Change all indentation
This commit is contained in:
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:30 -->
|
||||
<!-- 2021-01-08 ven. 15:53 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Stewart Platform - Decentralized Active Damping</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -42,25 +42,25 @@
|
||||
<li><a href="#orgddaf52f">1. Inertial Control</a>
|
||||
<ul>
|
||||
<li><a href="#org933440d">1.1. Identification of the Dynamics</a></li>
|
||||
<li><a href="#orged6d23c">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
|
||||
<li><a href="#org533c409">1.3. Obtained Damping</a></li>
|
||||
<li><a href="#orgc76021e">1.4. Conclusion</a></li>
|
||||
<li><a href="#org2875dd1">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
|
||||
<li><a href="#org0cea759">1.3. Obtained Damping</a></li>
|
||||
<li><a href="#orga866100">1.4. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgf8ed544">2. Integral Force Feedback</a>
|
||||
<ul>
|
||||
<li><a href="#org7b81fe5">2.1. Identification of the Dynamics with perfect Joints</a></li>
|
||||
<li><a href="#org3dca396">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
|
||||
<li><a href="#org7044ed4">2.3. Obtained Damping</a></li>
|
||||
<li><a href="#org9c769b9">2.4. Conclusion</a></li>
|
||||
<li><a href="#orga2d019b">2.1. Identification of the Dynamics with perfect Joints</a></li>
|
||||
<li><a href="#org6ac04ee">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
|
||||
<li><a href="#org06e1086">2.3. Obtained Damping</a></li>
|
||||
<li><a href="#orgfa832d6">2.4. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgabec4e1">3. Direct Velocity Feedback</a>
|
||||
<ul>
|
||||
<li><a href="#orga2d019b">3.1. Identification of the Dynamics with perfect Joints</a></li>
|
||||
<li><a href="#org2875dd1">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
|
||||
<li><a href="#org0cea759">3.3. Obtained Damping</a></li>
|
||||
<li><a href="#orga866100">3.4. Conclusion</a></li>
|
||||
<li><a href="#org19cbcee">3.1. Identification of the Dynamics with perfect Joints</a></li>
|
||||
<li><a href="#org0fabf01">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
|
||||
<li><a href="#org6c74c9a">3.3. Obtained Damping</a></li>
|
||||
<li><a href="#org81b2156">3.4. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgc7e2089">4. Compliance and Transmissibility Comparison</a>
|
||||
@@ -90,7 +90,7 @@ The following decentralized active damping techniques are briefly studied:
|
||||
<a id="org709d56c"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="org8a14d8c">
|
||||
<div class="note" id="org1ae7526">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_inertial.m">here</a>.
|
||||
</p>
|
||||
@@ -106,44 +106,44 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
|
||||
<h3 id="org933440d"><span class="section-number-3">1.1</span> Identification of the Dynamics</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(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);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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);
|
||||
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>);
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -159,17 +159,17 @@ The transfer function from actuator forces to force sensors is shown in Figure <
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orged6d23c" class="outline-3">
|
||||
<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 id="outline-container-org2875dd1" class="outline-3">
|
||||
<h3 id="org2875dd1"><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">
|
||||
<p>
|
||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||
</p>
|
||||
<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>);
|
||||
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.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 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.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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -177,10 +177,10 @@ We add some stiffness and damping in the flexible joints and we re-identify the
|
||||
We now use the amplified actuators and re-identify the dynamics
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
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.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 class="src src-matlab">stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -196,8 +196,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org533c409" class="outline-3">
|
||||
<h3 id="org533c409"><span class="section-number-3">1.3</span> Obtained Damping</h3>
|
||||
<div id="outline-container-org0cea759" class="outline-3">
|
||||
<h3 id="org0cea759"><span class="section-number-3">1.3</span> Obtained Damping</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
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 id="outline-container-orgc76021e" class="outline-3">
|
||||
<h3 id="orgc76021e"><span class="section-number-3">1.4</span> Conclusion</h3>
|
||||
<div id="outline-container-orga866100" class="outline-3">
|
||||
<h3 id="orga866100"><span class="section-number-3">1.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
<div class="important" id="org37b8ef0">
|
||||
<div class="important" id="org91c21ee">
|
||||
<p>
|
||||
We do not have guaranteed stability with Inertial control. This is because of the flexibility inside the internal sensor.
|
||||
</p>
|
||||
@@ -242,7 +242,7 @@ We do not have guaranteed stability with Inertial control. This is because of th
|
||||
<a id="org1f0d316"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="org54cec4b">
|
||||
<div class="note" id="org30f755d">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_iff.m">here</a>.
|
||||
</p>
|
||||
@@ -254,31 +254,31 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7b81fe5" class="outline-3">
|
||||
<h3 id="org7b81fe5"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||
<div id="outline-container-orga2d019b" class="outline-3">
|
||||
<h3 id="orga2d019b"><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">
|
||||
<p>
|
||||
We first initialize the Stewart platform without joint stiffness.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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);
|
||||
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>);
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -286,18 +286,18 @@ We first initialize the Stewart platform without joint stiffness.
|
||||
And we identify the dynamics from force actuators to force sensors.
|
||||
</p>
|
||||
<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>
|
||||
mdl = <span class="org-string">'stewart_platform_model'</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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -313,17 +313,17 @@ The transfer function from actuator forces to force sensors is shown in Figure <
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3dca396" class="outline-3">
|
||||
<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 id="outline-container-org6ac04ee" 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>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||
</p>
|
||||
<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>);
|
||||
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.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 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.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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -331,10 +331,10 @@ We add some stiffness and damping in the flexible joints and we re-identify the
|
||||
We now use the amplified actuators and re-identify the dynamics
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
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.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 class="src src-matlab">stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -350,8 +350,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7044ed4" class="outline-3">
|
||||
<h3 id="org7044ed4"><span class="section-number-3">2.3</span> Obtained Damping</h3>
|
||||
<div id="outline-container-org06e1086" class="outline-3">
|
||||
<h3 id="org06e1086"><span class="section-number-3">2.3</span> Obtained Damping</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
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 id="outline-container-org9c769b9" class="outline-3">
|
||||
<h3 id="org9c769b9"><span class="section-number-3">2.4</span> Conclusion</h3>
|
||||
<div id="outline-container-orgfa832d6" class="outline-3">
|
||||
<h3 id="orgfa832d6"><span class="section-number-3">2.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<div class="important" id="orged36719">
|
||||
<div class="important" id="orgad0c17b">
|
||||
<p>
|
||||
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.
|
||||
@@ -404,7 +404,7 @@ Thus, if Integral Force Feedback is to be used in a Stewart platform with flexib
|
||||
<a id="org63027d0"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="orgfb739d8">
|
||||
<div class="note" id="orgadea9d6">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_dvf.m">here</a>.
|
||||
</p>
|
||||
@@ -416,31 +416,31 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga2d019b" class="outline-3">
|
||||
<h3 id="orga2d019b"><span class="section-number-3">3.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||
<div id="outline-container-org19cbcee" class="outline-3">
|
||||
<h3 id="org19cbcee"><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">
|
||||
<p>
|
||||
We first initialize the Stewart platform without joint stiffness.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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);
|
||||
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>);
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -448,22 +448,22 @@ We first initialize the Stewart platform without joint stiffness.
|
||||
And we identify the dynamics from force actuators to force sensors.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -480,17 +480,17 @@ The transfer function from actuator forces to relative motion sensors is shown i
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org2875dd1" class="outline-3">
|
||||
<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 id="outline-container-org0fabf01" 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>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||
</p>
|
||||
<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>);
|
||||
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.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 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.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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -498,10 +498,10 @@ We add some stiffness and damping in the flexible joints and we re-identify the
|
||||
We now use the amplified actuators and re-identify the dynamics
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
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.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 class="src src-matlab">stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -517,8 +517,8 @@ The new dynamics from force actuator to relative motion sensor is shown in Figur
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0cea759" class="outline-3">
|
||||
<h3 id="org0cea759"><span class="section-number-3">3.3</span> Obtained Damping</h3>
|
||||
<div id="outline-container-org6c74c9a" class="outline-3">
|
||||
<h3 id="org6c74c9a"><span class="section-number-3">3.3</span> Obtained Damping</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
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 id="outline-container-orga866100" class="outline-3">
|
||||
<h3 id="orga866100"><span class="section-number-3">3.4</span> Conclusion</h3>
|
||||
<div id="outline-container-org81b2156" class="outline-3">
|
||||
<h3 id="org81b2156"><span class="section-number-3">3.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<div class="important" id="org2640d3c">
|
||||
<div class="important" id="orgb486ca9">
|
||||
<p>
|
||||
Joint stiffness does increase the resonance frequencies of the system but does not change the attainable damping when using relative motion sensors.
|
||||
</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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -585,9 +585,9 @@ We first initialize the Stewart platform without joint stiffness.
|
||||
The rotation point of the ground is located at the origin of frame \(\{A\}\).
|
||||
</p>
|
||||
<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);
|
||||
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>);
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -600,9 +600,9 @@ The rotation point of the ground is located at the origin of frame \(\{A\}\).
|
||||
Let’s first identify the transmissibility and compliance in the open-loop case.
|
||||
</p>
|
||||
<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>);
|
||||
[T_ol, T_norm_ol, freqs] = computeTransmissibility();
|
||||
[C_ol, C_norm_ol, freqs] = computeCompliance();
|
||||
<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();
|
||||
[C_ol, C_norm_ol, freqs] = computeCompliance();
|
||||
</pre>
|
||||
</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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
<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);
|
||||
|
||||
[T_iff, T_norm_iff, <span class="org-type">~</span>] = computeTransmissibility();
|
||||
[C_iff, C_norm_iff, <span class="org-type">~</span>] = computeCompliance();
|
||||
[T_iff, T_norm_iff, <span class="org-type">~</span>] = computeTransmissibility();
|
||||
[C_iff, C_norm_iff, <span class="org-type">~</span>] = computeCompliance();
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -622,11 +622,11 @@ Now, let’s identify the transmissibility and compliance for the Integral F
|
||||
And for the Direct Velocity Feedback.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
<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);
|
||||
|
||||
[T_dvf, T_norm_dvf, <span class="org-type">~</span>] = computeTransmissibility();
|
||||
[C_dvf, C_norm_dvf, <span class="org-type">~</span>] = computeCompliance();
|
||||
[T_dvf, T_norm_dvf, <span class="org-type">~</span>] = computeTransmissibility();
|
||||
[C_dvf, C_norm_dvf, <span class="org-type">~</span>] = computeCompliance();
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -661,7 +661,7 @@ And for the Direct Velocity Feedback.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:53</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:30 -->
|
||||
<!-- 2021-01-08 ven. 15:52 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Cubic configuration for the Stewart Platform</title>
|
||||
<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="#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="#org4e88cdb">1.5. Conclusion</a></li>
|
||||
<li><a href="#orgeb8ae82">1.5. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org312b7d4">2. Configuration with the Cube’s center above the mobile platform</a>
|
||||
<ul>
|
||||
<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="#org561a2bc">2.3. Conclusion</a></li>
|
||||
<li><a href="#org52825e8">2.3. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org2387b96">3. Cubic size analysis</a>
|
||||
<ul>
|
||||
<li><a href="#org3647f9f">3.1. Analysis</a></li>
|
||||
<li><a href="#org948a425">3.2. Conclusion</a></li>
|
||||
<li><a href="#org701701b">3.2. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org174af3a">4. Dynamic Coupling in the Cartesian Frame</a>
|
||||
<ul>
|
||||
<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="#org7d50eae">4.3. Conclusion</a></li>
|
||||
<li><a href="#orgf407e4d">4.3. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org7831cff">5. Dynamic Coupling between actuators and sensors of each strut</a>
|
||||
<ul>
|
||||
<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="#orgeb8ae82">5.3. Conclusion</a></li>
|
||||
<li><a href="#org0348380">5.3. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org3ce1c89">6. Functions</a>
|
||||
@@ -128,7 +128,7 @@ In this document, the cubic architecture is analyzed:
|
||||
<a id="org6bc5f56"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="org6a03293">
|
||||
<div class="note" id="org783c5d6">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_stiffnessl.m">here</a>.
|
||||
</p>
|
||||
@@ -182,21 +182,21 @@ The Jacobian matrix is estimated at the location of the center of the cube.
|
||||
</p>
|
||||
|
||||
<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>
|
||||
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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||
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);
|
||||
<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 = 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 = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||
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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -291,21 +291,21 @@ The Jacobian matrix is not estimated at the location of the center of the cube.
|
||||
</p>
|
||||
|
||||
<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>
|
||||
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>
|
||||
FOc = H<span class="org-type">/</span>2; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||
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);
|
||||
<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 = 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 = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||
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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -400,21 +400,21 @@ The Jacobian is estimated at the cube center.
|
||||
</p>
|
||||
|
||||
<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>
|
||||
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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||
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);
|
||||
<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 = 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 = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||
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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -520,21 +520,21 @@ The center of the cube from the top platform is at \(z = 110 - 175 = -65\).
|
||||
</p>
|
||||
|
||||
<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>
|
||||
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>
|
||||
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 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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||
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);
|
||||
<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 = 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 = initializeStrutDynamics(stewart, <span class="org-string">'K'</span>, ones(6,1));
|
||||
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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -620,10 +620,10 @@ The center of the cube from the top platform is at \(z = 110 - 175 = -65\).
