should plot the transmissilibty matrix and its Frobenius norm
|
% - plots [true/false] - Should plot the transmissilibty matrix and its Frobenius norm
|
||||||
% - freqs [] - Frequency vector to estimate the Frobenius norm
|
% - freqs [] - Frequency vector to estimate the Frobenius norm
|
||||||
%
|
%
|
||||||
% Outputs:
|
% Outputs:
|
||||||
% - C [6x6 ss] - Compliance matrix
|
% - C [6x6 ss] - Compliance matrix
|
||||||
% - C_norm [length(freqs)x1] - Frobenius norm of the Compliance matrix
|
% - C_norm [length(freqs)x1] - Frobenius norm of the Compliance matrix
|
||||||
% - freqs [length(freqs)x1] - Frequency vector in [Hz]
|
% - freqs [length(freqs)x1] - Frequency vector in [Hz]
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Optional Parameters
|
*** Optional Parameters
|
||||||
@ -616,14 +616,14 @@ function [C, C_norm, freqs] = computeCompliance(args)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
arguments
|
arguments
|
||||||
args.plots logical {mustBeNumericOrLogical} = false
|
args.plots logical {mustBeNumericOrLogical} = false
|
||||||
args.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
args.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
freqs = args.freqs;
|
freqs = args.freqs;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Identification of the Compliance Matrix
|
*** Identification of the Compliance Matrix
|
||||||
@ -631,29 +631,29 @@ freqs = args.freqs;
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Options for Linearized
|
%% Options for Linearized
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Disturbances/F_ext'], 1, 'openinput'); io_i = io_i + 1; % External forces [N, N*m]
|
io(io_i) = linio([mdl, '/Disturbances/F_ext'], 1, 'openinput'); io_i = io_i + 1; % External forces [N, N*m]
|
||||||
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'output'); io_i = io_i + 1; % Absolute Motion [m, rad]
|
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'output'); io_i = io_i + 1; % Absolute Motion [m, rad]
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
C = linearize(mdl, io, options);
|
C = linearize(mdl, io, options);
|
||||||
C.InputName = {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'};
|
C.InputName = {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'};
|
||||||
C.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
C.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
If wanted, the 6x6 transmissibility matrix is plotted.
|
If wanted, the 6x6 transmissibility matrix is plotted.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
p_handle = zeros(6*6,1);
|
p_handle = zeros(6*6,1);
|
||||||
|
|
||||||
if args.plots
|
if args.plots
|
||||||
fig = figure;
|
fig = figure;
|
||||||
for ix = 1:6
|
for ix = 1:6
|
||||||
for iy = 1:6
|
for iy = 1:6
|
||||||
@ -678,7 +678,7 @@ if args.plots
|
|||||||
han.YLabel.Visible = 'on';
|
han.YLabel.Visible = 'on';
|
||||||
xlabel(han, 'Frequency [Hz]');
|
xlabel(han, 'Frequency [Hz]');
|
||||||
ylabel(han, 'Compliance [m/N, rad/(N*m)]');
|
ylabel(han, 'Compliance [m/N, rad/(N*m)]');
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Computation of the Frobenius norm
|
*** Computation of the Frobenius norm
|
||||||
@ -686,21 +686,21 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
freqs = args.freqs;
|
freqs = args.freqs;
|
||||||
|
|
||||||
C_norm = zeros(length(freqs), 1);
|
C_norm = zeros(length(freqs), 1);
|
||||||
|
|
||||||
for i = 1:length(freqs)
|
for i = 1:length(freqs)
|
||||||
C_norm(i) = sqrt(trace(freqresp(C, freqs(i), 'Hz')*freqresp(C, freqs(i), 'Hz')'));
|
C_norm(i) = sqrt(trace(freqresp(C, freqs(i), 'Hz')*freqresp(C, freqs(i), 'Hz')'));
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
if args.plots
|
if args.plots
|
||||||
figure;
|
figure;
|
||||||
plot(freqs, C_norm)
|
plot(freqs, C_norm)
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
xlabel('Frequency [Hz]');
|
xlabel('Frequency [Hz]');
|
||||||
ylabel('Compliance - Frobenius Norm');
|
ylabel('Compliance - Frobenius Norm');
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|||||||
@ -234,30 +234,30 @@ This will also gives us the range for which the approximate forward kinematic is
|
|||||||
|
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :results none :exports none
|
#+begin_src matlab :results none :exports none
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Stewart architecture definition
|
** Stewart architecture definition
|
||||||
We first define some general Stewart architecture.
|
We first define some general Stewart architecture.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart);
|
stewart = initializeJointDynamics(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Comparison for "pure" translations
|
** Comparison for "pure" translations
|
||||||
@ -267,31 +267,31 @@ We compute the approximate and exact required strut stroke to have the wanted mo
|
|||||||
The estimate required strut stroke for both the approximate and exact solutions are shown in Figure [[fig:inverse_kinematics_approx_validity_x_translation]].
|
The estimate required strut stroke for both the approximate and exact solutions are shown in Figure [[fig:inverse_kinematics_approx_validity_x_translation]].
|
||||||
The relative strut length displacement is shown in Figure [[fig:inverse_kinematics_approx_validity_x_translation_relative]].
|
The relative strut length displacement is shown in Figure [[fig:inverse_kinematics_approx_validity_x_translation_relative]].
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Xrs = logspace(-6, -1, 100); % Wanted X translation of the mobile platform [m]
|
Xrs = logspace(-6, -1, 100); % Wanted X translation of the mobile platform [m]
|
||||||
|
|
||||||
Ls_approx = zeros(6, length(Xrs));
|
Ls_approx = zeros(6, length(Xrs));
|
||||||
Ls_exact = zeros(6, length(Xrs));
|
Ls_exact = zeros(6, length(Xrs));
|
||||||
|
|
||||||
for i = 1:length(Xrs)
|
for i = 1:length(Xrs)
|
||||||
Xr = Xrs(i);
|
Xr = Xrs(i);
|
||||||
L_approx(:, i) = stewart.kinematics.J*[Xr; 0; 0; 0; 0; 0;];
|
L_approx(:, i) = stewart.kinematics.J*[Xr; 0; 0; 0; 0; 0;];
|
||||||
[~, L_exact(:, i)] = inverseKinematics(stewart, 'AP', [Xr; 0; 0]);
|
[~, L_exact(:, i)] = inverseKinematics(stewart, 'AP', [Xr; 0; 0]);
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
figure;
|
figure;
|
||||||
hold on;
|
hold on;
|
||||||
for i = 1:6
|
for i = 1:6
|
||||||
set(gca,'ColorOrderIndex',i);
|
set(gca,'ColorOrderIndex',i);
|
||||||
plot(Xrs, abs(L_approx(i, :)));
|
plot(Xrs, abs(L_approx(i, :)));
|
||||||
set(gca,'ColorOrderIndex',i);
|
set(gca,'ColorOrderIndex',i);
|
||||||
plot(Xrs, abs(L_exact(i, :)), '--');
|
plot(Xrs, abs(L_exact(i, :)), '--');
|
||||||
end
|
end
|
||||||
hold off;
|
hold off;
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
xlabel('Wanted $x$ displacement [m]');
|
xlabel('Wanted $x$ displacement [m]');
|
||||||
ylabel('Estimated required stroke');
|
ylabel('Estimated required stroke');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
@ -304,15 +304,15 @@ ylabel('Estimated required stroke');
|
|||||||
[[file:figs/inverse_kinematics_approx_validity_x_translation.png]]
|
[[file:figs/inverse_kinematics_approx_validity_x_translation.png]]
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
figure;
|
figure;
|
||||||
hold on;
|
hold on;
|
||||||
for i = 1:6
|
for i = 1:6
|
||||||
plot(Xrs, abs(L_approx(i, :) - L_exact(i, :))./abs(L_approx(i, :) + L_exact(i, :)), 'k-');
|
plot(Xrs, abs(L_approx(i, :) - L_exact(i, :))./abs(L_approx(i, :) + L_exact(i, :)), 'k-');
|
||||||
end
|
end
|
||||||
hold off;
|
hold off;
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
xlabel('Wanted $x$ displacement [m]');
|
xlabel('Wanted $x$ displacement [m]');
|
||||||
ylabel('Relative Stroke Error');
|
ylabel('Relative Stroke Error');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
@ -349,41 +349,41 @@ This is what is analyzed in this section.
