749 lines
32 KiB
HTML
749 lines
32 KiB
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="./index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Stewart Platform - Dynamics Study</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgf59f0f9">1. Some tests</a>
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<ul>
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<li><a href="#orgaf3d924">1.1. Simscape Model</a></li>
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<li><a href="#org7312203">1.2. test</a></li>
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<li><a href="#org9daf767">1.3. Compare external forces and forces applied by the actuators</a></li>
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<li><a href="#org2a5345f">1.4. Comparison of the static transfer function and the Compliance matrix</a></li>
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<li><a href="#org089f223">1.5. Transfer function from forces applied in the legs to the displacement of the legs</a></li>
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</ul>
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</li>
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</ul>
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</div>
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<div id="outline-container-orgf59f0f9" class="outline-2">
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<h2 id="orgf59f0f9"><span class="section-number-2">1</span> Some tests</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-orgaf3d924" class="outline-3">
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<h3 id="orgaf3d924"><span class="section-number-3">1.1</span> Simscape Model</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_dynamics.slx'</span>)
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org7312203" class="outline-3">
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<h3 id="org7312203"><span class="section-number-3">1.2</span> test</h3>
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<div class="outline-text-3" id="text-1-2">
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|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">stewart = initializeFramesPositions(<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 = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 60e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
|
||
|
|
stewart = computeJointsPose(stewart);
|
||
|
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||
|
|
stewart = computeJacobian(stewart);
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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;
|
||
|
|
|
||
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||
|
|
mdl = <span class="org-string">'stewart_platform_dynamics'</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">'/F'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
|
||
|
|
<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">'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>};
|
||
|
|
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"><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_dynamics'</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">'/J-T'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
|
||
|
|
<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">G_cart = minreal(G<span class="org-type">*</span>inv(stewart.J<span class="org-type">'</span>));
|
||
|
|
G_cart.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>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>; bode(G, G_cart)
|
||
|
|
</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;
|
||
|
|
|
||
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||
|
|
mdl = <span class="org-string">'stewart_platform_dynamics'</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">'/Fext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
|
||
|
|
<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>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">freqs = logspace(0, 3, 1000);
|
||
|
|
|
||
|
|
<span class="org-type">figure</span>;
|
||
|
|
bode(Gd, G)
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org9daf767" class="outline-3">
|
||
|
|
<h3 id="org9daf767"><span class="section-number-3">1.3</span> Compare external forces and forces applied by the actuators</h3>
|
||
|
|
<div class="outline-text-3" id="text-1-3">
|
||
|
|
<p>
|
||
|
|
Initialization of the Stewart platform.
|
||
|
|
</p>
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">stewart = initializeFramesPositions(<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 = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 60e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
|
||
|
|
stewart = computeJointsPose(stewart);
|
||
|
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||
|
|
stewart = computeJacobian(stewart);
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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;
|
||
|
|
|
||
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||
|
|
mdl = <span class="org-string">'stewart_platform_dynamics'</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">'/F'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
|
||
|
|
<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">'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>};
|
||
|
|
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>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Estimation of the transfer function from \(\mathcal{\bm{F}}_{d}\) 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;
|
||
|
|
|
||
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||
|
|
mdl = <span class="org-string">'stewart_platform_dynamics'</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">'/Fext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
|
||
|
|
<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>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Comparison of the two transfer function matrices.
|
||
|
|
</p>
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">freqs = logspace(0, 4, 1000);
|
||
|
|
|
||
|
|
<span class="org-type">figure</span>;
|
||
|
|
bode(Gd, G, freqs)
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="important">
|
||
|
|
<p>
|
||
|
|
Seems quite similar.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org2a5345f" class="outline-3">
|
||
|
|
<h3 id="org2a5345f"><span class="section-number-3">1.4</span> Comparison of the static transfer function and the Compliance matrix</h3>
|
||
|
|
<div class="outline-text-3" id="text-1-4">
|
||
|
|
<p>
|
||
|
|
Initialization of the Stewart platform.
|
||
|
|
</p>
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">stewart = initializeFramesPositions(<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 = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 60e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
|
||
|
|
stewart = computeJointsPose(stewart);
|
||
|
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||
|
|
stewart = computeJacobian(stewart);
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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;
|
||
|
|
|
||
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||
|
|
mdl = <span class="org-string">'stewart_platform_dynamics'</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">'/F'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
|
||
|
|
<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">'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>};
|
||
|
|
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>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Let’s first look at the low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\).