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4e88cdb" class="outline-3">
|
||||
<h3 id="org4e88cdb"><span class="section-number-3">1.5</span> Conclusion</h3>
|
||||
<div id="outline-container-orgeb8ae82" class="outline-3">
|
||||
<h3 id="orgeb8ae82"><span class="section-number-3">1.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-1-5">
|
||||
<div class="important" id="org2fc62c4">
|
||||
<div class="important" id="orgb449c4a">
|
||||
<p>
|
||||
Here are the conclusion about the Stiffness matrix for the Cubic configuration:
|
||||
</p>
|
||||
@@ -644,7 +644,7 @@ Here are the conclusion about the Stiffness matrix for the Cubic configuration:
|
||||
<a id="org419cdb0"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="orgd5c0d4d">
|
||||
<div class="note" id="orge405fbc">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_above_platforml.m">here</a>.
|
||||
</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 \(\{B\}\):
|
||||
</p>
|
||||
<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>
|
||||
MO_B = 20e<span class="org-type">-</span>3; <span class="org-comment">% Position {B} with respect to {M} [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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -697,8 +697,8 @@ However, the rotational stiffnesses are increasing with the cube’s size bu
|
||||
</p>
|
||||
|
||||
<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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -783,8 +783,8 @@ However, the rotational stiffnesses are increasing with the cube’s size bu
|
||||
</table>
|
||||
|
||||
<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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -870,8 +870,8 @@ However, the rotational stiffnesses are increasing with the cube’s size bu
|
||||
</table>
|
||||
|
||||
<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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1049,10 +1049,10 @@ For a small cube:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org561a2bc" class="outline-3">
|
||||
<h3 id="org561a2bc"><span class="section-number-3">2.3</span> Conclusion</h3>
|
||||
<div id="outline-container-org52825e8" class="outline-3">
|
||||
<h3 id="org52825e8"><span class="section-number-3">2.3</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<div class="important" id="orga24e443">
|
||||
<div class="important" id="orgc3fb4db">
|
||||
<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.
|
||||
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>
|
||||
</p>
|
||||
|
||||
<div class="note" id="orgfd32e5a">
|
||||
<div class="note" id="org6ff8a60">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_size_analysisl.m">here</a>.
|
||||
</p>
|
||||
@@ -1132,8 +1132,8 @@ We only vary the size of the cube.
|
||||
We initialize the wanted cube’s size.
|
||||
</p>
|
||||
<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>
|
||||
Ks = zeros(6, 6, length(Hcs));
|
||||
<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));
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1141,7 +1141,7 @@ We initialize the wanted cube’s size.
|
||||
The height of the Stewart platform is fixed:
|
||||
</p>
|
||||
<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>
|
||||
</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:
|
||||
</p>
|
||||
<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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1168,14 +1168,14 @@ We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varyi
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org948a425" class="outline-3">
|
||||
<h3 id="org948a425"><span class="section-number-3">3.2</span> Conclusion</h3>
|
||||
<div id="outline-container-org701701b" class="outline-3">
|
||||
<h3 id="org701701b"><span class="section-number-3">3.2</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size.
|
||||
</p>
|
||||
|
||||
<div class="important" id="org60cc507">
|
||||
<div class="important" id="org93b8347">
|
||||
<p>
|
||||
In order to maximize the rotational stiffness of the Stewart platform, the size of the cube should be the highest possible.
|
||||
</p>
|
||||
@@ -1192,7 +1192,7 @@ In order to maximize the rotational stiffness of the Stewart platform, the size
|
||||
<a id="org3507b2b"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="org5934a9c">
|
||||
<div class="note" id="org265afc7">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_coupling_cartesianl.m">here</a>.
|
||||
</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 \(\{B\}\).
|
||||
</p>
|
||||
<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>
|
||||
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 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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1265,20 +1265,20 @@ We define the size of the Stewart platform and the position of frames \(\{A\}\)
|
||||
Now, we set the cube’s parameters such that the center of the cube is coincident with \(\{A\}\) and \(\{B\}\).
|
||||
</p>
|
||||
<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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
<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 = 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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1286,10 +1286,10 @@ Now, we set the cube’s parameters such that the center of the cube is coin
|
||||
Now we set the geometry and mass of the mobile platform such that its center of mass is coincident with \(\{A\}\) and \(\{B\}\).
|
||||
</p>
|
||||
<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)), ...
|
||||
<span class="org-string">'Mpm'</span>, 10, ...
|
||||
<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)));
|
||||
<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">'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)));
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -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.
|
||||
</p>
|
||||
<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);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1306,9 +1306,9 @@ And we set small mass for the struts.
|
||||
No flexibility below the Stewart platform and no payload.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</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 \(d \bm{\mathcal{L}}\).
|
||||
</p>
|
||||
<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>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -1352,10 +1352,10 @@ We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to
|
||||
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>
|
||||
<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>);
|
||||
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.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 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.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>};
|
||||
</pre>
|
||||
</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>
|
||||
</div>
|
||||
|
||||
<div class="important" id="org489ed3b">
|
||||
<div class="important" id="orgd31482e">
|
||||
<p>
|
||||
The dynamics is well decoupled at all frequencies.
|
||||
</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.
|
||||
</p>
|
||||
<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>
|
||||
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 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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1422,20 +1422,20 @@ Let’s create a Stewart platform with a cubic architecture where the cube&r
|
||||
Now, we set the cube’s parameters such that the center of the cube is coincident with \(\{A\}\) and \(\{B\}\).
|
||||
</p>
|
||||
<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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
<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 = 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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1443,10 +1443,10 @@ Now, we set the cube’s parameters such that the center of the cube is coin
|
||||
However, the Center of Mass of the mobile platform is <b>not</b> located at the cube’s center.
|
||||
</p>
|
||||
<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)), ...
|
||||
<span class="org-string">'Mpm'</span>, 10, ...
|
||||
<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)));
|
||||
<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">'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)));
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -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.
|
||||
</p>
|
||||
<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);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1463,9 +1463,9 @@ And we set small mass for the struts.
|
||||
No flexibility below the Stewart platform and no payload.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</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 \(d \bm{\mathcal{L}}\).
|
||||
</p>
|
||||
<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>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -1508,9 +1508,9 @@ We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to
|
||||
And we use the Jacobian to compute the transfer function from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\).
|
||||
</p>
|
||||
<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>);
|
||||
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>};
|
||||
<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.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>
|
||||
</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>
|
||||
</div>
|
||||
|
||||
<div class="important" id="org798e5c6">
|
||||
<div class="important" id="orgc60cb20">
|
||||
<p>
|
||||
The system is decoupled at low frequency (the Stiffness matrix being diagonal), but it is <b>not</b> decoupled at all frequencies.
|
||||
</p>
|
||||
@@ -1538,10 +1538,10 @@ This was expected as the mass matrix is not diagonal (the Center of Mass of the
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7d50eae" class="outline-3">
|
||||
<h3 id="org7d50eae"><span class="section-number-3">4.3</span> Conclusion</h3>
|
||||
<div id="outline-container-orgf407e4d" class="outline-3">
|
||||
<h3 id="orgf407e4d"><span class="section-number-3">4.3</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
<div class="important" id="org9b1be89">
|
||||
<div class="important" id="org982344b">
|
||||
<p>
|
||||
Some conclusions can be drawn from the above analysis:
|
||||
</p>
|
||||
@@ -1562,7 +1562,7 @@ Some conclusions can be drawn from the above analysis:
|
||||
<a id="org7b3ed31"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="org7a9b096">
|
||||
<div class="note" id="org96fba24">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/cubic_conf_coupling_strutsl.m">here</a>.
|
||||
</p>
|
||||
@@ -1593,28 +1593,28 @@ Let’s generate a Cubic architecture where the cube’s center and the
|
||||
</p>
|
||||
|
||||
<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>
|
||||
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>
|
||||
FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Center of the cube with respect to {F}</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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = 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 = computeJacobian(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)), ...
|
||||
<span class="org-string">'Mpm'</span>, 10, ...
|
||||
<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)));
|
||||
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);
|
||||
<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 = 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 = 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 = computeJacobian(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)), ...
|
||||
<span class="org-string">'Mpm'</span>, 10, ...
|
||||
<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)));
|
||||
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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1622,15 +1622,15 @@ Let’s generate a Cubic architecture where the cube’s center and the
|
||||
No flexibility below the Stewart platform and no payload.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1669,26 +1669,26 @@ Now we generate a Stewart platform which is not cubic but with approximately the
|
||||
</p>
|
||||
|
||||
<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>
|
||||
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 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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = 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 = computeJacobian(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)), ...
|
||||
<span class="org-string">'Mpm'</span>, 10, ...
|
||||
<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)));
|
||||
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);
|
||||
<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 = 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 = 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 = computeJacobian(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)), ...
|
||||
<span class="org-string">'Mpm'</span>, 10, ...
|
||||
<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)));
|
||||
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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1696,9 +1696,9 @@ Now we generate a Stewart platform which is not cubic but with approximately the
|
||||
No flexibility below the Stewart platform and no payload.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1729,10 +1729,10 @@ And we identify the dynamics from the actuator forces \(\tau_{i}\) to the relati
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgeb8ae82" class="outline-3">
|
||||
<h3 id="orgeb8ae82"><span class="section-number-3">5.3</span> Conclusion</h3>
|
||||
<div id="outline-container-org0348380" class="outline-3">
|
||||
<h3 id="org0348380"><span class="section-number-3">5.3</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-5-3">
|
||||
<div class="important" id="org74729c6">
|
||||
<div class="important" id="orgd92f0ac">
|
||||
<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.
|
||||
</p>
|
||||
@@ -1766,24 +1766,24 @@ This Matlab function is accessible <a href="../src/generateCubicConfiguration.m"
|
||||
<h4 id="org2cafc68">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org2cafc68">
|
||||
<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>)
|
||||
<span class="org-comment">% generateCubicConfiguration - Generate a Cubic Configuration</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Syntax: [stewart] = generateCubicConfiguration(stewart, args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - 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">% - 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">% - 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">% Outputs:</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_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}</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">%</span>
|
||||
<span class="org-comment">% Syntax: [stewart] = generateCubicConfiguration(stewart, args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - 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">% - 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">% - 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">% Outputs:</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_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1805,13 +1805,13 @@ This Matlab function is accessible <a href="../src/generateCubicConfiguration.m"
|
||||
<h4 id="org4fd2c96">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-org4fd2c96">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-keyword">arguments</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>.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>.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e<span class="org-type">-</span>3
|
||||
<span class="org-keyword">end</span>
|
||||
<pre class="src src-matlab"><span class="org-keyword">arguments</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>.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>.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e<span class="org-type">-</span>3
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</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>
|
||||
<div class="outline-text-4" id="text-orgac26a8b">
|
||||
<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>)
|
||||
H = stewart.geometry.H;
|
||||
<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;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1837,18 +1837,18 @@ We define the useful points of the cube with respect to the Cube’s center.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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];
|
||||
sz = [ 1; 1; 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];
|
||||
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>
|
||||
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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1861,7 +1861,7 @@ We define the useful points of the cube with respect to the Cube’s center.
|
||||
We can compute the vector of each leg \({}^{C}\hat{\bm{s}}_{i}\) (unit vector from \({}^{C}C_{f}\) to \({}^{C}C_{m}\)).
|
||||
</p>
|
||||
<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>
|
||||
</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 \(b_{i}\).
|
||||
</p>
|
||||
<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;
|
||||
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 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;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1880,8 +1880,8 @@ We now which to compute the position of the joints \(a_{i}\) and \(b_{i}\).
|
||||
<h4 id="org153763b">Populate the <code>stewart</code> structure</h4>
|
||||
<div class="outline-text-4" id="text-org153763b">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart.platform_F.Fa = Fa;
|
||||
stewart.platform_M.Mb = Mb;
|
||||
<pre class="src src-matlab">stewart.platform_F.Fa = Fa;
|
||||
stewart.platform_M.Mb = Mb;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1905,7 +1905,7 @@ We now which to compute the position of the joints \(a_{i}\) and \(b_{i}\).