|
|||||||
|
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :results none :exports none
|
#+begin_src matlab :results none :exports none
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Stewart architecture definition
|
** Stewart architecture definition
|
||||||
Let's first define the Stewart platform architecture that we want to study.
|
Let's first define the Stewart platform architecture that we want to study.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart);
|
stewart = initializeJointDynamics(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Wanted translations and rotations
|
** Wanted translations and rotations
|
||||||
Let's now define the wanted extreme translations and rotations.
|
Let's now define the wanted extreme translations and rotations.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Tx_max = 50e-6; % Translation [m]
|
Tx_max = 50e-6; % Translation [m]
|
||||||
Ty_max = 50e-6; % Translation [m]
|
Ty_max = 50e-6; % Translation [m]
|
||||||
Tz_max = 50e-6; % Translation [m]
|
Tz_max = 50e-6; % Translation [m]
|
||||||
Rx_max = 30e-6; % Rotation [rad]
|
Rx_max = 30e-6; % Rotation [rad]
|
||||||
Ry_max = 30e-6; % Rotation [rad]
|
Ry_max = 30e-6; % Rotation [rad]
|
||||||
Rz_max = 0; % Rotation [rad]
|
Rz_max = 0; % Rotation [rad]
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Needed stroke for "pure" rotations or translations
|
** Needed stroke for "pure" rotations or translations
|
||||||
@ -391,17 +391,17 @@ As a first estimation, we estimate the needed actuator stroke for "pure" rotatio
|
|||||||
We do that using either the Inverse Kinematic solution or the Jacobian matrix as an approximation.
|
We do that using either the Inverse Kinematic solution or the Jacobian matrix as an approximation.
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
LTx = stewart.kinematics.J*[Tx_max 0 0 0 0 0]';
|
LTx = stewart.kinematics.J*[Tx_max 0 0 0 0 0]';
|
||||||
LTy = stewart.kinematics.J*[0 Ty_max 0 0 0 0]';
|
LTy = stewart.kinematics.J*[0 Ty_max 0 0 0 0]';
|
||||||
LTz = stewart.kinematics.J*[0 0 Tz_max 0 0 0]';
|
LTz = stewart.kinematics.J*[0 0 Tz_max 0 0 0]';
|
||||||
LRx = stewart.kinematics.J*[0 0 0 Rx_max 0 0]';
|
LRx = stewart.kinematics.J*[0 0 0 Rx_max 0 0]';
|
||||||
LRy = stewart.kinematics.J*[0 0 0 0 Ry_max 0]';
|
LRy = stewart.kinematics.J*[0 0 0 0 Ry_max 0]';
|
||||||
LRz = stewart.kinematics.J*[0 0 0 0 0 Rz_max]';
|
LRz = stewart.kinematics.J*[0 0 0 0 0 Rz_max]';
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
The obtain required stroke is:
|
The obtain required stroke is:
|
||||||
#+begin_src matlab :results value replace :exports results
|
#+begin_src matlab :results value replace :exports results
|
||||||
ans = sprintf('From %.2g[m] to %.2g[m]: Total stroke = %.1f[um]', min(min([LTx,LTy,LTz,LRx,LRy])), max(max([LTx,LTy,LTz,LRx,LRy])), 1e6*(max(max([LTx,LTy,LTz,LRx,LRy]))-min(min([LTx,LTy,LTz,LRx,LRy]))))
|
ans = sprintf('From %.2g[m] to %.2g[m]: Total stroke = %.1f[um]', min(min([LTx,LTy,LTz,LRx,LRy])), max(max([LTx,LTy,LTz,LRx,LRy])), 1e6*(max(max([LTx,LTy,LTz,LRx,LRy]))-min(min([LTx,LTy,LTz,LRx,LRy]))))
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -416,11 +416,11 @@ To do so, we may estimate the required actuator stroke for all possible combinat
|
|||||||
|
|
||||||
Let's first generate all the possible combination of maximum translation and rotations.
|
Let's first generate all the possible combination of maximum translation and rotations.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Ps = [2*(dec2bin(0:5^2-1,5)-'0')-1, zeros(5^2, 1)].*[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
Ps = [2*(dec2bin(0:5^2-1,5)-'0')-1, zeros(5^2, 1)].*[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||||
data2orgtable(Ps, {}, {'*Tx [m]*', '*Ty [m]*', '*Tz [m]*', '*Rx [rad]*', '*Ry [rad]*', '*Rz [rad]*'}, ' %.1e ');
|
data2orgtable(Ps, {}, {'*Tx [m]*', '*Ty [m]*', '*Tz [m]*', '*Rx [rad]*', '*Ry [rad]*', '*Rz [rad]*'}, ' %.1e ');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -454,10 +454,10 @@ data2orgtable(Ps, {}, {'*Tx [m]*', '*Ty [m]*', '*Tz [m]*', '*Rx [rad]*', '*Ry [r
|
|||||||
|
|
||||||
For all possible combination, we compute the required actuator stroke using the inverse kinematic solution.
|
For all possible combination, we compute the required actuator stroke using the inverse kinematic solution.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
L_min = 0;
|
L_min = 0;
|
||||||
L_max = 0;
|
L_max = 0;
|
||||||
|
|
||||||
for i = 1:size(Ps,1)
|
for i = 1:size(Ps,1)
|
||||||
Rx = [1 0 0;
|
Rx = [1 0 0;
|
||||||
0 cos(Ps(i, 4)) -sin(Ps(i, 4));
|
0 cos(Ps(i, 4)) -sin(Ps(i, 4));
|
||||||
0 sin(Ps(i, 4)) cos(Ps(i, 4))];
|
0 sin(Ps(i, 4)) cos(Ps(i, 4))];
|
||||||
@ -479,12 +479,12 @@ for i = 1:size(Ps,1)
|
|||||||
if max(Ls) > L_max
|
if max(Ls) > L_max
|
||||||
L_max = max(Ls)
|
L_max = max(Ls)
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
We obtain the required actuator stroke:
|
We obtain the required actuator stroke:
|
||||||
#+begin_src matlab :results value replace :exports results
|
#+begin_src matlab :results value replace :exports results
|
||||||
ans = sprintf('From %.2g[m] to %.2g[m]: Total stroke = %.1f[um]', L_min, L_max, 1e6*(L_max-L_min))
|
ans = sprintf('From %.2g[m] to %.2g[m]: Total stroke = %.1f[um]', L_min, L_max, 1e6*(L_max-L_min))
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -513,36 +513,36 @@ However, for small displacements, we can use the Jacobian as an approximate solu
|
|||||||
|
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :results none :exports none
|
#+begin_src matlab :results none :exports none
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Stewart architecture definition
|
** Stewart architecture definition
|
||||||
Let's first define the Stewart platform architecture that we want to study.
|
Let's first define the Stewart platform architecture that we want to study.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart);
|
stewart = initializeJointDynamics(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Let's now define the actuator stroke.
|
Let's now define the actuator stroke.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
L_min = -50e-6; % [m]
|
L_min = -50e-6; % [m]
|
||||||
L_max = 50e-6; % [m]
|
L_max = 50e-6; % [m]
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Pure translations
|
** Pure translations
|
||||||
@ -557,11 +557,11 @@ To obtain the mobility "volume" attainable by the Stewart platform when it's ori
|
|||||||
|
|
||||||
For each possible value of $(\theta, \phi)$, we compute the maximum radius $r$ attainable with the constraint that the stroke of each actuator should be between =L_min= and =L_max=.