|
||
|
|
</p>
|
||
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||
|
|
|
||
|
|
|
||
|
|
<colgroup>
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
</colgroup>
|
||
|
|
<tbody>
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">2.0e-06</td>
|
||
|
|
<td class="org-right">-9.1e-19</td>
|
||
|
|
<td class="org-right">-5.3e-12</td>
|
||
|
|
<td class="org-right">7.3e-18</td>
|
||
|
|
<td class="org-right">1.7e-05</td>
|
||
|
|
<td class="org-right">1.3e-18</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">-1.7e-18</td>
|
||
|
|
<td class="org-right">2.0e-06</td>
|
||
|
|
<td class="org-right">8.6e-19</td>
|
||
|
|
<td class="org-right">-1.7e-05</td>
|
||
|
|
<td class="org-right">-1.5e-17</td>
|
||
|
|
<td class="org-right">6.7e-12</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">3.6e-13</td>
|
||
|
|
<td class="org-right">3.2e-19</td>
|
||
|
|
<td class="org-right">5.0e-07</td>
|
||
|
|
<td class="org-right">-2.5e-18</td>
|
||
|
|
<td class="org-right">8.1e-12</td>
|
||
|
|
<td class="org-right">-1.5e-19</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">1.0e-17</td>
|
||
|
|
<td class="org-right">-1.7e-05</td>
|
||
|
|
<td class="org-right">-5.0e-18</td>
|
||
|
|
<td class="org-right">1.9e-04</td>
|
||
|
|
<td class="org-right">9.1e-17</td>
|
||
|
|
<td class="org-right">-3.5e-11</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">1.7e-05</td>
|
||
|
|
<td class="org-right">-6.9e-19</td>
|
||
|
|
<td class="org-right">-5.3e-11</td>
|
||
|
|
<td class="org-right">6.9e-18</td>
|
||
|
|
<td class="org-right">1.9e-04</td>
|
||
|
|
<td class="org-right">4.8e-18</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">-3.5e-18</td>
|
||
|
|
<td class="org-right">-4.5e-12</td>
|
||
|
|
<td class="org-right">1.5e-18</td>
|
||
|
|
<td class="org-right">7.1e-11</td>
|
||
|
|
<td class="org-right">-3.4e-17</td>
|
||
|
|
<td class="org-right">4.6e-05</td>
|
||
|
|
</tr>
|
||
|
|
</tbody>
|
||
|
|
</table>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
And now at the Compliance matrix.
|
||
|
|
</p>
|
||
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||
|
|
|
||
|
|
|
||
|
|
<colgroup>
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
</colgroup>
|
||
|
|
<tbody>
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">2.0e-06</td>
|
||
|
|
<td class="org-right">2.9e-22</td>
|
||
|
|
<td class="org-right">2.8e-22</td>
|
||
|
|
<td class="org-right">-3.2e-21</td>
|
||
|
|
<td class="org-right">1.7e-05</td>
|
||
|
|
<td class="org-right">1.5e-37</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">-2.1e-22</td>
|
||
|
|
<td class="org-right">2.0e-06</td>
|
||
|
|
<td class="org-right">-1.8e-23</td>
|
||
|
|
<td class="org-right">-1.7e-05</td>
|
||
|
|
<td class="org-right">-2.3e-21</td>
|
||
|
|
<td class="org-right">1.1e-22</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">3.1e-22</td>
|
||
|
|
<td class="org-right">-1.6e-23</td>
|
||
|
|
<td class="org-right">5.0e-07</td>
|
||
|
|
<td class="org-right">1.7e-22</td>
|
||
|
|
<td class="org-right">2.2e-21</td>
|
||
|
|
<td class="org-right">-8.1e-39</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">2.1e-21</td>
|
||
|
|
<td class="org-right">-1.7e-05</td>
|
||
|
|
<td class="org-right">2.0e-22</td>
|
||
|
|
<td class="org-right">1.9e-04</td>
|
||
|
|
<td class="org-right">2.3e-20</td>
|
||
|
|
<td class="org-right">-8.7e-21</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">1.7e-05</td>
|
||
|
|
<td class="org-right">2.5e-21</td>
|
||
|
|
<td class="org-right">2.0e-21</td>
|
||
|
|
<td class="org-right">-2.8e-20</td>
|
||
|
|
<td class="org-right">1.9e-04</td>
|
||
|
|
<td class="org-right">1.3e-36</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-right">3.7e-23</td>
|
||
|
|
<td class="org-right">3.1e-22</td>
|
||
|
|
<td class="org-right">-6.0e-39</td>
|
||
|
|
<td class="org-right">-1.0e-20</td>
|
||
|
|
<td class="org-right">3.1e-22</td>
|
||
|
|
<td class="org-right">4.6e-05</td>
|
||
|
|
</tr>
|
||
|
|
</tbody>
|
||
|
|
</table>
|
||
|
|
|
||
|
|
<div class="important">
|
||
|
|
<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>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org089f223" class="outline-3">
|
||
|
|
<h3 id="org089f223"><span class="section-number-3">1.5</span> Transfer function from forces applied in the legs to the displacement of the legs</h3>
|
||
|
|
<div class="outline-text-3" id="text-1-5">
|
||
|
|
<p>
|
||
|
|
Initialization of the Stewart platform.
|
||
|
|
</p>
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">stewart = initializeFramesPositions(<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 = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 60e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
|
||
|
|
stewart = computeJointsPose(stewart);
|
||
|
|
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||
|
|
stewart = computeJacobian(stewart);
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Estimation of the transfer function from \(\bm{\tau}\) to \(\bm{L}\):
|
||
|
|
</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;
|
||
|
|
|
||
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||
|
|
mdl = <span class="org-string">'stewart_platform_dynamics'</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">'/J-T'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
io(io_i) = linio([mdl, <span class="org-string">'/L'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||
|
|
|
||
|
|
<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">'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">freqs = logspace(1, 3, 1000);
|
||
|
|
<span class="org-type">figure</span>; bode(G, 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freqs)
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">bodeFig({G(1,1), G(1,2)}, freqs, struct(<span class="org-string">'phase'</span>, <span class="org-constant">true</span>));
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div id="postamble" class="status">
|
||
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
||
|
|
<p class="date">Created: 2020-01-22 mer. 16:31</p>
|
||
|
|
</div>
|
||
|
|
</body>
|
||
|
|
</html>
|