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:30 -->
|
||||
<!-- 2021-01-08 ven. 15:52 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Stewart Platform - Dynamics Study</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -43,13 +43,13 @@
|
||||
<ul>
|
||||
<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="#org53765b8">1.3. Conclusion</a></li>
|
||||
<li><a href="#orga9eb2fd">1.3. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgb6a1ef7">2. Comparison of the static transfer function and the Compliance matrix</a>
|
||||
<ul>
|
||||
<li><a href="#org3f1c253">2.1. Analysis</a></li>
|
||||
<li><a href="#orga9eb2fd">2.2. Conclusion</a></li>
|
||||
<li><a href="#orge261263">2.2. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
</pre>
|
||||
</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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -100,22 +100,22 @@ We also don’t put any payload on top of the Stewart platform.
|
||||
The transfer function from actuator forces \(\bm{\tau}\) to the relative displacement of the mobile platform \(\mathcal{\bm{X}}\) is extracted.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -123,8 +123,8 @@ The transfer function from actuator forces \(\bm{\tau}\) to the relative displac
|
||||
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>
|
||||
<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>));
|
||||
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 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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -132,15 +132,15 @@ Using the Jacobian matrix, we compute the transfer function from force/torques 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>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</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.
|
||||
</p>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -183,28 +183,28 @@ We now add a flexible support under the Stewart platform.
|
||||
And we perform again the identification.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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.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 = 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>};
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -235,10 +235,10 @@ And thus \(\mathcal{F}_{x}\) and \(\mathcal{F}_{x,\text{ext}}\) have clearly <b>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org53765b8" class="outline-3">
|
||||
<h3 id="org53765b8"><span class="section-number-3">1.3</span> Conclusion</h3>
|
||||
<div id="outline-container-orga9eb2fd" class="outline-3">
|
||||
<h3 id="orga9eb2fd"><span class="section-number-3">1.3</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<div class="important" id="org35e4b5f">
|
||||
<div class="important" id="org4878fef">
|
||||
<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.
|
||||
</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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -281,9 +281,9 @@ Initialization of the Stewart platform.
|
||||
No flexibility below the Stewart platform and no payload.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -291,28 +291,28 @@ No flexibility below the Stewart platform and no payload.
|
||||
Estimation of the transfer function from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\):
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
<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>));
|
||||
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 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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -470,10 +470,10 @@ And now at the Compliance matrix.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga9eb2fd" class="outline-3">
|
||||
<h3 id="orga9eb2fd"><span class="section-number-3">2.2</span> Conclusion</h3>
|
||||
<div id="outline-container-orge261263" class="outline-3">
|
||||
<h3 id="orge261263"><span class="section-number-3">2.2</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<div class="important" id="orgcecc007">
|
||||
<div class="important" id="org2428297">
|
||||
<p>
|
||||
The low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\) corresponds to the compliance matrix of the Stewart platform.
|
||||
</p>
|
||||
@@ -485,7 +485,7 @@ The low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathc
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:29 -->
|
||||
<!-- 2021-01-08 ven. 15:52 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Stewart Platform with Flexible Elements</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -24,48 +24,48 @@
|
||||
<ul>
|
||||
<li><a href="#orgc309c7b">1. Simscape Model</a>
|
||||
<ul>
|
||||
<li><a href="#orgae23ac5">1.1. Flexible APA</a></li>
|
||||
<li><a href="#org0e00e94">1.1. Flexible APA</a></li>
|
||||
<li><a href="#orgf337fe9">1.2. Flexible Joint</a></li>
|
||||
<li><a href="#orga8d83ce">1.3. Identification</a></li>
|
||||
<li><a href="#orgc239ed1">1.3. Identification</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="#org0e00e94">1.6. Flexible APA</a></li>
|
||||
<li><a href="#org4cccff6">1.6. Flexible 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="#org1e66228">1.9. Direct Velocity 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="#org52c4099">1.12. Conclusion</a></li>
|
||||
<li><a href="#org55fe34f">1.12. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org2d65f84">2. Control with flexible elements</a>
|
||||
<ul>
|
||||
<li><a href="#org7f0d75c">2.1. Flexible APA and Flexible Joint</a></li>
|
||||
<li><a href="#orgc239ed1">2.2. Identification</a></li>
|
||||
<li><a href="#org5f84aea">2.2. Identification</a></li>
|
||||
<li><a href="#org5ae25be">2.3. Decentralized Direct Velocity Feedback</a></li>
|
||||
<li><a href="#org3d014d0">2.4. HAC</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org2b937bc">3. Flexible Joint Specifications</a>
|
||||
<ul>
|
||||
<li><a href="#org166293c">3.1. Stewart Platform Initialization</a></li>
|
||||
<li><a href="#org775a387">3.1. Stewart Platform Initialization</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="#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="#orgd67ef9e">3.6. Comparison of perfect joint and worst specified joint</a></li>
|
||||
<li><a href="#org55fe34f">3.7. Conclusion</a></li>
|
||||
<li><a href="#orge0f8240">3.6. Comparison of perfect joint and worst specified joint</a></li>
|
||||
<li><a href="#org79b6e2d">3.7. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org8798d60">4. Flexible Joint Specifications with the APA300ML</a>
|
||||
<ul>
|
||||
<li><a href="#org6fc554b">4.1. Stewart Platform Initialization</a></li>
|
||||
<li><a href="#orge0f8240">4.2. Comparison of perfect joint and worst specified joint</a></li>
|
||||
<li><a href="#org6d56b33">4.1. Stewart Platform Initialization</a></li>
|
||||
<li><a href="#orgdc3d576">4.2. Comparison of perfect joint and worst specified joint</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgbae1ad3">5. Relative Motion Sensors</a>
|
||||
<ul>
|
||||
<li><a href="#org775a387">5.1. Stewart Platform Initialization</a></li>
|
||||
<li><a href="#org74f7ec9">5.1. Stewart Platform Initialization</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<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>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
</div>
|
||||
<div id="outline-container-orgae23ac5" class="outline-3">
|
||||
<h3 id="orgae23ac5"><span class="section-number-3">1.1</span> Flexible APA</h3>
|
||||
<div id="outline-container-org0e00e94" class="outline-3">
|
||||
<h3 id="org0e00e94"><span class="section-number-3">1.1</span> Flexible APA</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -209,7 +209,7 @@
|
||||
<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="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>
|
||||
</div>
|
||||
|
||||
@@ -325,37 +325,37 @@
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga8d83ce" class="outline-3">
|
||||
<h3 id="orga8d83ce"><span class="section-number-3">1.3</span> Identification</h3>
|
||||
<div id="outline-container-orgc239ed1" class="outline-3">
|
||||
<h3 id="orgc239ed1"><span class="section-number-3">1.3</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
And we identify the dynamics from force actuators to force sensors.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -365,36 +365,36 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
<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="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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">'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">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<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">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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">'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">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<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">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
|
||||
references = initializeReferences(stewart);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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.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>};
|
||||
<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.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>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -411,32 +411,32 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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 = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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 = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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.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>};
|
||||
<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.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>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0e00e94" class="outline-3">
|
||||
<h3 id="org0e00e94"><span class="section-number-3">1.6</span> Flexible APA</h3>
|
||||
<div id="outline-container-org4cccff6" class="outline-3">
|
||||
<h3 id="org4cccff6"><span class="section-number-3">1.6</span> Flexible APA</h3>
|
||||
<div class="outline-text-3" id="text-1-6">
|
||||
|
||||
<div id="org6abb282" class="figure">
|
||||
@@ -446,34 +446,34 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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">'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">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<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">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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">'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">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<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">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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.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>};
|
||||
<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.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>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -490,24 +490,24 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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 = 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 = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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 = 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 = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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.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 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.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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -517,7 +517,7 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
<h3 id="orga39e477"><span class="section-number-3">1.8</span> Save</h3>
|
||||
<div class="outline-text-3" id="text-1-8">
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -566,10 +566,10 @@ In order to model a flexible element with only few mass-spring-damper elements:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org52c4099" class="outline-3">
|
||||
<h3 id="org52c4099"><span class="section-number-3">1.12</span> Conclusion</h3>
|
||||
<div id="outline-container-org55fe34f" class="outline-3">
|
||||
<h3 id="org55fe34f"><span class="section-number-3">1.12</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-1-12">
|
||||
<div class="important" id="org7acf160">
|
||||
<div class="important" id="orgba069e0">
|
||||
<p>
|
||||
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.