|
For each possible value of $(\theta, \phi)$, we compute the maximum radius $r$ attainable with the constraint that the stroke of each actuator should be between =L_min= and =L_max=.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
thetas = linspace(0, pi, 50);
|
thetas = linspace(0, pi, 50);
|
||||||
phis = linspace(0, 2*pi, 50);
|
phis = linspace(0, 2*pi, 50);
|
||||||
rs = zeros(length(thetas), length(phis));
|
rs = zeros(length(thetas), length(phis));
|
||||||
|
|
||||||
for i = 1:length(thetas)
|
for i = 1:length(thetas)
|
||||||
for j = 1:length(phis)
|
for j = 1:length(phis)
|
||||||
Tx = sin(thetas(i))*cos(phis(j));
|
Tx = sin(thetas(i))*cos(phis(j));
|
||||||
Ty = sin(thetas(i))*sin(phis(j));
|
Ty = sin(thetas(i))*sin(phis(j));
|
||||||
@ -571,7 +571,7 @@ for i = 1:length(thetas)
|
|||||||
|
|
||||||
rs(i, j) = max([dL(dL<0)*L_min; dL(dL>0)*L_max]);
|
rs(i, j) = max([dL(dL<0)*L_min; dL(dL>0)*L_max]);
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
|
|
||||||
@ -588,13 +588,13 @@ data2orgtable([1e6*L_min, 1e6*L_max, 1e6*(min(min(rs)))], {}, {'=L_min= [$\mu m$
|
|||||||
| -50.0 | 50.0 | 31.5 |
|
| -50.0 | 50.0 | 31.5 |
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
figure;
|
figure;
|
||||||
plot3(reshape(rs.*(sin(thetas)'*cos(phis)), [1, length(thetas)*length(phis)]), ...
|
plot3(reshape(rs.*(sin(thetas)'*cos(phis)), [1, length(thetas)*length(phis)]), ...
|
||||||
reshape(rs.*(sin(thetas)'*sin(phis)), [1, length(thetas)*length(phis)]), ...
|
reshape(rs.*(sin(thetas)'*sin(phis)), [1, length(thetas)*length(phis)]), ...
|
||||||
reshape(rs.*(cos(thetas)'*ones(1, length(phis))), [1, length(thetas)*length(phis)]))
|
reshape(rs.*(cos(thetas)'*ones(1, length(phis))), [1, length(thetas)*length(phis)]))
|
||||||
xlabel('X Translation [m]');
|
xlabel('X Translation [m]');
|
||||||
ylabel('Y Translation [m]');
|
ylabel('Y Translation [m]');
|
||||||
zlabel('Z Translation [m]');
|
zlabel('Z Translation [m]');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
@ -613,48 +613,48 @@ using this function https://fr.mathworks.com/help/matlab/ref/contour3.html
|
|||||||
** Introduction :ignore:
|
** Introduction :ignore:
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :results none :exports none
|
#+begin_src matlab :results none :exports none
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Estimation with an analytical model
|
** Estimation with an analytical model
|
||||||
Let's first define the Stewart Platform Geometry.
|
Let's first define the Stewart Platform Geometry.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 150e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 150e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart, 'AP', [0; 0; 0]);
|
stewart = computeJointsPose(stewart, 'AP', [0; 0; 0]);
|
||||||
|
|
||||||
As_init = stewart.geometry.As;
|
As_init = stewart.geometry.As;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Tx_max = 60e-6; % Translation [m]
|
Tx_max = 60e-6; % Translation [m]
|
||||||
Ty_max = 60e-6; % Translation [m]
|
Ty_max = 60e-6; % Translation [m]
|
||||||
Tz_max = 60e-6; % Translation [m]
|
Tz_max = 60e-6; % Translation [m]
|
||||||
Rx_max = 30e-6; % Rotation [rad]
|
Rx_max = 30e-6; % Rotation [rad]
|
||||||
Ry_max = 30e-6; % Rotation [rad]
|
Ry_max = 30e-6; % Rotation [rad]
|
||||||
Rz_max = 0; % Rotation [rad]
|
Rz_max = 0; % Rotation [rad]
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Ps = [2*(dec2bin(0:5^2-1,5)-'0')-1, zeros(5^2, 1)].*[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
Ps = [2*(dec2bin(0:5^2-1,5)-'0')-1, zeros(5^2, 1)].*[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
flex_ang = zeros(size(Ps, 1), 6);
|
flex_ang = zeros(size(Ps, 1), 6);
|
||||||
Rxs = zeros(size(Ps, 1), 6)
|
Rxs = zeros(size(Ps, 1), 6)
|
||||||
Rys = zeros(size(Ps, 1), 6)
|
Rys = zeros(size(Ps, 1), 6)
|
||||||
Rzs = zeros(size(Ps, 1), 6)
|
Rzs = zeros(size(Ps, 1), 6)
|
||||||
|
|
||||||
for Ps_i = 1:size(Ps, 1)
|
for Ps_i = 1:size(Ps, 1)
|
||||||
Rx = [1 0 0;
|
Rx = [1 0 0;
|
||||||
0 cos(Ps(Ps_i, 4)) -sin(Ps(Ps_i, 4));
|
0 cos(Ps(Ps_i, 4)) -sin(Ps(Ps_i, 4));
|
||||||
0 sin(Ps(Ps_i, 4)) cos(Ps(Ps_i, 4))];
|
0 sin(Ps(Ps_i, 4)) cos(Ps(Ps_i, 4))];
|
||||||
@ -680,26 +680,26 @@ for Ps_i = 1:size(Ps, 1)
|
|||||||
Rxs(Ps_i, l_i) = atan2(-MRf(2,3)/cos(Rys(Ps_i, l_i)), MRf(3,3)/cos(Rys(Ps_i, l_i)));
|
Rxs(Ps_i, l_i) = atan2(-MRf(2,3)/cos(Rys(Ps_i, l_i)), MRf(3,3)/cos(Rys(Ps_i, l_i)));
|
||||||
Rzs(Ps_i, l_i) = atan2(-MRf(1,2)/cos(Rys(Ps_i, l_i)), MRf(1,1)/cos(Rys(Ps_i, l_i)));
|
Rzs(Ps_i, l_i) = atan2(-MRf(1,2)/cos(Rys(Ps_i, l_i)), MRf(1,1)/cos(Rys(Ps_i, l_i)));
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
And the maximum bending of the flexible joints is: (in [mrad])
|
And the maximum bending of the flexible joints is: (in [mrad])
|
||||||
#+begin_src matlab :results replace value
|
#+begin_src matlab :results replace value
|
||||||
1e3*max(max(abs(flex_ang)))
|
1e3*max(max(abs(flex_ang)))
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
: 1.1704
|
: 1.1704
|
||||||
|
|
||||||
#+begin_src matlab :results replace value
|
#+begin_src matlab :results replace value
|
||||||
1e3*max(max(sqrt(Rxs.^2 + Rys.^2)))
|
1e3*max(max(sqrt(Rxs.^2 + Rys.^2)))
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
: 0.075063
|
: 0.075063
|
||||||
|
|
||||||
#+begin_src matlab :results replace value
|
#+begin_src matlab :results replace value
|
||||||
1e3*max(max(Rzs))
|
1e3*max(max(Rzs))
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -708,75 +708,75 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
|||||||
** Estimation using the Simscape Model
|
** Estimation using the Simscape Model
|
||||||
*** Model Init
|
*** Model Init
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
open('stewart_platform_model.slx')
|
open('stewart_platform_model.slx')
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
|
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground = initializeGround('type', 'rigid');
|
ground = initializeGround('type', 'rigid');
|
||||||
payload = initializePayload('type', 'none');
|
payload = initializePayload('type', 'none');
|
||||||
controller = initializeController('type', 'open-loop');
|
controller = initializeController('type', 'open-loop');
|
||||||
disturbances = initializeDisturbances();
|
disturbances = initializeDisturbances();
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Controller design to be close to the wanted displacement
|
*** Controller design to be close to the wanted displacement
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_model';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
||||||
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
|
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io);
|
||||||
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||||||
G.OutputName = {'L1', 'L2', 'L3', 'L4', 'L5', 'L6'};
|
G.OutputName = {'L1', 'L2', 'L3', 'L4', 'L5', 'L6'};
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
wc = 2*pi*30;
|
wc = 2*pi*30;
|
||||||
Kl = diag(1./diag(abs(freqresp(G, wc)))) * wc/s * 1/(1 + s/3/wc);
|
