1058 lines
60 KiB
HTML
1058 lines
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HTML
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<div id="content">
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<h1 class="title">Stewart Platform - Simscape Model</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="#org527cc13">1. initializeGeneralConfiguration</a>
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<ul>
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<li><a href="#orgea5f8f5">1.1. Function description</a></li>
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<li><a href="#org2db42cb">1.2. Optional Parameters</a></li>
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<li><a href="#org2f9279a">1.3. Geometry Description</a></li>
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<li><a href="#org1409cf0">1.4. Compute Aa and Ab</a></li>
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<li><a href="#orgb91c416">1.5. Returns Stewart Structure</a></li>
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</ul>
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</li>
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<li><a href="#orgc3aa910">2. computeGeometricalProperties</a>
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<ul>
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<li><a href="#org180196f">2.1. Function description</a></li>
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<li><a href="#org12cee4f">2.2. Optional Parameters</a></li>
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<li><a href="#org0010af5">2.3. Rotation matrices</a></li>
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<li><a href="#org98f4bad">2.4. Jacobian matrices</a></li>
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</ul>
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</li>
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<li><a href="#orgb3e53d1">3. initializeMechanicalElements</a>
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<ul>
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<li><a href="#orge7f185e">3.1. Function description</a></li>
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<li><a href="#org6bd219d">3.2. Optional Parameters</a></li>
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<li><a href="#org8d0d9c0">3.3. Bottom Plate</a></li>
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<li><a href="#org23fd88c">3.4. Top Plate</a></li>
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<li><a href="#org96d7dab">3.5. Legs</a></li>
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<li><a href="#org66df86f">3.6. Ball Joints</a></li>
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</ul>
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</li>
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<li><a href="#orgf3c4474">4. initializeSample</a>
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<ul>
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<li><a href="#org1ec4152">4.1. Function description</a></li>
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<li><a href="#orgcd3268d">4.2. Optional Parameters</a></li>
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<li><a href="#org29ee9ed">4.3. Save the Sample structure</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>
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<p>
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Stewart platforms are generated in multiple steps.
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</p>
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<p>
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First, geometrical parameters are defined:
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</p>
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<ul class="org-ul">
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<li>\({}^Aa_i\) - Position of the joints fixed to the fixed base w.r.t \(\{A\}\)</li>
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<li>\({}^Ab_i\) - Position of the joints fixed to the mobile platform w.r.t \(\{A\}\)</li>
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<li>\({}^Bb_i\) - Position of the joints fixed to the mobile platform w.r.t \(\{B\}\)</li>
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<li>\(H\) - Total height of the mobile platform</li>
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</ul>
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<p>
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These parameter are enough to determine all the kinematic properties of the platform like the Jacobian, stroke, stiffness, …
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These geometrical parameters can be generated using different functions: <code>initializeCubicConfiguration</code> for cubic configuration or <code>initializeGeneralConfiguration</code> for more general configuration.
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</p>
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<p>
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A function <code>computeGeometricalProperties</code> is then used to compute:
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</p>
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<ul class="org-ul">
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<li>\(J_f\) - Jacobian matrix for the force location</li>
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<li>\(J_d\) - Jacobian matrix for displacement estimation</li>
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<li>\(R_m\) - Rotation matrices to position the leg vectors</li>
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</ul>
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<p>
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Then, geometrical parameters are computed for all the mechanical elements with the function <code>initializeMechanicalElements</code>:
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</p>
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<ul class="org-ul">
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<li>Shape of the platforms
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<ul class="org-ul">
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<li>External Radius</li>
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<li>Internal Radius</li>
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<li>Density</li>
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<li>Thickness</li>
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</ul></li>
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<li>Shape of the Legs
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<ul class="org-ul">
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<li>Radius</li>
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<li>Size of ball joint</li>
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<li>Density</li>
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</ul></li>
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</ul>
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<p>
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Other Parameters are defined for the Simscape simulation:
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</p>
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<ul class="org-ul">
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<li>Sample mass, volume and position (<code>initializeSample</code> function)</li>
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<li>Location of the inertial sensor</li>
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<li>Location of the point for the differential measurements</li>
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<li>Location of the Jacobian point for velocity/displacement computation</li>
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</ul>
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<div id="outline-container-org527cc13" class="outline-2">
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<h2 id="org527cc13"><span class="section-number-2">1</span> initializeGeneralConfiguration</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-orgea5f8f5" class="outline-3">
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<h3 id="orgea5f8f5"><span class="section-number-3">1.1</span> Function description</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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|
The <code>initializeGeneralConfiguration</code> function takes one structure that contains configurations for the hexapod and returns one structure representing the Hexapod.