|
||||
@@ -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>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<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>);
|
||||
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 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>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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 = 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 = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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 = 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 = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc239ed1" class="outline-3">
|
||||
<h3 id="orgc239ed1"><span class="section-number-3">2.2</span> Identification</h3>
|
||||
<div id="outline-container-org5f84aea" class="outline-3">
|
||||
<h3 id="org5f84aea"><span class="section-number-3">2.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
And we identify the dynamics from force actuators to force sensors.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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.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 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.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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -660,12 +660,12 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
Controller Design
|
||||
</p>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -679,37 +679,37 @@ Controller Design
|
||||
<h3 id="org3d014d0"><span class="section-number-3">2.4</span> HAC</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
mdl = <span class="org-string">'stewart_platform_model'</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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
<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;
|
||||
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 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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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;
|
||||
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 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);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -720,39 +720,39 @@ Controller Design
|
||||
<h2 id="org2b937bc"><span class="section-number-2">3</span> Flexible Joint Specifications</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
</div>
|
||||
<div id="outline-container-org166293c" class="outline-3">
|
||||
<h3 id="org166293c"><span class="section-number-3">3.1</span> Stewart Platform Initialization</h3>
|
||||
<div id="outline-container-org775a387" class="outline-3">
|
||||
<h3 id="org775a387"><span class="section-number-3">3.1</span> Stewart Platform Initialization</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
|
||||
references = initializeReferences(stewart);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -762,7 +762,7 @@ Controller Design
|
||||
<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="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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -772,7 +772,7 @@ Controller Design
|
||||
<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="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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -782,7 +782,7 @@ Controller Design
|
||||
<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="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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -792,17 +792,17 @@ Controller Design
|
||||
<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="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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd67ef9e" class="outline-3">
|
||||
<h3 id="orgd67ef9e"><span class="section-number-3">3.6</span> Comparison of perfect joint and worst specified joint</h3>
|
||||
<div id="outline-container-orge0f8240" class="outline-3">
|
||||
<h3 id="orge0f8240"><span class="section-number-3">3.6</span> Comparison of perfect joint and worst specified joint</h3>
|
||||
</div>
|
||||
<div id="outline-container-org55fe34f" class="outline-3">
|
||||
<h3 id="org55fe34f"><span class="section-number-3">3.7</span> Conclusion</h3>
|
||||
<div id="outline-container-org79b6e2d" class="outline-3">
|
||||
<h3 id="org79b6e2d"><span class="section-number-3">3.7</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-7">
|
||||
<p>
|
||||
Qualitatively:
|
||||
@@ -891,118 +891,118 @@ Quantitatively:
|
||||
<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>
|
||||
<div id="outline-container-org6fc554b" class="outline-3">
|
||||
<h3 id="org6fc554b"><span class="section-number-3">4.1</span> Stewart Platform Initialization</h3>
|
||||
<div id="outline-container-org6d56b33" class="outline-3">
|
||||
<h3 id="org6d56b33"><span class="section-number-3">4.1</span> Stewart Platform Initialization</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
|
||||
references = initializeReferences(stewart);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge0f8240" class="outline-3">
|
||||
<h3 id="orge0f8240"><span class="section-number-3">4.2</span> Comparison of perfect joint and worst specified joint</h3>
|
||||
<div id="outline-container-orgdc3d576" class="outline-3">
|
||||
<h3 id="orgdc3d576"><span class="section-number-3">4.2</span> Comparison of perfect joint and worst specified joint</h3>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgbae1ad3" class="outline-2">
|
||||
<h2 id="orgbae1ad3"><span class="section-number-2">5</span> Relative Motion Sensors</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
</div>
|
||||
<div id="outline-container-org775a387" class="outline-3">
|
||||
<h3 id="org775a387"><span class="section-number-3">5.1</span> Stewart Platform Initialization</h3>
|
||||
<div id="outline-container-org74f7ec9" class="outline-3">
|
||||
<h3 id="org74f7ec9"><span class="section-number-3">5.1</span> Stewart Platform Initialization</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>);
|
||||
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>
|
||||
<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));
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<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>);
|
||||
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">'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">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<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">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
<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>, ...
|
||||
<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">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<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">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeCylindricalPlatforms(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeCylindricalPlatforms(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeCylindricalStruts(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeCylindricalStruts(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
|
||||
references = initializeReferences(stewart);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1017,7 +1017,7 @@ Quantitatively:
|
||||
<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="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>
|
||||
</div>
|
||||
|
||||
@@ -1148,60 +1148,60 @@ Quantitatively:
|
||||
<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="org-src-container">
|
||||
<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 = 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));
|
||||
stewart = computeJointsPose(stewart);
|
||||
<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 = 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));
|
||||
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)), ...
|
||||
<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 = 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">'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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
references = initializeReferences(stewart);
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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.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">'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 class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1216,7 +1216,7 @@ Quantitatively:
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:29</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:29 -->
|
||||
<!-- 2021-01-08 ven. 15:52 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Identification of the Stewart Platform using Simscape</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -50,13 +50,13 @@
|
||||
</li>
|
||||
<li><a href="#orgfeed9a3">2. Transmissibility Analysis</a>
|
||||
<ul>
|
||||
<li><a href="#org7c6996a">2.1. Initialize the Stewart platform</a></li>
|
||||
<li><a href="#org5ba3096">2.1. Initialize the Stewart platform</a></li>
|
||||
<li><a href="#org279dcc8">2.2. Transmissibility</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org3ad92e9">3. Compliance Analysis</a>
|
||||
<ul>
|
||||
<li><a href="#org5ba3096">3.1. Initialize the Stewart platform</a></li>
|
||||
<li><a href="#orgc957431">3.1. Initialize the Stewart platform</a></li>
|
||||
<li><a href="#org26cb46a">3.2. Compliance</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
@@ -64,18 +64,18 @@
|
||||
<ul>
|
||||
<li><a href="#org25ca725">4.1. Compute the Transmissibility</a>
|
||||
<ul>
|
||||
<li><a href="#orgeae7abf">Function description</a></li>
|
||||
<li><a href="#orge4c0895">Optional Parameters</a></li>
|
||||
<li><a href="#orgafb57d0">Function description</a></li>
|
||||
<li><a href="#orga00af61">Optional Parameters</a></li>
|
||||
<li><a href="#org17a8811">Identification of the Transmissibility Matrix</a></li>
|
||||
<li><a href="#orgfd96322">Computation of the Frobenius norm</a></li>
|
||||
<li><a href="#orgbc9a383">Computation of the Frobenius norm</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgb6e05b3">4.2. Compute the Compliance</a>
|
||||
<ul>
|
||||
<li><a href="#orgafb57d0">Function description</a></li>
|
||||
<li><a href="#orga00af61">Optional Parameters</a></li>
|
||||
<li><a href="#org210c0ca">Function description</a></li>
|
||||
<li><a href="#org24feeb1">Optional Parameters</a></li>
|
||||
<li><a href="#org2c35042">Identification of the Compliance Matrix</a></li>
|
||||
<li><a href="#orgbc9a383">Computation of the Frobenius norm</a></li>
|
||||
<li><a href="#orgb002200">Computation of the Frobenius norm</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</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>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -132,23 +132,23 @@ In this document, we discuss the various methods to identify the behavior of the
|
||||
<h3 id="orgd9529ee"><span class="section-number-3">1.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io);
|
||||
<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-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io);
|
||||
<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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -156,7 +156,7 @@ In this document, we discuss the various methods to identify the behavior of the
|
||||
Let’s check the size of <code>G</code>:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> size(G)
|
||||
<pre class="src src-matlab">size(G)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -173,7 +173,7 @@ ans =
|
||||
We expect to have only 12 states (corresponding to the 6dof of the mobile platform).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Gm = minreal(G);
|
||||
<pre class="src src-matlab">Gm = minreal(G);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -196,7 +196,7 @@ And indeed, we obtain 12 states.
|
||||
We can perform the following transformation using the <code>ss2ss</code> command.
|
||||
</p>
|
||||
<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>
|
||||
</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:
|
||||
</p>
|
||||
<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);
|
||||
Dt = zeros(12, 6);
|
||||
Ct = eye(12);
|
||||
Dt = zeros(12, 6);
|
||||
|
||||
Gt = ss(At, Bt, Ct, Dt);
|
||||
Gt = ss(At, Bt, Ct, Dt);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -229,7 +229,7 @@ We could perform the transformation by hand:
|
||||
<h3 id="org11e3698"><span class="section-number-3">1.4</span> Analysis</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
<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>
|
||||
</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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ws = imag(diag(D));
|
||||
[ws,I] = sort(ws)
|
||||
ws = ws(7<span class="org-type">:</span>end); I = I(7<span class="org-type">:</span>end);
|
||||
<pre class="src src-matlab">ws = imag(diag(D));
|
||||
[ws,I] = sort(ws)
|
||||
ws = ws(7<span class="org-type">:</span>end); I = I(7<span class="org-type">:</span>end);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> lambda_i = D(i_mode, i_mode);
|
||||
xi_i = V(<span class="org-type">:</span>,i_mode);
|
||||
<pre class="src src-matlab">lambda_i = D(i_mode, i_mode);
|
||||
xi_i = V(<span class="org-type">:</span>,i_mode);
|
||||
|
||||
a_i = real(lambda_i);
|
||||
b_i = imag(lambda_i);
|
||||
a_i = real(lambda_i);
|
||||
b_i = imag(lambda_i);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -335,13 +335,13 @@ Let’s first sort the modes and just take the modes corresponding to a eige
|
||||
Let do 10 periods of the mode.
|
||||
</p>
|
||||
<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);
|
||||
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 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)));
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -349,9 +349,9 @@ Let do 10 periods of the mode.
|
||||
Simulation:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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">sim</span>(mdl);
|
||||
<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">sim</span>(mdl);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -359,15 +359,15 @@ Simulation:
|
||||
Save the movie of the mode shape.
|
||||
</p>
|
||||
<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>), ...
|
||||
<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">'FrameSize'</span>, [800, 400]);
|
||||
<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">'FrameRate'</span>, 30, ...
|
||||
<span class="org-string">'FrameSize'</span>, [800, 400]);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -402,21 +402,21 @@ Save the movie of the mode shape.
|
||||
<a id="org5213401"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org7c6996a" class="outline-3">
|
||||
<h3 id="org7c6996a"><span class="section-number-3">2.1</span> Initialize the Stewart platform</h3>
|
||||
<div id="outline-container-org5ba3096" class="outline-3">
|
||||
<h3 id="org5ba3096"><span class="section-number-3">2.1</span> Initialize the Stewart platform</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(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);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -424,9 +424,9 @@ Save the movie of the mode shape.
|
||||
We set the rotation point of the ground to be at the same point at frames \(\{A\}\) and \(\{B\}\).
|
||||
</p>
|
||||
<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);
|
||||
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>);
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -436,45 +436,45 @@ We set the rotation point of the ground to be at the same point at frames \(\{A\
|
||||
<h3 id="org279dcc8"><span class="section-number-3">2.2</span> Transmissibility</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
<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-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</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">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);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(T(ix, iy), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</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>);
|
||||
ylim([1e<span class="org-type">-</span>5, 10]);
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
<span class="org-keyword">if</span> ix <span class="org-type"><</span> 6
|
||||
xticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">if</span> iy <span class="org-type">></span> 1
|
||||
yticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
subplot(6, 6, (ix<span class="org-type">-</span>1)<span class="org-type">*</span>6 <span class="org-type">+</span> iy);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(T(ix, iy), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</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>);
|
||||
ylim([1e<span class="org-type">-</span>5, 10]);
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
<span class="org-keyword">if</span> ix <span class="org-type"><</span> 6
|
||||
xticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">if</span> iy <span class="org-type">></span> 1
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -487,13 +487,13 @@ From (<a href="#citeproc_bib_item_1">Preumont et al. 2007</a>), one can use the
|
||||
\end{align*}
|
||||
|
||||
<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>));
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -503,14 +503,14 @@ And we normalize by a factor \(\sqrt{6}\) to obtain a performance metric compara
|
||||
</p>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-type">figure</span>;
|
||||
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>);
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
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>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -524,21 +524,21 @@ And we normalize by a factor \(\sqrt{6}\) to obtain a performance metric compara
|
||||
<a id="org39baa25"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org5ba3096" class="outline-3">
|
||||
<h3 id="org5ba3096"><span class="section-number-3">3.1</span> Initialize the Stewart platform</h3>
|
||||
<div id="outline-container-orgc957431" class="outline-3">
|
||||
<h3 id="orgc957431"><span class="section-number-3">3.1</span> Initialize the Stewart platform</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(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);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -546,9 +546,9 @@ And we normalize by a factor \(\sqrt{6}\) to obtain a performance metric compara
|
||||
We set the rotation point of the ground to be at the same point at frames \(\{A\}\) and \(\{B\}\).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -558,45 +558,45 @@ We set the rotation point of the ground to be at the same point at frames \(\{A\
|
||||
<h3 id="org26cb46a"><span class="section-number-3">3.2</span> Compliance</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
<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-keyword">for</span> <span class="org-variable-name">ix</span> = <span class="org-constant">1:6</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">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);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(C(ix, iy), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</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>);
|
||||
ylim([1e<span class="org-type">-</span>10, 1e<span class="org-type">-</span>3]);
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
<span class="org-keyword">if</span> ix <span class="org-type"><</span> 6
|
||||
xticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">if</span> iy <span class="org-type">></span> 1
|
||||
yticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
subplot(6, 6, (ix<span class="org-type">-</span>1)<span class="org-type">*</span>6 <span class="org-type">+</span> iy);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(C(ix, iy), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</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>);
|
||||
ylim([1e<span class="org-type">-</span>10, 1e<span class="org-type">-</span>3]);
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
<span class="org-keyword">if</span> ix <span class="org-type"><</span> 6
|
||||
xticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">if</span> iy <span class="org-type">></span> 1
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -605,20 +605,20 @@ We can try to use the Frobenius norm to obtain a scalar value representing the 6
|
||||
</p>
|
||||
|
||||
<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>));
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-type">figure</span>;
|
||||
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>);
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
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>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -637,42 +637,42 @@ We can try to use the Frobenius norm to obtain a scalar value representing the 6
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgeae7abf" class="outline-4">
|
||||
<h4 id="orgeae7abf">Function description</h4>
|
||||
<div class="outline-text-4" id="text-orgeae7abf">
|
||||
<div id="outline-container-orgafb57d0" class="outline-4">
|
||||
<h4 id="orgafb57d0">Function description</h4>
|
||||
<div class="outline-text-4" id="text-orgafb57d0">
|
||||
<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>)
|
||||
<span class="org-comment">% computeTransmissibility -</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Syntax: [T, T_norm, freqs] = computeTransmissibility(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - freqs [] - Frequency vector to estimate the Frobenius norm</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Outputs:</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">% - freqs [length(freqs)x1] - Frequency vector in [Hz]</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">%</span>
|
||||
<span class="org-comment">% Syntax: [T, T_norm, freqs] = computeTransmissibility(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - freqs [] - Frequency vector to estimate the Frobenius norm</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Outputs:</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">% - freqs [length(freqs)x1] - Frequency vector in [Hz]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge4c0895" class="outline-4">
|
||||
<h4 id="orge4c0895">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orge4c0895">
|
||||
<div id="outline-container-orga00af61" class="outline-4">
|
||||
<h4 id="orga00af61">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orga00af61">
|
||||
<div class="org-src-container">
|
||||
<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>.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
||||
<span class="org-keyword">end</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>.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> freqs = args.freqs;
|
||||
<pre class="src src-matlab">freqs = args.freqs;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -682,22 +682,22 @@ We can try to use the Frobenius norm to obtain a scalar value representing the 6
|
||||
<h4 id="org17a8811">Identification of the Transmissibility Matrix</h4>
|
||||
<div class="outline-text-4" id="text-org17a8811">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -705,23 +705,23 @@ We can try to use the Frobenius norm to obtain a scalar value representing the 6
|
||||
If wanted, the 6x6 transmissibility matrix is plotted.