Kl = diag(1./diag(abs(freqresp(G, wc)))) * wc/s * 1/(1 + s/3/wc);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
controller = initializeController('type', 'ref-track-L');
|
controller = initializeController('type', 'ref-track-L');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Simulations
|
*** Simulations
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Tx_max = 60e-6; % Translation [m]
|
Tx_max = 60e-6; % Translation [m]
|
||||||
Ty_max = 60e-6; % Translation [m]
|
Ty_max = 60e-6; % Translation [m]
|
||||||
Tz_max = 60e-6; % Translation [m]
|
Tz_max = 60e-6; % Translation [m]
|
||||||
Rx_max = 30e-6; % Rotation [rad]
|
Rx_max = 30e-6; % Rotation [rad]
|
||||||
Ry_max = 30e-6; % Rotation [rad]
|
Ry_max = 30e-6; % Rotation [rad]
|
||||||
Rz_max = 0; % Rotation [rad]
|
Rz_max = 0; % Rotation [rad]
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Ps = [2*(dec2bin(0:5^2-1,5)-'0')-1, zeros(5^2, 1)].*[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
Ps = [2*(dec2bin(0:5^2-1,5)-'0')-1, zeros(5^2, 1)].*[Tx_max Ty_max Tz_max Rx_max Ry_max Rz_max];
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
cl_perf = zeros(size(Ps, 1), 1); % Closed loop performance [percentage]
|
cl_perf = zeros(size(Ps, 1), 1); % Closed loop performance [percentage]
|
||||||
Rs = zeros(size(Ps, 1), 5); % Max Flexor angles for the 6 legs [mrad]
|
Rs = zeros(size(Ps, 1), 5); % Max Flexor angles for the 6 legs [mrad]
|
||||||
|
|
||||||
for Ps_i = 1:size(Ps, 1)
|
for Ps_i = 1:size(Ps, 1)
|
||||||
fprintf('Experiment %i over %i', Ps_i, size(Ps, 1));
|
fprintf('Experiment %i over %i', Ps_i, size(Ps, 1));
|
||||||
|
|
||||||
references = initializeReferences(stewart, 't', 0, 'r', Ps(Ps_i, :)');
|
references = initializeReferences(stewart, 't', 0, 'r', Ps(Ps_i, :)');
|
||||||
@ -785,12 +785,12 @@ for Ps_i = 1:size(Ps, 1)
|
|||||||
|
|
||||||
cl_perf(Ps_i) = 100*max(abs((simout.y.dLm.Data(end, :) - references.rL.Data(:,1,1)')./simout.y.dLm.Data(end, :)));
|
cl_perf(Ps_i) = 100*max(abs((simout.y.dLm.Data(end, :) - references.rL.Data(:,1,1)')./simout.y.dLm.Data(end, :)));
|
||||||
Rs(Ps_i, :) = [max(abs(1e3*simout.y.Rf.Data(end, 1:2:end))), max(abs(1e3*simout.y.Rf.Data(end, 2:2:end))), max(abs(1e3*simout.y.Rm.Data(end, 1:3:end))), max(abs(1e3*simout.y.Rm.Data(end, 2:3:end))), max(abs(1e3*simout.y.Rm.Data(end, 3:3:end)))]';
|
Rs(Ps_i, :) = [max(abs(1e3*simout.y.Rf.Data(end, 1:2:end))), max(abs(1e3*simout.y.Rf.Data(end, 2:2:end))), max(abs(1e3*simout.y.Rm.Data(end, 1:3:end))), max(abs(1e3*simout.y.Rm.Data(end, 2:3:end))), max(abs(1e3*simout.y.Rm.Data(end, 3:3:end)))]';
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
Verify that the simulations are all correct:
|
Verify that the simulations are all correct:
|
||||||
#+begin_src matlab :results replace value
|
#+begin_src matlab :results replace value
|
||||||
max(cl_perf)
|
max(cl_perf)
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -798,7 +798,7 @@ max(cl_perf)
|
|||||||
|
|
||||||
*** Results
|
*** Results
|
||||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||||
data2orgtable(max(Rs)', {'Rx bot', 'Ry bot', 'Rx top', 'Ry top', 'Rz top'}, {'Stroke [mrad]'}, ' %.2f ');
|
data2orgtable(max(Rs)', {'Rx bot', 'Ry bot', 'Rx top', 'Ry top', 'Rz top'}, {'Stroke [mrad]'}, ' %.2f ');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
@ -826,22 +826,22 @@ This Matlab function is accessible [[file:../src/computeJacobian.m][here]].
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [stewart] = computeJacobian(stewart)
|
function [stewart] = computeJacobian(stewart)
|
||||||
% computeJacobian -
|
% computeJacobian -
|
||||||
%
|
%
|
||||||
% Syntax: [stewart] = computeJacobian(stewart)
|
% Syntax: [stewart] = computeJacobian(stewart)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - stewart - With at least the following fields:
|
% - stewart - With at least the following fields:
|
||||||
% - geometry.As [3x6] - The 6 unit vectors for each strut expressed in {A}
|
% - geometry.As [3x6] - The 6 unit vectors for each strut expressed in {A}
|
||||||
% - geometry.Ab [3x6] - The 6 position of the joints bi expressed in {A}
|
% - geometry.Ab [3x6] - The 6 position of the joints bi expressed in {A}
|
||||||
% - actuators.K [6x1] - Total stiffness of the actuators
|
% - actuators.K [6x1] - Total stiffness of the actuators
|
||||||
%
|
%
|
||||||
% Outputs:
|
% Outputs:
|
||||||
% - stewart - With the 3 added field:
|
% - stewart - With the 3 added field:
|
||||||
% - kinematics.J [6x6] - The Jacobian Matrix
|
% - kinematics.J [6x6] - The Jacobian Matrix
|
||||||
% - kinematics.K [6x6] - The Stiffness Matrix
|
% - kinematics.K [6x6] - The Stiffness Matrix
|
||||||
% - kinematics.C [6x6] - The Compliance Matrix
|
% - kinematics.C [6x6] - The Compliance Matrix
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Check the =stewart= structure elements
|
*** Check the =stewart= structure elements
|
||||||
@ -849,14 +849,14 @@ function [stewart] = computeJacobian(stewart)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
assert(isfield(stewart.geometry, 'As'), 'stewart.geometry should have attribute As')
|
assert(isfield(stewart.geometry, 'As'), 'stewart.geometry should have attribute As')
|
||||||
As = stewart.geometry.As;
|
As = stewart.geometry.As;
|
||||||
|
|
||||||
assert(isfield(stewart.geometry, 'Ab'), 'stewart.geometry should have attribute Ab')
|
assert(isfield(stewart.geometry, 'Ab'), 'stewart.geometry should have attribute Ab')
|
||||||
Ab = stewart.geometry.Ab;
|
Ab = stewart.geometry.Ab;
|
||||||
|
|
||||||
assert(isfield(stewart.actuators, 'K'), 'stewart.actuators should have attribute K')
|
assert(isfield(stewart.actuators, 'K'), 'stewart.actuators should have attribute K')
|
||||||
Ki = stewart.actuators.K;
|
Ki = stewart.actuators.K;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
|
|
||||||
@ -865,7 +865,7 @@ Ki = stewart.actuators.K;
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
J = [As' , cross(Ab, As)'];
|
J = [As' , cross(Ab, As)'];
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Compute Stiffness Matrix
|
*** Compute Stiffness Matrix
|
||||||
@ -873,7 +873,7 @@ J = [As' , cross(Ab, As)'];
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
K = J'*diag(Ki)*J;
|
K = J'*diag(Ki)*J;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Compute Compliance Matrix
|
*** Compute Compliance Matrix
|
||||||
@ -881,7 +881,7 @@ K = J'*diag(Ki)*J;
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
C = inv(K);
|
C = inv(K);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Populate the =stewart= structure
|
*** Populate the =stewart= structure
|
||||||
@ -889,9 +889,9 @@ C = inv(K);
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart.kinematics.J = J;
|
stewart.kinematics.J = J;
|
||||||
stewart.kinematics.K = K;
|
stewart.kinematics.K = K;
|
||||||
stewart.kinematics.C = C;
|
stewart.kinematics.C = C;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
|
|
||||||
@ -934,23 +934,23 @@ Otherwise, when the limbs' lengths derived yield complex numbers, then the posit
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [Li, dLi] = inverseKinematics(stewart, args)
|
function [Li, dLi] = inverseKinematics(stewart, args)