|
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</p>
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<div class="org-src-container">
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|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">initializeGeneralConfiguration</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">opts_param</span><span style="color: #DCDCCC;">)</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-org2db42cb" class="outline-3">
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<h3 id="org2db42cb"><span class="section-number-3">1.2</span> Optional Parameters</h3>
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<div class="outline-text-3" id="text-1-2">
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<p>
|
|
Default values for opts.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">opts = struct<span style="color: #DCDCCC;">(</span><span style="text-decoration: underline;">...</span>
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<span style="color: #CC9393;">'H_tot'</span>, <span style="color: #BFEBBF;">90</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Height of the platform [mm]</span>
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<span style="color: #CC9393;">'H_joint'</span>, <span style="color: #BFEBBF;">15</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Height of the joints [mm]</span>
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<span style="color: #CC9393;">'H_plate'</span>, <span style="color: #BFEBBF;">10</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Thickness of the fixed and mobile platforms [mm]</span>
|
|
<span style="color: #CC9393;">'R_bot'</span>, <span style="color: #BFEBBF;">100</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Radius where the legs articulations are positionned [mm]</span>
|
|
<span style="color: #CC9393;">'R_top'</span>, <span style="color: #BFEBBF;">80</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Radius where the legs articulations are positionned [mm]</span>
|
|
<span style="color: #CC9393;">'a_bot'</span>, <span style="color: #BFEBBF;">10</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Angle Offset [deg]</span>
|
|
<span style="color: #CC9393;">'a_top'</span>, <span style="color: #BFEBBF;">40</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Angle Offset [deg]</span>
|
|
<span style="color: #CC9393;">'da_top'</span>, <span style="color: #BFEBBF;">0</span> <span style="text-decoration: underline;">...</span> % Angle Offset from <span style="color: #BFEBBF;">0</span> position [deg]
|
|
<span style="color: #DCDCCC;">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Populate opts with input parameters
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">if</span> exist<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'opts_param','var'</span><span style="color: #DCDCCC;">)</span>
|
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">opt</span> = <span style="color: #BFEBBF;">fieldnames</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">opts_param</span><span style="color: #DCDCCC;">)</span><span style="color: #BFEBBF;">'</span>
|
|
opts.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span> = opts_param.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2f9279a" class="outline-3">
|
|
<h3 id="org2f9279a"><span class="section-number-3">1.3</span> Geometry Description</h3>
|
|
<div class="outline-text-3" id="text-1-3">
|
|
|
|
<div id="orgc30ce24" class="figure">
|
|
<p><img src="./figs/stewart_bottom_plate.png" alt="stewart_bottom_plate.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Schematic of the bottom plates with all the parameters</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1409cf0" class="outline-3">
|
|
<h3 id="org1409cf0"><span class="section-number-3">1.4</span> Compute Aa and Ab</h3>
|
|
<div class="outline-text-3" id="text-1-4">
|
|
<p>
|
|
We compute \([a_1, a_2, a_3, a_4, a_5, a_6]^T\) and \([b_1, b_2, b_3, b_4, b_5, b_6]^T\).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Aa = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
|
Ab = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
|
Bb = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">3</span>
|
|
Aa<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = <span style="color: #DCDCCC;">[</span>opts.R_bot<span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">-</span> opts.a_bot<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
|
opts.R_bot<span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">-</span> opts.a_bot<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
|
opts.H_plate<span style="color: #7CB8BB;">+</span>opts.H_joint<span style="color: #DCDCCC;">]</span>;
|
|
Aa<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = <span style="color: #DCDCCC;">[</span>opts.R_bot<span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> opts.a_bot<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
|
opts.R_bot<span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> opts.a_bot<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
|
opts.H_plate<span style="color: #7CB8BB;">+</span>opts.H_joint<span style="color: #DCDCCC;">]</span>;
|
|
|
|
Ab<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = <span style="color: #DCDCCC;">[</span>opts.R_top<span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> opts.da_top <span style="color: #7CB8BB;">-</span> opts.a_top<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
|
opts.R_top<span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> opts.da_top <span style="color: #7CB8BB;">-</span> opts.a_top<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
|
opts.H_tot <span style="color: #7CB8BB;">-</span> opts.H_plate <span style="color: #7CB8BB;">-</span> opts.H_joint<span style="color: #DCDCCC;">]</span>;
|
|
Ab<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = <span style="color: #DCDCCC;">[</span>opts.R_top<span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> opts.da_top <span style="color: #7CB8BB;">+</span> opts.a_top<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
|
opts.R_top<span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> opts.da_top <span style="color: #7CB8BB;">+</span> opts.a_top<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
|
opts.H_tot <span style="color: #7CB8BB;">-</span> opts.H_plate <span style="color: #7CB8BB;">-</span> opts.H_joint<span style="color: #DCDCCC;">]</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