|
||||
</p>
|
||||
<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>;
|
||||
<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>
|
||||
p_handle((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;
|
||||
plot(freqs, abs(squeeze(freqresp(T(ix, iy), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</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>);
|
||||
<span class="org-keyword">if</span> ix <span class="org-type"><</span> 6
|
||||
xticklabels({});
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
||||
p_handle((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;
|
||||
plot(freqs, abs(squeeze(freqresp(T(ix, iy), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</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>);
|
||||
<span class="org-keyword">if</span> ix <span class="org-type"><</span> 6
|
||||
xticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">if</span> iy <span class="org-type">></span> 1
|
||||
yticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">if</span> iy <span class="org-type">></span> 1
|
||||
yticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
|
||||
linkaxes(p_handle, <span class="org-string">'xy'</span>)
|
||||
@@ -733,37 +733,37 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
||||
han.YLabel.Visible = <span class="org-string">'on'</span>;
|
||||
xlabel(han, <span class="org-string">'Frequency [Hz]'</span>);
|
||||
ylabel(han, <span class="org-string">'Transmissibility [m/m]'</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfd96322" class="outline-4">
|
||||
<h4 id="orgfd96322">Computation of the Frobenius norm</h4>
|
||||
<div class="outline-text-4" id="text-orgfd96322">
|
||||
<div id="outline-container-orgbc9a383" class="outline-4">
|
||||
<h4 id="orgbc9a383">Computation of the Frobenius norm</h4>
|
||||
<div class="outline-text-4" id="text-orgbc9a383">
|
||||
<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>));
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<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>;
|
||||
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>);
|
||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>);
|
||||
ylabel(<span class="org-string">'Transmissibility - Frobenius Norm'</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -778,42 +778,42 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgafb57d0" class="outline-4">
|
||||
<h4 id="orgafb57d0">Function description</h4>
|
||||
<div class="outline-text-4" id="text-orgafb57d0">
|
||||
<div id="outline-container-org210c0ca" class="outline-4">
|
||||
<h4 id="org210c0ca">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org210c0ca">
|
||||
<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>)
|
||||
<span class="org-comment">% computeCompliance -</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Syntax: [C, C_norm, freqs] = computeCompliance(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - freqs [] - Frequency vector to estimate the Frobenius norm</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Outputs:</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">% - freqs [length(freqs)x1] - Frequency vector in [Hz]</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">%</span>
|
||||
<span class="org-comment">% Syntax: [C, C_norm, freqs] = computeCompliance(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - freqs [] - Frequency vector to estimate the Frobenius norm</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Outputs:</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">% - freqs [length(freqs)x1] - Frequency vector in [Hz]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga00af61" class="outline-4">
|
||||
<h4 id="orga00af61">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orga00af61">
|
||||
<div id="outline-container-org24feeb1" class="outline-4">
|
||||
<h4 id="org24feeb1">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-org24feeb1">
|
||||
<div class="org-src-container">
|
||||
<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>.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
||||
<span class="org-keyword">end</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>.freqs double {mustBeNumeric, mustBeNonnegative} = logspace(1,4,1000)
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> freqs = args.freqs;
|
||||
<pre class="src src-matlab">freqs = args.freqs;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -823,22 +823,22 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
||||
<h4 id="org2c35042">Identification of the Compliance Matrix</h4>
|
||||
<div class="outline-text-4" id="text-org2c35042">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
@@ -846,23 +846,23 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
||||
If wanted, the 6x6 transmissibility matrix is plotted.
|
||||
</p>
|
||||
<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>;
|
||||
<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>
|
||||
p_handle((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;
|
||||
plot(freqs, abs(squeeze(freqresp(C(ix, iy), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</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>);
|
||||
<span class="org-keyword">if</span> ix <span class="org-type"><</span> 6
|
||||
xticklabels({});
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name">iy</span> = <span class="org-constant">1:6</span>
|
||||
p_handle((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;
|
||||
plot(freqs, abs(squeeze(freqresp(C(ix, iy), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</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>);
|
||||
<span class="org-keyword">if</span> ix <span class="org-type"><</span> 6
|
||||
xticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">if</span> iy <span class="org-type">></span> 1
|
||||
yticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">if</span> iy <span class="org-type">></span> 1
|
||||
yticklabels({});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
|
||||
linkaxes(p_handle, <span class="org-string">'xy'</span>)
|
||||
@@ -873,34 +873,34 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
||||
han.YLabel.Visible = <span class="org-string">'on'</span>;
|
||||
xlabel(han, <span class="org-string">'Frequency [Hz]'</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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbc9a383" class="outline-4">
|
||||
<h4 id="orgbc9a383">Computation of the Frobenius norm</h4>
|
||||
<div class="outline-text-4" id="text-orgbc9a383">
|
||||
<div id="outline-container-orgb002200" class="outline-4">
|
||||
<h4 id="orgb002200">Computation of the Frobenius norm</h4>
|
||||
<div class="outline-text-4" id="text-orgb002200">
|
||||
<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>));
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>;
|
||||
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>);
|
||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>);
|
||||
ylabel(<span class="org-string">'Compliance - Frobenius Norm'</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -915,7 +915,7 @@ If wanted, the 6x6 transmissibility matrix is plotted.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:29</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:17 -->
|
||||
<!-- 2021-01-08 ven. 15:52 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Kinematic Study of the Stewart Platform</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -11,22 +11,22 @@
|
||||
<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
||||
<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
||||
<script>
|
||||
MathJax = {
|
||||
svg: {
|
||||
scale: 1,
|
||||
fontCache: "global"
|
||||
},
|
||||
tex: {
|
||||
tags: "ams",
|
||||
multlineWidth: "%MULTLINEWIDTH",
|
||||
tagSide: "right",
|
||||
macros: {bm: ["\\boldsymbol{#1}",1],},
|
||||
tagIndent: ".8em"
|
||||
}
|
||||
};
|
||||
</script>
|
||||
<script id="MathJax-script" async
|
||||
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
|
||||
MathJax = {
|
||||
svg: {
|
||||
scale: 1,
|
||||
fontCache: "global"
|
||||
},
|
||||
tex: {
|
||||
tags: "ams",
|
||||
multlineWidth: "%MULTLINEWIDTH",
|
||||
tagSide: "right",
|
||||
macros: {bm: ["\\boldsymbol{#1}",1],},
|
||||
tagIndent: ".8em"
|
||||
}
|
||||
};
|
||||
</script>
|
||||
<script id="MathJax-script" async
|
||||
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
|
||||
</head>
|
||||
<body>
|
||||
<div id="org-div-home-and-up">
|
||||
@@ -60,14 +60,14 @@
|
||||
</li>
|
||||
<li><a href="#orgbb09f83">4. Estimation of the range validity of the approximate inverse kinematics</a>
|
||||
<ul>
|
||||
<li><a href="#org78ce060">4.1. Stewart architecture definition</a></li>
|
||||
<li><a href="#orga79cde2">4.1. Stewart architecture definition</a></li>
|
||||
<li><a href="#org34777fa">4.2. Comparison for “pure” translations</a></li>
|
||||
<li><a href="#org76d9fc1">4.3. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org091e857">5. Estimated required actuator stroke from specified platform mobility</a>
|
||||
<ul>
|
||||
<li><a href="#org34f6e0e">5.1. Stewart architecture definition</a></li>
|
||||
<li><a href="#org7b16d1f">5.1. Stewart architecture definition</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="#org1674055">5.4. Needed stroke for “combined” rotations or translations</a></li>
|
||||
@@ -75,7 +75,7 @@
|
||||
</li>
|
||||
<li><a href="#orgb685a81">6. Estimated platform mobility from specified actuator stroke</a>
|
||||
<ul>
|
||||
<li><a href="#orga79cde2">6.1. Stewart architecture definition</a></li>
|
||||
<li><a href="#org555f3a5">6.1. Stewart architecture definition</a></li>
|
||||
<li><a href="#orga6e12fe">6.2. Pure translations</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
@@ -96,8 +96,8 @@
|
||||
<ul>
|
||||
<li><a href="#org7a0813a">8.1. <code>computeJacobian</code>: Compute the Jacobian Matrix</a>
|
||||
<ul>
|
||||
<li><a href="#org7f0fcca">Function description</a></li>
|
||||
<li><a href="#orgf06bd47">Check the <code>stewart</code> structure elements</a></li>
|
||||
<li><a href="#org8a3d2ba">Function description</a></li>
|
||||
<li><a href="#org5f6ad77">Check the <code>stewart</code> structure elements</a></li>
|
||||
<li><a href="#org01f1158">Compute Jacobian Matrix</a></li>
|
||||
<li><a href="#org91d652d">Compute Stiffness 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>
|
||||
<ul>
|
||||
<li><a href="#orge7e6266">Theory</a></li>
|
||||
<li><a href="#org39a0af1">Function description</a></li>
|
||||
<li><a href="#orgcb9b73a">Optional Parameters</a></li>
|
||||
<li><a href="#org31e89c1">Check the <code>stewart</code> structure elements</a></li>
|
||||
<li><a href="#org6586e8a">Function description</a></li>
|
||||
<li><a href="#orgf078a15">Optional Parameters</a></li>
|
||||
<li><a href="#org4151034">Check the <code>stewart</code> structure elements</a></li>
|
||||
<li><a href="#org7189e65">Compute</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgdc218cd">8.3. <code>forwardKinematicsApprox</code>: Compute the Approximate Forward Kinematics</a>
|
||||
<ul>
|
||||
<li><a href="#org8a3d2ba">Function description</a></li>
|
||||
<li><a href="#orgf078a15">Optional Parameters</a></li>
|
||||
<li><a href="#org5f6ad77">Check the <code>stewart</code> structure elements</a></li>
|
||||
<li><a href="#org9b19ae7">Function description</a></li>
|
||||
<li><a href="#orgdf60206">Optional Parameters</a></li>
|
||||
<li><a href="#org2c19f08">Check the <code>stewart</code> structure elements</a></li>
|
||||
<li><a href="#orga496714">Computation</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
@@ -442,7 +442,7 @@ The function <code>forwardKinematicsApprox</code> (described <a href="#orgb960ae
|
||||
<a id="org5f8c5ea"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="org919aba4">
|
||||
<div class="note" id="org9501cc6">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_approximation_validity.m">here</a>.