|
||||||
% inverseKinematics - Compute the needed length of each strut to have the wanted position and orientation of {B} with respect to {A}
|
% inverseKinematics - Compute the needed length of each strut to have the wanted position and orientation of {B} with respect to {A}
|
||||||
%
|
%
|
||||||
% Syntax: [stewart] = inverseKinematics(stewart)
|
% Syntax: [stewart] = inverseKinematics(stewart)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - stewart - A structure with the following fields
|
% - stewart - A structure with the following fields
|
||||||
% - geometry.Aa [3x6] - The positions ai expressed in {A}
|
% - geometry.Aa [3x6] - The positions ai expressed in {A}
|
||||||
% - geometry.Bb [3x6] - The positions bi expressed in {B}
|
% - geometry.Bb [3x6] - The positions bi expressed in {B}
|
||||||
% - geometry.l [6x1] - Length of each strut
|
% - geometry.l [6x1] - Length of each strut
|
||||||
% - args - Can have the following fields:
|
% - args - Can have the following fields:
|
||||||
% - AP [3x1] - The wanted position of {B} with respect to {A}
|
% - AP [3x1] - The wanted position of {B} with respect to {A}
|
||||||
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
|
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
|
||||||
%
|
%
|
||||||
% Outputs:
|
% Outputs:
|
||||||
% - Li [6x1] - The 6 needed length of the struts in [m] to have the wanted pose of {B} w.r.t. {A}
|
% - Li [6x1] - The 6 needed length of the struts in [m] to have the wanted pose of {B} w.r.t. {A}
|
||||||
% - dLi [6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}
|
% - dLi [6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Optional Parameters
|
*** Optional Parameters
|
||||||
@ -958,11 +958,11 @@ function [Li, dLi] = inverseKinematics(stewart, args)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
arguments
|
arguments
|
||||||
stewart
|
stewart
|
||||||
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||||
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Check the =stewart= structure elements
|
*** Check the =stewart= structure elements
|
||||||
@ -970,14 +970,14 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
assert(isfield(stewart.geometry, 'Aa'), 'stewart.geometry should have attribute Aa')
|
assert(isfield(stewart.geometry, 'Aa'), 'stewart.geometry should have attribute Aa')
|
||||||
Aa = stewart.geometry.Aa;
|
Aa = stewart.geometry.Aa;
|
||||||
|
|
||||||
assert(isfield(stewart.geometry, 'Bb'), 'stewart.geometry should have attribute Bb')
|
assert(isfield(stewart.geometry, 'Bb'), 'stewart.geometry should have attribute Bb')
|
||||||
Bb = stewart.geometry.Bb;
|
Bb = stewart.geometry.Bb;
|
||||||
|
|
||||||
assert(isfield(stewart.geometry, 'l'), 'stewart.geometry should have attribute l')
|
assert(isfield(stewart.geometry, 'l'), 'stewart.geometry should have attribute l')
|
||||||
l = stewart.geometry.l;
|
l = stewart.geometry.l;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
|
|
||||||
@ -986,11 +986,11 @@ l = stewart.geometry.l;
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Li = sqrt(args.AP'*args.AP + diag(Bb'*Bb) + diag(Aa'*Aa) - (2*args.AP'*Aa)' + (2*args.AP'*(args.ARB*Bb))' - diag(2*(args.ARB*Bb)'*Aa));
|
Li = sqrt(args.AP'*args.AP + diag(Bb'*Bb) + diag(Aa'*Aa) - (2*args.AP'*Aa)' + (2*args.AP'*(args.ARB*Bb))' - diag(2*(args.ARB*Bb)'*Aa));
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
dLi = Li-l;
|
dLi = Li-l;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** =forwardKinematicsApprox=: Compute the Approximate Forward Kinematics
|
** =forwardKinematicsApprox=: Compute the Approximate Forward Kinematics
|
||||||
@ -1007,21 +1007,21 @@ This Matlab function is accessible [[file:../src/forwardKinematicsApprox.m][here
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [P, R] = forwardKinematicsApprox(stewart, args)
|
function [P, R] = forwardKinematicsApprox(stewart, args)
|
||||||
% forwardKinematicsApprox - Computed the approximate pose of {B} with respect to {A} from the length of each strut and using
|
% forwardKinematicsApprox - Computed the approximate pose of {B} with respect to {A} from the length of each strut and using
|
||||||
% the Jacobian Matrix
|
% the Jacobian Matrix
|
||||||
%
|
%
|
||||||
% Syntax: [P, R] = forwardKinematicsApprox(stewart, args)
|
% Syntax: [P, R] = forwardKinematicsApprox(stewart, args)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - stewart - A structure with the following fields
|
% - stewart - A structure with the following fields
|
||||||
% - kinematics.J [6x6] - The Jacobian Matrix
|
% - kinematics.J [6x6] - The Jacobian Matrix
|
||||||
% - args - Can have the following fields:
|
% - args - Can have the following fields:
|
||||||
% - dL [6x1] - Displacement of each strut [m]
|
% - dL [6x1] - Displacement of each strut [m]
|
||||||
%
|
%
|
||||||
% Outputs:
|
% Outputs:
|
||||||
% - P [3x1] - The estimated position of {B} with respect to {A}
|
% - P [3x1] - The estimated position of {B} with respect to {A}
|
||||||
% - R [3x3] - The estimated rotation matrix that gives the orientation of {B} with respect to {A}
|
% - R [3x3] - The estimated rotation matrix that gives the orientation of {B} with respect to {A}
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Optional Parameters
|
*** Optional Parameters
|
||||||
@ -1029,10 +1029,10 @@ function [P, R] = forwardKinematicsApprox(stewart, args)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
arguments
|
arguments
|
||||||
stewart
|
stewart
|
||||||
args.dL (6,1) double {mustBeNumeric} = zeros(6,1)
|
args.dL (6,1) double {mustBeNumeric} = zeros(6,1)
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Check the =stewart= structure elements
|
*** Check the =stewart= structure elements
|
||||||
@ -1040,8 +1040,8 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
assert(isfield(stewart.kinematics, 'J'), 'stewart.kinematics should have attribute J')
|
assert(isfield(stewart.kinematics, 'J'), 'stewart.kinematics should have attribute J')
|
||||||
J = stewart.kinematics.J;
|
J = stewart.kinematics.J;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Computation
|
*** Computation
|
||||||
@ -1052,24 +1052,24 @@ From a small displacement of each strut $d\bm{\mathcal{L}}$, we can compute the
|
|||||||
position and orientation of {B} with respect to {A} using the following formula:
|
position and orientation of {B} with respect to {A} using the following formula:
|
||||||
\[ d \bm{\mathcal{X}} = \bm{J}^{-1} d\bm{\mathcal{L}} \]
|
\[ d \bm{\mathcal{X}} = \bm{J}^{-1} d\bm{\mathcal{L}} \]
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
X = J\args.dL;
|
X = J\args.dL;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
The position vector corresponds to the first 3 elements.
|
The position vector corresponds to the first 3 elements.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
P = X(1:3);
|
P = X(1:3);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
The next 3 elements are the orientation of {B} with respect to {A} expressed
|
The next 3 elements are the orientation of {B} with respect to {A} expressed
|
||||||
using the screw axis.
|
using the screw axis.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
theta = norm(X(4:6));
|
theta = norm(X(4:6));
|
||||||
s = X(4:6)/theta;
|
s = X(4:6)/theta;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
We then compute the corresponding rotation matrix.
|
We then compute the corresponding rotation matrix.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
R = [s(1)^2*(1-cos(theta)) + cos(theta) , s(1)*s(2)*(1-cos(theta)) - s(3)*sin(theta), s(1)*s(3)*(1-cos(theta)) + s(2)*sin(theta);
|
R = [s(1)^2*(1-cos(theta)) + cos(theta) , s(1)*s(2)*(1-cos(theta)) - s(3)*sin(theta), s(1)*s(3)*(1-cos(theta)) + s(2)*sin(theta);
|
||||||
s(2)*s(1)*(1-cos(theta)) + s(3)*sin(theta), s(2)^2*(1-cos(theta)) + cos(theta), s(2)*s(3)*(1-cos(theta)) - s(1)*sin(theta);
|
s(2)*s(1)*(1-cos(theta)) + s(3)*sin(theta), s(2)^2*(1-cos(theta)) + cos(theta), s(2)*s(3)*(1-cos(theta)) - s(1)*sin(theta);
|
||||||
s(3)*s(1)*(1-cos(theta)) - s(2)*sin(theta), s(3)*s(2)*(1-cos(theta)) + s(1)*sin(theta), s(3)^2*(1-cos(theta)) + cos(theta)];
|
s(3)*s(1)*(1-cos(theta)) - s(2)*sin(theta), s(3)*s(2)*(1-cos(theta)) + s(1)*sin(theta), s(3)^2*(1-cos(theta)) + cos(theta)];
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|||||||
40
org/nass.org
40
org/nass.org
@ -45,40 +45,40 @@
|
|||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
open('stewart_platform_model.slx')
|
open('stewart_platform_model.slx')
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Identification of the Dynamics
|
** Identification of the Dynamics
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
apa = load('./mat/APA300ML.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
|
apa = load('./mat/APA300ML.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
|
||||||
flex_joint = load('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
|
flex_joint = load('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
stewart = initializeStewartPlatform();
|
||||||
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 175e-3);
|
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 175e-3);
|
||||||
stewart = generateGeneralConfiguration(stewart, 'FH', 20e-3, 'MH', 20e-3, 'FR', 228e-3/2, 'MR', 220e-3/2, 'FTh', [-9, 9, 120-9, 120+9, 240-9, 240+9]*(pi/180), 'MTh', [-60+15, 60-15, 60+15, 180-15, 180+15, -60-15]*(pi/180));
|
stewart = generateGeneralConfiguration(stewart, 'FH', 20e-3, 'MH', 20e-3, 'FR', 228e-3/2, 'MR', 220e-3/2, 'FTh', [-9, 9, 120-9, 120+9, 240-9, 240+9]*(pi/180), 'MTh', [-60+15, 60-15, 60+15, 180-15, 180+15, -60-15]*(pi/180));
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeFlexibleStrutDynamics(stewart, 'H', 0.03, 'K', apa.K, 'M', apa.M, 'n_xyz', apa.n_xyz, 'xi', 0.1, 'step_file', 'mat/APA300ML.STEP');
|
stewart = initializeFlexibleStrutDynamics(stewart, 'H', 0.03, 'K', apa.K, 'M', apa.M, 'n_xyz', apa.n_xyz, 'xi', 0.1, 'step_file', 'mat/APA300ML.STEP');
|
||||||
stewart = initializeJointDynamics(stewart, 'type_F', 'flexible', 'K_F', flex_joint.K, 'M_F', flex_joint.M, 'n_xyz_F', flex_joint.n_xyz, 'xi_F', 0.1, 'step_file_F', 'mat/flexor_ID16.STEP', 'type_M', 'flexible', 'K_M', flex_joint.K, 'M_M', flex_joint.M, 'n_xyz_M', flex_joint.n_xyz, 'xi_M', 0.1, 'step_file_M', 'mat/flexor_ID16.STEP');
|
stewart = initializeJointDynamics(stewart, 'type_F', 'flexible', 'K_F', flex_joint.K, 'M_F', flex_joint.M, 'n_xyz_F', flex_joint.n_xyz, 'xi_F', 0.1, 'step_file_F', 'mat/flexor_ID16.STEP', 'type_M', 'flexible', 'K_M', flex_joint.K, 'M_M', flex_joint.M, 'n_xyz_M', flex_joint.n_xyz, 'xi_M', 0.1, 'step_file_M', 'mat/flexor_ID16.STEP');
|
||||||
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 150e-3, 'Mpr', 125e-3);
|
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 150e-3, 'Mpr', 125e-3);
|
||||||
stewart = initializeCylindricalStruts(stewart, 'type_F', 'none', 'type_M', 'none');
|
stewart = initializeCylindricalStruts(stewart, 'type_F', 'none', 'type_M', 'none');
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
stewart = initializeInertialSensor(stewart);
|
stewart = initializeInertialSensor(stewart);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground = initializeGround('type', 'none');
|
ground = initializeGround('type', 'none');
|
||||||
payload = initializePayload('type', 'rigid', 'm', 50);
|
payload = initializePayload('type', 'rigid', 'm', 50);
|
||||||
controller = initializeController('type', 'open-loop');
|
controller = initializeController('type', 'open-loop');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
disturbances = initializeDisturbances();
|
disturbances = initializeDisturbances();
|
||||||
references = initializeReferences(stewart);
|
references = initializeReferences(stewart);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|||||||
@ -65,12 +65,12 @@ This is done using something called "*Configuration Reference*" ([[https://fr.ma
|
|||||||
Basically, the configuration is stored in a mat file =conf_simscape.mat= and then loaded in the workspace for it to be accessible to all the simulink models.
|
Basically, the configuration is stored in a mat file =conf_simscape.mat= and then loaded in the workspace for it to be accessible to all the simulink models.
|
||||||
It is automatically loaded when the Simulink project is open. It can be loaded manually with the command:
|
It is automatically loaded when the Simulink project is open. It can be loaded manually with the command:
|
||||||
#+begin_src matlab :eval no
|
#+begin_src matlab :eval no
|
||||||
load('mat/conf_simscape.mat');
|
load('mat/conf_simscape.mat');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
It is however possible to modify specific parameters just for one simulation using the =set_param= command:
|
It is however possible to modify specific parameters just for one simulation using the =set_param= command:
|
||||||
#+begin_src matlab :eval no
|
#+begin_src matlab :eval no
|
||||||
set_param(conf_simscape, 'StopTime', 1);
|
set_param(conf_simscape, 'StopTime', 1);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
* Subsystem Reference
|
* Subsystem Reference
|
||||||
@ -158,29 +158,29 @@ This Matlab function is accessible [[file:../src/initializePayload.m][here]].