|
||||
</p>
|
||||
@@ -464,23 +464,23 @@ This will also gives us the range for which the approximate forward kinematic is
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org78ce060" class="outline-3">
|
||||
<h3 id="org78ce060"><span class="section-number-3">4.1</span> Stewart architecture definition</h3>
|
||||
<div id="outline-container-orga79cde2" class="outline-3">
|
||||
<h3 id="orga79cde2"><span class="section-number-3">4.1</span> Stewart architecture definition</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<p>
|
||||
We first define some general Stewart architecture.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
</pre>
|
||||
</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>.
|
||||
</p>
|
||||
<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_exact = zeros(6, length(Xrs));
|
||||
Ls_approx = 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>);
|
||||
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-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -531,7 +531,7 @@ The relative strut length displacement is shown in Figure <a href="#orgb451b90">
|
||||
<div id="outline-container-org76d9fc1" class="outline-3">
|
||||
<h3 id="org76d9fc1"><span class="section-number-3">4.3</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
<div class="important" id="org3d5a817">
|
||||
<div class="important" id="orgfe0578a">
|
||||
<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.
|
||||
</p>
|
||||
@@ -548,7 +548,7 @@ For small wanted displacements (up to \(\approx 1\%\) of the size of the Hexapod
|
||||
<a id="orgb1464b6"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="org7858fd4">
|
||||
<div class="note" id="org4fab0bc">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_required_actuator_stroke.m">here</a>.
|
||||
</p>
|
||||
@@ -565,23 +565,23 @@ This is what is analyzed in this section.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org34f6e0e" class="outline-3">
|
||||
<h3 id="org34f6e0e"><span class="section-number-3">5.1</span> Stewart architecture definition</h3>
|
||||
<div id="outline-container-org7b16d1f" class="outline-3">
|
||||
<h3 id="org7b16d1f"><span class="section-number-3">5.1</span> Stewart architecture definition</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
<p>
|
||||
Let’s first define the Stewart platform architecture that we want to study.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -594,12 +594,12 @@ Let’s first define the Stewart platform architecture that we want to study
|
||||
Let’s now define the wanted extreme translations and rotations.
|
||||
</p>
|
||||
<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>
|
||||
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>
|
||||
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>
|
||||
Rz_max = 0; <span class="org-comment">% Rotation [rad]</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>
|
||||
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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -614,12 +614,12 @@ We do that using either the Inverse Kinematic solution or the Jacobian matrix as
|
||||
</p>
|
||||
|
||||
<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>;
|
||||
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>;
|
||||
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>;
|
||||
LRz = stewart.kinematics.J<span class="org-type">*</span>[0 0 0 0 0 Rz_max]<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>;
|
||||
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>;
|
||||
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>;
|
||||
</pre>
|
||||
</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.
|
||||
</p>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -914,17 +914,17 @@ 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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> L_min = 0;
|
||||
L_max = 0;
|
||||
<pre class="src src-matlab">L_min = 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;
|
||||
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))];
|
||||
|
||||
Ry = [ cos(Ps(<span class="org-constant">i</span>, 5)) 0 sin(Ps(<span class="org-constant">i</span>, 5));
|
||||
0 1 0;
|
||||
<span class="org-type">-</span>sin(Ps(<span class="org-constant">i</span>, 5)) 0 cos(Ps(<span class="org-constant">i</span>, 5))];
|
||||
0 1 0;
|
||||
<span class="org-type">-</span>sin(Ps(<span class="org-constant">i</span>, 5)) 0 cos(Ps(<span class="org-constant">i</span>, 5))];
|
||||
|
||||
Rz = [cos(Ps(<span class="org-constant">i</span>, 6)) <span class="org-type">-</span>sin(Ps(<span class="org-constant">i</span>, 6)) 0;
|
||||
sin(Ps(<span class="org-constant">i</span>, 6)) cos(Ps(<span class="org-constant">i</span>, 6)) 0;
|
||||
@@ -934,12 +934,12 @@ For all possible combination, we compute the required actuator stroke using the
|
||||
[<span class="org-type">~</span>, Ls] = inverseKinematics(stewart, <span class="org-string">'AP'</span>, Ps(<span class="org-constant">i</span>, 1<span class="org-type">:</span>3)<span class="org-type">'</span>, <span class="org-string">'ARB'</span>, ARB);
|
||||
|
||||
<span class="org-keyword">if</span> min(Ls) <span class="org-type"><</span> L_min
|
||||
L_min = min(Ls)
|
||||
L_min = min(Ls)
|
||||
<span class="org-keyword">end</span>
|
||||
<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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -965,7 +965,7 @@ This is probably a much realistic estimation of the required actuator stroke.
|
||||
<a id="orge61164c"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="orge5bfdd7">
|
||||
<div class="note" id="orgc9ecb6b">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/kinematic_study_mobility.m">here</a>.
|
||||
</p>
|
||||
@@ -985,23 +985,23 @@ However, for small displacements, we can use the Jacobian as an approximate solu
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga79cde2" class="outline-3">
|
||||
<h3 id="orga79cde2"><span class="section-number-3">6.1</span> Stewart architecture definition</h3>
|
||||
<div id="outline-container-org555f3a5" class="outline-3">
|
||||
<h3 id="org555f3a5"><span class="section-number-3">6.1</span> Stewart architecture definition</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
<p>
|
||||
Let’s first define the Stewart platform architecture that we want to study.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1009,8 +1009,8 @@ Let’s first define the Stewart platform architecture that we want to study
|
||||
Let’s now define the actuator stroke.
|
||||
</p>
|
||||
<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>
|
||||
L_max = 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>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1038,21 +1038,21 @@ 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>.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
rs = zeros(length(thetas), length(phis));
|
||||
<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);
|
||||
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>
|
||||
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>));
|
||||
Tz = cos(thetas(<span class="org-constant">i</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>));
|
||||
Tz = cos(thetas(<span class="org-constant">i</span>));
|
||||
|
||||
dL = stewart.kinematics.J<span class="org-type">*</span>[Tx; Ty; Tz; 0; 0; 0;]; <span class="org-comment">% dL required for 1m displacement in theta/phi direction</span>
|
||||
dL = stewart.kinematics.J<span class="org-type">*</span>[Tx; Ty; Tz; 0; 0; 0;]; <span class="org-comment">% dL required for 1m displacement in theta/phi direction</span>
|
||||
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1109,63 +1109,63 @@ We can also approximate the mobility by a sphere with a radius equal to the mini
|
||||
Let’s first define the Stewart Platform Geometry.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart, <span class="org-string">'AP'</span>, [0; 0; 0]);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart, <span class="org-string">'AP'</span>, [0; 0; 0]);
|
||||
|
||||
As_init = stewart.geometry.As;
|
||||
As_init = stewart.geometry.As;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
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>
|
||||
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>
|
||||
Rz_max = 0; <span class="org-comment">% Rotation [rad]</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>
|
||||
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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> flex_ang = zeros(size(Ps, 1), 6);
|
||||
Rxs = zeros(size(Ps, 1), 6)
|
||||
Rys = zeros(size(Ps, 1), 6)
|
||||
Rzs = zeros(size(Ps, 1), 6)
|
||||
<pre class="src src-matlab">flex_ang = zeros(size(Ps, 1), 6);
|
||||
Rxs = zeros(size(Ps, 1), 6)
|
||||
Rys = 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>
|
||||
Rx = [1 0 0;
|
||||
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))];
|
||||
<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;
|
||||
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))];
|
||||
|
||||
Ry = [ cos(Ps(Ps_i, 5)) 0 sin(Ps(Ps_i, 5));
|
||||
0 1 0;
|
||||
<span class="org-type">-</span>sin(Ps(Ps_i, 5)) 0 cos(Ps(Ps_i, 5))];
|
||||
Ry = [ cos(Ps(Ps_i, 5)) 0 sin(Ps(Ps_i, 5));
|
||||
0 1 0;
|
||||
<span class="org-type">-</span>sin(Ps(Ps_i, 5)) 0 cos(Ps(Ps_i, 5))];
|
||||
|
||||
Rz = [cos(Ps(Ps_i, 6)) <span class="org-type">-</span>sin(Ps(Ps_i, 6)) 0;
|
||||
sin(Ps(Ps_i, 6)) cos(Ps(Ps_i, 6)) 0;
|
||||
0 0 1];
|
||||
Rz = [cos(Ps(Ps_i, 6)) <span class="org-type">-</span>sin(Ps(Ps_i, 6)) 0;
|
||||
sin(Ps(Ps_i, 6)) cos(Ps(Ps_i, 6)) 0;
|
||||
0 0 1];
|
||||
|
||||
ARB = Rz<span class="org-type">*</span>Ry<span class="org-type">*</span>Rx;
|
||||
ARB = Rz<span class="org-type">*</span>Ry<span class="org-type">*</span>Rx;
|
||||
|
||||
stewart = computeJointsPose(stewart, <span class="org-string">'AP'</span>, Ps(Ps_i, 1<span class="org-type">:</span>3)<span class="org-type">'</span>, <span class="org-string">'ARB'</span>, ARB);
|
||||
stewart = computeJointsPose(stewart, <span class="org-string">'AP'</span>, Ps(Ps_i, 1<span class="org-type">:</span>3)<span class="org-type">'</span>, <span class="org-string">'ARB'</span>, ARB);
|
||||
|
||||
flex_ang(Ps_i, <span class="org-type">:</span>) = acos(sum(As_init<span class="org-type">.*</span>stewart.geometry.As));
|
||||
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name">l_i</span> = <span class="org-constant">1:6</span>
|
||||
MRf = stewart.platform_M.MRb(<span class="org-type">:</span>,<span class="org-type">:</span>,l_i)<span class="org-type">*</span>(ARB<span class="org-type">'</span>)<span class="org-type">*</span>(stewart.platform_F.FRa(<span class="org-type">:</span>,<span class="org-type">:</span>,l_i)<span class="org-type">'</span>);
|
||||
|
||||
Rys(Ps_i, l_i) = atan2(MRf(1,3), sqrt(MRf(1,1)<span class="org-type">^</span>2 <span class="org-type">+</span> MRf(2,2)<span class="org-type">^</span>2));
|
||||
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)));
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
flex_ang(Ps_i, <span class="org-type">:</span>) = acos(sum(As_init<span class="org-type">.*</span>stewart.geometry.As));
|
||||
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name">l_i</span> = <span class="org-constant">1:6</span>
|
||||
MRf = stewart.platform_M.MRb(<span class="org-type">:</span>,<span class="org-type">:</span>,l_i)<span class="org-type">*</span>(ARB<span class="org-type">'</span>)<span class="org-type">*</span>(stewart.platform_F.FRa(<span class="org-type">:</span>,<span class="org-type">:</span>,l_i)<span class="org-type">'</span>);
|
||||
|
||||
Rys(Ps_i, l_i) = atan2(MRf(1,3), sqrt(MRf(1,1)<span class="org-type">^</span>2 <span class="org-type">+</span> MRf(2,2)<span class="org-type">^</span>2));
|
||||
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)));
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1173,7 +1173,7 @@ Let’s first define the Stewart Platform Geometry.
|
||||
And the maximum bending of the flexible joints is: (in [mrad])
|
||||
</p>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -1183,7 +1183,7 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
||||
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -1193,7 +1193,7 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
||||
|
||||
|
||||
<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>
|
||||
</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>
|
||||
<div class="outline-text-4" id="text-7-2-1">
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(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);
|
||||
<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 = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(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 = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
<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>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1245,29 +1245,29 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
||||
<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="org-src-container">
|
||||
<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>;
|
||||
<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>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/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">%% Input/Output definition</span></span>
|
||||
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">'/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>
|
||||
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.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>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
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.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>
|
||||
</div>
|
||||
|
||||
<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;
|
||||
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 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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1277,34 +1277,34 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
||||
<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="org-src-container">
|
||||
<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>
|
||||
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>
|
||||
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>
|
||||
<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>
|
||||
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>
|
||||
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>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
Rs = zeros(size(Ps, 1), 5); <span class="org-comment">% Max Flexor angles for the 6 legs [mrad]</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>
|
||||
|
||||
<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));
|
||||
|
||||
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>);
|
||||
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-string">'stewart_platform_model'</span>,<span class="org-string">'StopTime'</span>,<span class="org-string">'0.1'</span>);
|
||||
<span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'stewart_platform_model'</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));
|
||||
|
||||
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>;
|
||||
<span class="org-keyword">end</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>);
|
||||
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-string">'stewart_platform_model'</span>,<span class="org-string">'StopTime'</span>,<span class="org-string">'0.1'</span>);
|
||||
<span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'stewart_platform_model'</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>;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1312,7 +1312,7 @@ And the maximum bending of the flexible joints is: (in [mrad])
|
||||
Verify that the simulations are all correct:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> max(cl_perf)
|
||||
<pre class="src src-matlab">max(cl_perf)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1390,43 +1390,43 @@ This Matlab function is accessible <a href="../src/computeJacobian.m">here</a>.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7f0fcca" class="outline-4">
|
||||
<h4 id="org7f0fcca">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org7f0fcca">
|
||||
<div id="outline-container-org8a3d2ba" class="outline-4">
|
||||
<h4 id="org8a3d2ba">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org8a3d2ba">
|
||||
<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>)
|
||||
<span class="org-comment">% computeJacobian -</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Syntax: [stewart] = computeJacobian(stewart)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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.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">%</span>
|
||||
<span class="org-comment">% Outputs:</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.K [6x6] - The Stiffness Matrix</span>
|
||||
<span class="org-comment">% - kinematics.C [6x6] - The Compliance Matrix</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">%</span>
|
||||
<span class="org-comment">% Syntax: [stewart] = computeJacobian(stewart)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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.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">%</span>
|
||||
<span class="org-comment">% Outputs:</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.K [6x6] - The Stiffness Matrix</span>
|
||||
<span class="org-comment">% - kinematics.C [6x6] - The Compliance Matrix</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf06bd47" class="outline-4">
|
||||
<h4 id="orgf06bd47">Check the <code>stewart</code> structure elements</h4>
|
||||
<div class="outline-text-4" id="text-orgf06bd47">
|
||||
<div id="outline-container-org5f6ad77" class="outline-4">
|
||||
<h4 id="org5f6ad77">Check the <code>stewart</code> structure elements</h4>
|
||||
<div class="outline-text-4" id="text-org5f6ad77">
|
||||
<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>)
|
||||
As = stewart.geometry.As;
|
||||
<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;
|
||||
|
||||
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;
|
||||
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;
|
||||
|
||||
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;
|
||||
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;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1437,7 +1437,7 @@ This Matlab function is accessible <a href="../src/computeJacobian.m">here</a>.
|
||||
<h4 id="org01f1158">Compute Jacobian Matrix</h4>
|
||||
<div class="outline-text-4" id="text-org01f1158">
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1447,7 +1447,7 @@ This Matlab function is accessible <a href="../src/computeJacobian.m">here</a>.
|
||||
<h4 id="org91d652d">Compute Stiffness Matrix</h4>
|
||||
<div class="outline-text-4" id="text-org91d652d">
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1457,7 +1457,7 @@ This Matlab function is accessible <a href="../src/computeJacobian.m">here</a>.
|
||||
<h4 id="org323b34e">Compute Compliance Matrix</h4>
|
||||
<div class="outline-text-4" id="text-org323b34e">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> C = inv(K);
|
||||
<pre class="src src-matlab">C = inv(K);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1467,9 +1467,9 @@ This Matlab function is accessible <a href="../src/computeJacobian.m">here</a>.
|
||||
<h4 id="orgebce485">Populate the <code>stewart</code> structure</h4>
|
||||
<div class="outline-text-4" id="text-orgebce485">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart.kinematics.J = J;
|
||||
stewart.kinematics.K = K;
|
||||
stewart.kinematics.C = C;
|
||||
<pre class="src src-matlab">stewart.kinematics.J = J;
|
||||
stewart.kinematics.K = K;
|
||||
stewart.kinematics.C = C;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1525,58 +1525,58 @@ Otherwise, when the limbs’ lengths derived yield complex numbers, then the
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org39a0af1" class="outline-4">
|
||||
<h4 id="org39a0af1">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org39a0af1">
|
||||
<div id="outline-container-org6586e8a" class="outline-4">
|
||||
<h4 id="org6586e8a">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org6586e8a">
|
||||
<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>)
|
||||
<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">% Syntax: [stewart] = inverseKinematics(stewart)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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.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">% - 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">% - 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">% 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">% - 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 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">%</span>
|
||||
<span class="org-comment">% Syntax: [stewart] = inverseKinematics(stewart)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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.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">% - 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">% - 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">% 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">% - 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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcb9b73a" class="outline-4">
|
||||
<h4 id="orgcb9b73a">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orgcb9b73a">
|
||||
<div id="outline-container-orgf078a15" class="outline-4">
|
||||
<h4 id="orgf078a15">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orgf078a15">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-keyword">arguments</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>.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||
<span class="org-keyword">end</span>
|
||||
<pre class="src src-matlab"><span class="org-keyword">arguments</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>.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org31e89c1" class="outline-4">
|
||||
<h4 id="org31e89c1">Check the <code>stewart</code> structure elements</h4>
|
||||
<div class="outline-text-4" id="text-org31e89c1">
|
||||
<div id="outline-container-org4151034" class="outline-4">
|
||||
<h4 id="org4151034">Check the <code>stewart</code> structure elements</h4>
|
||||
<div class="outline-text-4" id="text-org4151034">
|
||||
<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>)
|
||||
Aa = stewart.geometry.Aa;
|
||||
<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;
|
||||
|
||||
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;
|
||||
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;
|
||||
|
||||
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;
|
||||
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;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1587,12 +1587,12 @@ Otherwise, when the limbs’ lengths derived yield complex numbers, then the
|
||||
<h4 id="org7189e65">Compute</h4>
|
||||
<div class="outline-text-4" id="text-org7189e65">
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1611,49 +1611,49 @@ This Matlab function is accessible <a href="../src/forwardKinematicsApprox.m">he
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8a3d2ba" class="outline-4">
|
||||
<h4 id="org8a3d2ba">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org8a3d2ba">
|
||||
<div id="outline-container-org9b19ae7" class="outline-4">
|
||||
<h4 id="org9b19ae7">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org9b19ae7">
|
||||
<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>)
|
||||
<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">%</span>
|
||||
<span class="org-comment">% Syntax: [P, R] = forwardKinematicsApprox(stewart, args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - args - Can have the following fields:</span>
|
||||
<span class="org-comment">% - dL [6x1] - Displacement of each strut [m]</span>
|
||||
<span class="org-comment">%</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">% - R [3x3] - The estimated rotation matrix that gives the orientation of {B} with respect to {A}</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">% the Jacobian Matrix</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Syntax: [P, R] = forwardKinematicsApprox(stewart, args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - args - Can have the following fields:</span>
|
||||
<span class="org-comment">% - dL [6x1] - Displacement of each strut [m]</span>
|
||||
<span class="org-comment">%</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">% - R [3x3] - The estimated rotation matrix that gives the orientation of {B} with respect to {A}</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf078a15" class="outline-4">
|
||||
<h4 id="orgf078a15">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orgf078a15">
|
||||
<div id="outline-container-orgdf60206" class="outline-4">
|
||||
<h4 id="orgdf60206">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orgdf60206">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-keyword">arguments</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-keyword">end</span>
|
||||
<pre class="src src-matlab"><span class="org-keyword">arguments</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-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5f6ad77" class="outline-4">
|
||||
<h4 id="org5f6ad77">Check the <code>stewart</code> structure elements</h4>
|
||||
<div class="outline-text-4" id="text-org5f6ad77">
|
||||
<div id="outline-container-org2c19f08" class="outline-4">
|
||||
<h4 id="org2c19f08">Check the <code>stewart</code> structure elements</h4>
|
||||
<div class="outline-text-4" id="text-org2c19f08">
|
||||
<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>)
|
||||
J = stewart.kinematics.J;
|
||||
<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;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1668,7 +1668,7 @@ position and orientation of {B} with respect to {A} using the following formula:
|
||||
\[ d \bm{\mathcal{X}} = \bm{J}^{-1} d\bm{\mathcal{L}} \]
|
||||
</p>
|
||||
<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>
|
||||
</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.
|
||||
</p>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -1685,8 +1685,8 @@ The next 3 elements are the orientation of {B} with respect to {A} expressed
|
||||
using the screw axis.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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;
|
||||
<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;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1694,9 +1694,9 @@ using the screw axis.
|
||||
We then compute the corresponding rotation matrix.