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [payload] = initializePayload(args)
|
function [payload] = initializePayload(args)
|
||||||
% initializePayload - Initialize the Payload that can then be used for simulations and analysis
|
% initializePayload - Initialize the Payload that can then be used for simulations and analysis
|
||||||
%
|
%
|
||||||
% Syntax: [payload] = initializePayload(args)
|
% Syntax: [payload] = initializePayload(args)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - args - Structure with the following fields:
|
% - args - Structure with the following fields:
|
||||||
% - type - 'none', 'rigid', 'flexible', 'cartesian'
|
% - type - 'none', 'rigid', 'flexible', 'cartesian'
|
||||||
% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]
|
% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]
|
||||||
% This also the position where K and C are defined
|
% This also the position where K and C are defined
|
||||||
% - K [6x1] - Stiffness of the Payload [N/m, N/rad]
|
% - K [6x1] - Stiffness of the Payload [N/m, N/rad]
|
||||||
% - C [6x1] - Damping of the Payload [N/(m/s), N/(rad/s)]
|
% - C [6x1] - Damping of the Payload [N/(m/s), N/(rad/s)]
|
||||||
% - m [1x1] - Mass of the Payload [kg]
|
% - m [1x1] - Mass of the Payload [kg]
|
||||||
% - I [3x3] - Inertia matrix for the Payload [kg*m2]
|
% - I [3x3] - Inertia matrix for the Payload [kg*m2]
|
||||||
%
|
%
|
||||||
% Outputs:
|
% Outputs:
|
||||||
% - payload - Struture with the following properties:
|
% - payload - Struture with the following properties:
|
||||||
% - type - 1 (none), 2 (rigid), 3 (flexible)
|
% - type - 1 (none), 2 (rigid), 3 (flexible)
|
||||||
% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]
|
% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]
|
||||||
% - K [6x1] - Stiffness of the Payload [N/m, N/rad]
|
% - K [6x1] - Stiffness of the Payload [N/m, N/rad]
|
||||||
% - C [6x1] - Stiffness of the Payload [N/(m/s), N/(rad/s)]
|
% - C [6x1] - Stiffness of the Payload [N/(m/s), N/(rad/s)]
|
||||||
% - m [1x1] - Mass of the Payload [kg]
|
% - m [1x1] - Mass of the Payload [kg]
|
||||||
% - I [3x3] - Inertia matrix for the Payload [kg*m2]
|
% - I [3x3] - Inertia matrix for the Payload [kg*m2]
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Optional Parameters
|
*** Optional Parameters
|
||||||
@ -188,14 +188,14 @@ function [payload] = initializePayload(args)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
arguments
|
arguments
|
||||||
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'cartesian'})} = 'none'
|
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'cartesian'})} = 'none'
|
||||||
args.K (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e8*ones(6,1)
|
args.K (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e8*ones(6,1)
|
||||||
args.C (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
|
args.C (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
|
||||||
args.h (1,1) double {mustBeNumeric, mustBeNonnegative} = 100e-3
|
args.h (1,1) double {mustBeNumeric, mustBeNonnegative} = 100e-3
|
||||||
args.m (1,1) double {mustBeNumeric, mustBeNonnegative} = 10
|
args.m (1,1) double {mustBeNumeric, mustBeNonnegative} = 10
|
||||||
args.I (3,3) double {mustBeNumeric, mustBeNonnegative} = 1*eye(3)
|
args.I (3,3) double {mustBeNumeric, mustBeNonnegative} = 1*eye(3)
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Add Payload Type
|
*** Add Payload Type
|
||||||
@ -203,7 +203,7 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
switch args.type
|
switch args.type
|
||||||
case 'none'
|
case 'none'
|
||||||
payload.type = 1;
|
payload.type = 1;
|
||||||
case 'rigid'
|
case 'rigid'
|
||||||
@ -212,7 +212,7 @@ switch args.type
|
|||||||
payload.type = 3;
|
payload.type = 3;
|
||||||
case 'cartesian'
|
case 'cartesian'
|
||||||
payload.type = 4;
|
payload.type = 4;
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Add Stiffness, Damping and Mass properties of the Payload
|
*** Add Stiffness, Damping and Mass properties of the Payload
|
||||||
@ -220,12 +220,12 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
payload.K = args.K;
|
payload.K = args.K;
|
||||||
payload.C = args.C;
|
payload.C = args.C;
|
||||||
payload.m = args.m;
|
payload.m = args.m;
|
||||||
payload.I = args.I;
|
payload.I = args.I;
|
||||||
|
|
||||||
payload.h = args.h;
|
payload.h = args.h;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Ground
|
** Ground
|
||||||
@ -242,23 +242,23 @@ This Matlab function is accessible [[file:../src/initializeGround.m][here]].
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [ground] = initializeGround(args)
|
function [ground] = initializeGround(args)
|
||||||
% initializeGround - Initialize the Ground that can then be used for simulations and analysis
|
% initializeGround - Initialize the Ground that can then be used for simulations and analysis
|
||||||
%
|
%
|
||||||
% Syntax: [ground] = initializeGround(args)
|
% Syntax: [ground] = initializeGround(args)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - args - Structure with the following fields:
|
% - args - Structure with the following fields:
|
||||||
% - type - 'none', 'solid', 'flexible'
|
% - type - 'none', 'solid', 'flexible'
|
||||||
% - rot_point [3x1] - Rotation point for the ground motion [m]
|
% - rot_point [3x1] - Rotation point for the ground motion [m]
|
||||||
% - K [3x1] - Translation Stiffness of the Ground [N/m]
|
% - K [3x1] - Translation Stiffness of the Ground [N/m]
|
||||||
% - C [3x1] - Translation Damping of the Ground [N/(m/s)]
|
% - C [3x1] - Translation Damping of the Ground [N/(m/s)]
|
||||||
%
|
%
|
||||||
% Outputs:
|
% Outputs:
|
||||||
% - ground - Struture with the following properties:
|
% - ground - Struture with the following properties:
|
||||||
% - type - 1 (none), 2 (rigid), 3 (flexible)
|
% - type - 1 (none), 2 (rigid), 3 (flexible)
|
||||||
% - K [3x1] - Translation Stiffness of the Ground [N/m]
|
% - K [3x1] - Translation Stiffness of the Ground [N/m]
|
||||||
% - C [3x1] - Translation Damping of the Ground [N/(m/s)]
|
% - C [3x1] - Translation Damping of the Ground [N/(m/s)]
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Optional Parameters
|
*** Optional Parameters
|
||||||
@ -266,12 +266,12 @@ function [ground] = initializeGround(args)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
arguments
|
arguments
|
||||||
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'none'
|
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'none'
|
||||||
args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1)
|
args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||||
args.K (3,1) double {mustBeNumeric, mustBeNonnegative} = 1e8*ones(3,1)
|
args.K (3,1) double {mustBeNumeric, mustBeNonnegative} = 1e8*ones(3,1)
|
||||||
args.C (3,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(3,1)
|
args.C (3,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(3,1)
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Add Ground Type
|
*** Add Ground Type
|
||||||
@ -279,14 +279,14 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
switch args.type
|
switch args.type
|
||||||
case 'none'
|
case 'none'
|
||||||
ground.type = 1;
|
ground.type = 1;
|
||||||
case 'rigid'
|
case 'rigid'
|
||||||
ground.type = 2;
|
ground.type = 2;
|
||||||
case 'flexible'
|
case 'flexible'
|
||||||
ground.type = 3;
|
ground.type = 3;
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Add Stiffness and Damping properties of the Ground
|
*** Add Stiffness and Damping properties of the Ground
|
||||||
@ -294,8 +294,8 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground.K = args.K;
|
ground.K = args.K;
|
||||||
ground.C = args.C;
|
ground.C = args.C;
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
*** Rotation Point
|
*** Rotation Point
|
||||||
@ -303,7 +303,7 @@ ground.C = args.C;
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
ground.rot_point = args.rot_point;
|
ground.rot_point = args.rot_point;
|
||||||
#+end_src
|
#+end_src
|
||||||
* Initialize Disturbances
|
* Initialize Disturbances
|
||||||
:PROPERTIES:
|
:PROPERTIES:
|
||||||
@ -318,13 +318,13 @@ ground.rot_point = args.rot_point;
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [disturbances] = initializeDisturbances(args)
|
function [disturbances] = initializeDisturbances(args)
|
||||||
% initializeDisturbances - Initialize the disturbances
|
% initializeDisturbances - Initialize the disturbances
|
||||||
%
|
%
|
||||||
% Syntax: [disturbances] = initializeDisturbances(args)
|
% Syntax: [disturbances] = initializeDisturbances(args)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - args -
|
% - args -
|
||||||
|
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
@ -333,12 +333,12 @@ function [disturbances] = initializeDisturbances(args)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
arguments
|
arguments
|
||||||
args.Fd double {mustBeNumeric, mustBeReal} = zeros(6,1)
|
args.Fd double {mustBeNumeric, mustBeReal} = zeros(6,1)
|
||||||
args.Fd_t double {mustBeNumeric, mustBeReal} = 0
|
args.Fd_t double {mustBeNumeric, mustBeReal} = 0
|
||||||
args.Dw double {mustBeNumeric, mustBeReal} = zeros(6,1)
|
args.Dw double {mustBeNumeric, mustBeReal} = zeros(6,1)
|
||||||
args.Dw_t double {mustBeNumeric, mustBeReal} = 0
|
args.Dw_t double {mustBeNumeric, mustBeReal} = 0
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
|
|
||||||
@ -347,7 +347,7 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
disturbances = struct();
|
disturbances = struct();
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Ground Motion
|
** Ground Motion
|
||||||
@ -355,7 +355,7 @@ disturbances = struct();
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
disturbances.Dw = timeseries([args.Dw], args.Dw_t);
|
disturbances.Dw = timeseries([args.Dw], args.Dw_t);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Direct Forces
|
** Direct Forces
|
||||||
@ -363,7 +363,7 @@ disturbances.Dw = timeseries([args.Dw], args.Dw_t);
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
disturbances.Fd = timeseries([args.Fd], args.Fd_t);
|
disturbances.Fd = timeseries([args.Fd], args.Fd_t);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
* Initialize References
|
* Initialize References
|
||||||
@ -379,13 +379,13 @@ disturbances.Fd = timeseries([args.Fd], args.Fd_t);
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
function [references] = initializeReferences(stewart, args)
|
function [references] = initializeReferences(stewart, args)
|
||||||
% initializeReferences - Initialize the references
|
% initializeReferences - Initialize the references
|
||||||
%
|
%
|
||||||
% Syntax: [references] = initializeReferences(args)
|
% Syntax: [references] = initializeReferences(args)
|
||||||
%
|
%
|
||||||
% Inputs:
|
% Inputs:
|
||||||
% - args -
|
% - args -
|
||||||
|
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
@ -394,18 +394,18 @@ function [references] = initializeReferences(stewart, args)
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
arguments
|
arguments
|
||||||
stewart
|
stewart
|
||||||
args.t double {mustBeNumeric, mustBeReal} = 0
|
args.t double {mustBeNumeric, mustBeReal} = 0
|
||||||
args.r double {mustBeNumeric, mustBeReal} = zeros(6, 1)
|
args.r double {mustBeNumeric, mustBeReal} = zeros(6, 1)
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Compute the corresponding strut length
|
** Compute the corresponding strut length
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
rL = zeros(6, length(args.t));
|
rL = zeros(6, length(args.t));
|
||||||
|
|
||||||
for i = 1:length(args.t)
|
for i = 1:length(args.t)
|
||||||
R = [cos(args.r(6,i)) -sin(args.r(6,i)) 0;
|
R = [cos(args.r(6,i)) -sin(args.r(6,i)) 0;
|
||||||
sin(args.r(6,i)) cos(args.r(6,i)) 0;
|
sin(args.r(6,i)) cos(args.r(6,i)) 0;
|
||||||
0 0 1] * ...
|
0 0 1] * ...
|
||||||
@ -418,7 +418,7 @@ for i = 1:length(args.t)
|
|||||||
|
|
||||||
[Li, dLi] = inverseKinematics(stewart, 'AP', [args.r(1,i); args.r(2,i); args.r(3,i)], 'ARB', R);
|
[Li, dLi] = inverseKinematics(stewart, 'AP', [args.r(1,i); args.r(2,i); args.r(3,i)], 'ARB', R);
|
||||||
rL(:, i) = dLi;
|
rL(:, i) = dLi;
|
||||||
end
|
end
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** References
|
** References
|
||||||
@ -426,6 +426,6 @@ end
|
|||||||
:UNNUMBERED: t
|
:UNNUMBERED: t
|
||||||
:END:
|
:END:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
references.r = timeseries(args.r, args.t);
|
references.r = timeseries(args.r, args.t);
|
||||||
references.rL = timeseries(rL, args.t);
|
references.rL = timeseries(rL, args.t);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|||||||
@ -49,30 +49,30 @@ From the [[https://mathworks.com/products/simulink/projects.html][Simulink proje
|
|||||||
The project can be opened using the =simulinkproject= function:
|
The project can be opened using the =simulinkproject= function:
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
When the project opens, a startup script is ran.
|
When the project opens, a startup script is ran.
|
||||||
The startup script is defined below and is exported to the =project_startup.m= script.
|
The startup script is defined below and is exported to the =project_startup.m= script.
|
||||||
#+begin_src matlab :eval no :tangle ../src/project_startup.m
|
#+begin_src matlab :eval no :tangle ../src/project_startup.m
|
||||||
project = simulinkproject;
|
project = simulinkproject;
|
||||||
projectRoot = project.RootFolder;
|
projectRoot = project.RootFolder;
|
||||||
|
|
||||||
myCacheFolder = fullfile(projectRoot, '.SimulinkCache');
|
myCacheFolder = fullfile(projectRoot, '.SimulinkCache');
|
||||||
myCodeFolder = fullfile(projectRoot, '.SimulinkCode');
|
myCodeFolder = fullfile(projectRoot, '.SimulinkCode');
|
||||||
|
|
||||||
Simulink.fileGenControl('set',...
|
Simulink.fileGenControl('set',...
|
||||||
'CacheFolder', myCacheFolder,...
|
'CacheFolder', myCacheFolder,...
|
||||||
'CodeGenFolder', myCodeFolder,...
|
'CodeGenFolder', myCodeFolder,...
|
||||||
'createDir', true);
|
'createDir', true);
|
||||||
|
|
||||||
%% Load the Simscape Configuration
|
%% Load the Simscape Configuration
|
||||||
load('mat/conf_simscape.mat');
|
load('mat/conf_simscape.mat');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
When the project closes, it runs the =project_shutdown.m= script defined below.
|
When the project closes, it runs the =project_shutdown.m= script defined below.
|
||||||
#+begin_src matlab :eval no :tangle ../src/project_shutdown.m
|
#+begin_src matlab :eval no :tangle ../src/project_shutdown.m
|
||||||
Simulink.fileGenControl('reset');
|
Simulink.fileGenControl('reset');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
The project also permits to automatically add defined folder to the path when the project is opened.
|
The project also permits to automatically add defined folder to the path when the project is opened.
|
||||||
|
|||||||
@ -38,7 +38,7 @@
|
|||||||
What causes the coupling from $F_i$ to $X_i$ ?
|
What causes the coupling from $F_i$ to $X_i$ ?
|
||||||
|
|
||||||
#+begin_src latex :file coupling.pdf
|
#+begin_src latex :file coupling.pdf
|
||||||
\begin{tikzpicture}
|
\begin{tikzpicture}
|
||||||
\node[block] (Jt) at (0, 0) {$J^{-T}$};
|
\node[block] (Jt) at (0, 0) {$J^{-T}$};
|
||||||
\node[block, right= of Jt] (G) {$G$};
|
\node[block, right= of Jt] (G) {$G$};
|
||||||
\node[block, right= of G] (J) {$J^{-1}$};
|
\node[block, right= of G] (J) {$J^{-1}$};
|
||||||
@ -47,7 +47,7 @@ What causes the coupling from $F_i$ to $X_i$ ?
|
|||||||
\draw[->] (Jt.east) -- (G.west) node[above left]{$\tau_i$};
|
\draw[->] (Jt.east) -- (G.west) node[above left]{$\tau_i$};
|
||||||
\draw[->] (G.east) -- (J.west) node[above left]{$q_i$};
|
\draw[->] (G.east) -- (J.west) node[above left]{$q_i$};
|
||||||
\draw[->] (J.east) -- ++(0.8, 0) node[above left]{$X_i$};
|
\draw[->] (J.east) -- ++(0.8, 0) node[above left]{$X_i$};
|
||||||
\end{tikzpicture}
|
\end{tikzpicture}
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+name: fig:block_diag_coupling
|
#+name: fig:block_diag_coupling
|
||||||
|
|||||||
File diff suppressed because it is too large
Load Diff
Loading…
Reference in New Issue
Block a user