|
||||
</p>
|
||||
<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);
|
||||
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>
|
||||
<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">(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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1715,7 +1715,7 @@ We then compute the corresponding rotation matrix.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:17</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:30 -->
|
||||
<!-- 2021-01-08 ven. 15:53 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Stewart Platform - NASS</title>
|
||||
<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>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<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>);
|
||||
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 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>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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 = 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 = 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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<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 = 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 = 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 = 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 = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</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);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -77,7 +77,7 @@
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:53</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:29 -->
|
||||
<!-- 2021-01-08 ven. 15:52 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Stewart Platform - Simscape Model</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -48,16 +48,16 @@
|
||||
<ul>
|
||||
<li><a href="#orgf4bef70">6.1. Payload</a>
|
||||
<ul>
|
||||
<li><a href="#org9c0e404">Function description</a></li>
|
||||
<li><a href="#orgabc81c1">Optional Parameters</a></li>
|
||||
<li><a href="#org920bdd0">Function description</a></li>
|
||||
<li><a href="#orgbc7950f">Optional Parameters</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>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgd9e12ef">6.2. Ground</a>
|
||||
<ul>
|
||||
<li><a href="#org920bdd0">Function description</a></li>
|
||||
<li><a href="#orgfa4bbf4">Optional Parameters</a></li>
|
||||
<li><a href="#orgc300ecf">Function description</a></li>
|
||||
<li><a href="#org1ee272a">Optional Parameters</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="#orgdb67a68">Rotation Point</a></li>
|
||||
@@ -67,8 +67,8 @@
|
||||
</li>
|
||||
<li><a href="#org6d3b61e">7. Initialize Disturbances</a>
|
||||
<ul>
|
||||
<li><a href="#orgf14752d">Function Declaration and Documentation</a></li>
|
||||
<li><a href="#orga64679c">Optional Parameters</a></li>
|
||||
<li><a href="#orgf124972">Function Declaration and Documentation</a></li>
|
||||
<li><a href="#org668f4bb">Optional Parameters</a></li>
|
||||
<li><a href="#org0f7e4dd">Structure initialization</a></li>
|
||||
<li><a href="#org1a28fcd">Ground Motion</a></li>
|
||||
<li><a href="#org90b72d6">Direct Forces</a></li>
|
||||
@@ -76,8 +76,8 @@
|
||||
</li>
|
||||
<li><a href="#org93f2d30">8. Initialize References</a>
|
||||
<ul>
|
||||
<li><a href="#orgf124972">Function Declaration and Documentation</a></li>
|
||||
<li><a href="#orgbc7950f">Optional Parameters</a></li>
|
||||
<li><a href="#org81500bb">Function Declaration and Documentation</a></li>
|
||||
<li><a href="#org05322ee">Optional Parameters</a></li>
|
||||
<li><a href="#org6f05adc">8.1. Compute the corresponding strut length</a></li>
|
||||
<li><a href="#orgda73a50">References</a></li>
|
||||
</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:
|
||||
</p>
|
||||
<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>
|
||||
</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:
|
||||
</p>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -303,50 +303,50 @@ This Matlab function is accessible <a href="../src/initializePayload.m">here</a>
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9c0e404" class="outline-4">
|
||||
<h4 id="org9c0e404">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org9c0e404">
|
||||
<div id="outline-container-org920bdd0" class="outline-4">
|
||||
<h4 id="org920bdd0">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org920bdd0">
|
||||
<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>)
|
||||
<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">% Syntax: [payload] = initializePayload(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - 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">% - 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">% - 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">%</span>
|
||||
<span class="org-comment">% Outputs:</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">% - 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">% - 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">% - I [3x3] - Inertia matrix for the Payload [kg*m2]</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">%</span>
|
||||
<span class="org-comment">% Syntax: [payload] = initializePayload(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - 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">% - 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">% - 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">%</span>
|
||||
<span class="org-comment">% Outputs:</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">% - 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">% - 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">% - I [3x3] - Inertia matrix for the Payload [kg*m2]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgabc81c1" class="outline-4">
|
||||
<h4 id="orgabc81c1">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orgabc81c1">
|
||||
<div id="outline-container-orgbc7950f" class="outline-4">
|
||||
<h4 id="orgbc7950f">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orgbc7950f">
|
||||
<div class="org-src-container">
|
||||
<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>.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>.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>.I (3,3) double {mustBeNumeric, mustBeNonnegative} = 1<span class="org-type">*</span>eye(3)
|
||||
<span class="org-keyword">end</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>.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>.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>.I (3,3) double {mustBeNumeric, mustBeNonnegative} = 1<span class="org-type">*</span>eye(3)
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -356,16 +356,16 @@ This Matlab function is accessible <a href="../src/initializePayload.m">here</a>
|
||||
<h4 id="org4ef4a9f">Add Payload Type</h4>
|
||||
<div class="outline-text-4" id="text-org4ef4a9f">
|
||||
<div class="org-src-container">
|
||||
<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>
|
||||
payload.type = 1;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
||||
payload.type = 2;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
||||
payload.type = 3;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'cartesian'</span>
|
||||
payload.type = 4;
|
||||
<span class="org-keyword">end</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>
|
||||
payload.type = 1;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
||||
payload.type = 2;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
||||
payload.type = 3;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'cartesian'</span>
|
||||
payload.type = 4;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</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>
|
||||
<div class="outline-text-4" id="text-org3243d76">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> payload.K = args.K;
|
||||
payload.C = args.C;
|
||||
payload.m = args.m;
|
||||
payload.I = args.I;
|
||||
<pre class="src src-matlab">payload.K = args.K;
|
||||
payload.C = args.C;
|
||||
payload.m = args.m;
|
||||
payload.I = args.I;
|
||||
|
||||
payload.h = args.h;
|
||||
payload.h = args.h;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -399,42 +399,42 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org920bdd0" class="outline-4">
|
||||
<h4 id="org920bdd0">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org920bdd0">
|
||||
<div id="outline-container-orgc300ecf" class="outline-4">
|
||||
<h4 id="orgc300ecf">Function description</h4>
|
||||
<div class="outline-text-4" id="text-orgc300ecf">
|
||||
<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>)
|
||||
<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">% Syntax: [ground] = initializeGround(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - 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">% - C [3x1] - Translation Damping of the Ground [N/(m/s)]</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Outputs:</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">% - 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>
|
||||
<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">%</span>
|
||||
<span class="org-comment">% Syntax: [ground] = initializeGround(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</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">% - 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">% - C [3x1] - Translation Damping of the Ground [N/(m/s)]</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Outputs:</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">% - 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>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfa4bbf4" class="outline-4">
|
||||
<h4 id="orgfa4bbf4">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-orgfa4bbf4">
|
||||
<div id="outline-container-org1ee272a" class="outline-4">
|
||||
<h4 id="org1ee272a">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-org1ee272a">
|
||||
<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>.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>.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>
|
||||
</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>
|
||||
<div class="outline-text-4" id="text-org2d22970">
|
||||
<div class="org-src-container">
|
||||
<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>
|
||||
ground.type = 1;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
||||
ground.type = 2;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
||||
ground.type = 3;
|
||||
<span class="org-keyword">end</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>
|
||||
ground.type = 1;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
||||
ground.type = 2;
|
||||
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
||||
ground.type = 3;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</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>
|
||||
<div class="outline-text-4" id="text-orgf76def4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ground.K = args.K;
|
||||
ground.C = args.C;
|
||||
<pre class="src src-matlab">ground.K = args.K;
|
||||
ground.C = args.C;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -472,7 +472,7 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
<h4 id="orgdb67a68">Rotation Point</h4>
|
||||
<div class="outline-text-4" id="text-orgdb67a68">
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -487,33 +487,33 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf14752d" class="outline-3">
|
||||
<h3 id="orgf14752d">Function Declaration and Documentation</h3>
|
||||
<div class="outline-text-3" id="text-orgf14752d">
|
||||
<div id="outline-container-orgf124972" class="outline-3">
|
||||
<h3 id="orgf124972">Function Declaration and Documentation</h3>
|
||||
<div class="outline-text-3" id="text-orgf124972">
|
||||
<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>)
|
||||
<span class="org-comment">% initializeDisturbances - Initialize the disturbances</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Syntax: [disturbances] = initializeDisturbances(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</span>
|
||||
<span class="org-comment">% - 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">%</span>
|
||||
<span class="org-comment">% Syntax: [disturbances] = initializeDisturbances(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</span>
|
||||
<span class="org-comment">% - args -</span>
|
||||
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga64679c" class="outline-3">
|
||||
<h3 id="orga64679c">Optional Parameters</h3>
|
||||
<div class="outline-text-3" id="text-orga64679c">
|
||||
<div id="outline-container-org668f4bb" class="outline-3">
|
||||
<h3 id="org668f4bb">Optional Parameters</h3>
|
||||
<div class="outline-text-3" id="text-org668f4bb">
|
||||
<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_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_t double {mustBeNumeric, mustBeReal} = 0
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -524,7 +524,7 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
<h3 id="org0f7e4dd">Structure initialization</h3>
|
||||
<div class="outline-text-3" id="text-org0f7e4dd">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = struct();
|
||||
<pre class="src src-matlab">disturbances = struct();
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -534,7 +534,7 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
<h3 id="org1a28fcd">Ground Motion</h3>
|
||||
<div class="outline-text-3" id="text-org1a28fcd">
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -544,7 +544,7 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
<h3 id="org90b72d6">Direct Forces</h3>
|
||||
<div class="outline-text-3" id="text-org90b72d6">
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -559,32 +559,32 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf124972" class="outline-3">
|
||||
<h3 id="orgf124972">Function Declaration and Documentation</h3>
|
||||
<div class="outline-text-3" id="text-orgf124972">
|
||||
<div id="outline-container-org81500bb" class="outline-3">
|
||||
<h3 id="org81500bb">Function Declaration and Documentation</h3>
|
||||
<div class="outline-text-3" id="text-org81500bb">
|
||||
<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>)
|
||||
<span class="org-comment">% initializeReferences - Initialize the references</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Syntax: [references] = initializeReferences(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</span>
|
||||
<span class="org-comment">% - 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">%</span>
|
||||
<span class="org-comment">% Syntax: [references] = initializeReferences(args)</span>
|
||||
<span class="org-comment">%</span>
|
||||
<span class="org-comment">% Inputs:</span>
|
||||
<span class="org-comment">% - args -</span>
|
||||
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbc7950f" class="outline-3">
|
||||
<h3 id="orgbc7950f">Optional Parameters</h3>
|
||||
<div class="outline-text-3" id="text-orgbc7950f">
|
||||
<div id="outline-container-org05322ee" class="outline-3">
|
||||
<h3 id="org05322ee">Optional Parameters</h3>
|
||||
<div class="outline-text-3" id="text-org05322ee">
|
||||
<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">args</span>.t double {mustBeNumeric, mustBeReal} = 0
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
@@ -594,22 +594,22 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
<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="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;
|
||||
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> ...
|
||||
[cos(args.r(5,<span class="org-constant">i</span>)) 0 sin(args.r(5,<span class="org-constant">i</span>));
|
||||
0 1 0;
|
||||
<span class="org-type">-</span>sin(args.r(5,<span class="org-constant">i</span>)) 0 cos(args.r(5,<span class="org-constant">i</span>))] <span class="org-type">*</span> ...
|
||||
<span class="org-type">-</span>sin(args.r(5,<span class="org-constant">i</span>)) 0 cos(args.r(5,<span class="org-constant">i</span>))] <span class="org-type">*</span> ...
|
||||
[1 0 0;
|
||||
0 cos(args.r(4,<span class="org-constant">i</span>)) <span class="org-type">-</span>sin(args.r(4,<span class="org-constant">i</span>));
|
||||
0 sin(args.r(4,<span class="org-constant">i</span>)) cos(args.r(4,<span class="org-constant">i</span>))];
|
||||
|
||||
[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;
|
||||
<span class="org-keyword">end</span>
|
||||
[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;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -619,8 +619,8 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
<h3 id="orgda73a50">References</h3>
|
||||
<div class="outline-text-3" id="text-orgda73a50">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> references.r = timeseries(args.r, args.t);
|
||||
references.rL = timeseries(rL, args.t);
|
||||
<pre class="src src-matlab">references.r = timeseries(args.r, args.t);
|
||||
references.rL = timeseries(rL, args.t);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -629,7 +629,7 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:29</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:30 -->
|
||||
<!-- 2021-01-08 ven. 15:52 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Simulink Project for the Stewart Simscape folder</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -45,7 +45,7 @@ The project can be opened using the <code>simulinkproject</code> function:
|
||||
</p>
|
||||
|
||||
<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>
|
||||
</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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> project = simulinkproject;
|
||||
projectRoot = project.RootFolder;
|
||||
<pre class="src src-matlab">project = simulinkproject;
|
||||
projectRoot = project.RootFolder;
|
||||
|
||||
myCacheFolder = fullfile(projectRoot, <span class="org-string">'.SimulinkCache'</span>);
|
||||
myCodeFolder = fullfile(projectRoot, <span class="org-string">'.SimulinkCode'</span>);
|
||||
myCacheFolder = fullfile(projectRoot, <span class="org-string">'.SimulinkCache'</span>);
|
||||
myCodeFolder = fullfile(projectRoot, <span class="org-string">'.SimulinkCode'</span>);
|
||||
|
||||
Simulink.fileGenControl(<span class="org-string">'set'</span>,...
|
||||
<span class="org-string">'CacheFolder'</span>, myCacheFolder,...
|
||||
<span class="org-string">'CodeGenFolder'</span>, myCodeFolder,...
|
||||
<span class="org-string">'createDir'</span>, <span class="org-constant">true</span>);
|
||||
Simulink.fileGenControl(<span class="org-string">'set'</span>,...
|
||||
<span class="org-string">'CacheFolder'</span>, myCacheFolder,...
|
||||
<span class="org-string">'CodeGenFolder'</span>, myCodeFolder,...
|
||||
<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>
|
||||
load(<span class="org-string">'mat/conf_simscape.mat'</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>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -74,7 +74,7 @@ The startup script is defined below and is exported to the <code>project_startup
|
||||
When the project closes, it runs the <code>project_shutdown.m</code> script defined below.
|
||||
</p>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
@@ -84,7 +84,7 @@ The project also permits to automatically add defined folder to the path when th
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-01-08 ven. 15:30 -->
|
||||
<!-- 2021-01-08 ven. 15:53 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Stewart Platform - Static Analysis</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -74,7 +74,7 @@ Thus, the system is uncoupled if \(G\) and \(K\) are diagonal.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:53</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
Reference in New Issue
Block a user