|
|
Bb = Ab <span style="color: #7CB8BB;">-</span> opts.H_tot<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>,<span style="color: #BFEBBF;">0</span>,<span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">]</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb91c416" class="outline-3">
|
|
<h3 id="orgb91c416"><span class="section-number-3">1.5</span> Returns Stewart Structure</h3>
|
|
<div class="outline-text-3" id="text-1-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"> stewart = struct<span style="color: #DCDCCC;">()</span>;
|
|
stewart.Aa = Aa;
|
|
stewart.Ab = Ab;
|
|
stewart.Bb = Bb;
|
|
stewart.H_tot = opts.H_tot;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc3aa910" class="outline-2">
|
|
<h2 id="orgc3aa910"><span class="section-number-2">2</span> computeGeometricalProperties</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
</div>
|
|
|
|
<div id="outline-container-org180196f" class="outline-3">
|
|
<h3 id="org180196f"><span class="section-number-3">2.1</span> Function description</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">computeGeometricalProperties</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">stewart</span>, <span style="color: #DFAF8F;">opts_param</span><span style="color: #DCDCCC;">)</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org12cee4f" class="outline-3">
|
|
<h3 id="org12cee4f"><span class="section-number-3">2.2</span> Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<p>
|
|
Default values for opts.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">opts = struct<span style="color: #DCDCCC;">(</span><span style="text-decoration: underline;">...</span>
|
|
<span style="color: #CC9393;">'Jd_pos'</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">30</span><span style="color: #BFEBBF;">]</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
|
<span style="color: #CC9393;">'Jf_pos'</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">30</span><span style="color: #BFEBBF;">]</span> <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
|
<span style="color: #DCDCCC;">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Populate opts with input parameters
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">if</span> exist<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'opts_param','var'</span><span style="color: #DCDCCC;">)</span>
|
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">opt</span> = <span style="color: #BFEBBF;">fieldnames</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">opts_param</span><span style="color: #DCDCCC;">)</span><span style="color: #BFEBBF;">'</span>
|
|
opts.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span> = opts_param.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0010af5" class="outline-3">
|
|
<h3 id="org0010af5"><span class="section-number-3">2.3</span> Rotation matrices</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<p>
|
|
We initialize \(l_i\) and \(\hat{s}_i\)
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">leg_length = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
|
leg_vectors = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We compute \(b_i - a_i\), and then:
|
|
</p>
|
|
\begin{align*}
|
|
l_i &= \left|b_i - a_i\right| \\
|
|
\hat{s}_i &= \frac{b_i - a_i}{l_i}
|
|
\end{align*}
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">legs = stewart.Ab <span style="color: #7CB8BB;">-</span> stewart.Aa;
|
|
|
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">6</span>
|
|
leg_length<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #DCDCCC;">)</span> = norm<span style="color: #DCDCCC;">(</span>legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
|
leg_vectors<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = legs<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> <span style="color: #7CB8BB;">/</span> leg_length<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #DCDCCC;">)</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We compute rotation matrices to have the orientation of the legs.
|
|
The rotation matrix transforms the \(z\) axis to the axis of the leg. The other axis are not important here.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">stewart.Rm = struct<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'R'</span>, eye<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
|
|
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">6</span>
|
|
sx = cross<span style="color: #DCDCCC;">(</span>leg_vectors<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #BFEBBF;">]</span><span style="color: #DCDCCC;">)</span>;
|
|
sx = sx<span style="color: #7CB8BB;">/</span>norm<span style="color: #DCDCCC;">(</span>sx<span style="color: #DCDCCC;">)</span>;
|
|
|
|
sy = <span style="color: #7CB8BB;">-</span>cross<span style="color: #DCDCCC;">(</span>sx, leg_vectors<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
|
sy = sy<span style="color: #7CB8BB;">/</span>norm<span style="color: #DCDCCC;">(</span>sy<span style="color: #DCDCCC;">)</span>;
|
|
|
|
sz = leg_vectors<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span>;
|
|
sz = sz<span style="color: #7CB8BB;">/</span>norm<span style="color: #DCDCCC;">(</span>sz<span style="color: #DCDCCC;">)</span>;
|
|
|
|
stewart.Rm<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #DCDCCC;">)</span>.R = <span style="color: #DCDCCC;">[</span>sx', sy', sz'<span style="color: #DCDCCC;">]</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org98f4bad" class="outline-3">
|
|
<h3 id="org98f4bad"><span class="section-number-3">2.4</span> Jacobian matrices</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<p>
|
|
Compute Jacobian Matrix
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Jd = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span>;
|
|
|
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">6</span>
|
|
Jd<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span> = leg_vectors<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span>;
|
|
Jd<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">4</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span> = cross<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">001</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">(</span>stewart.Bb<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #D0BF8F;">)</span> <span style="color: #7CB8BB;">-</span> opts.Jd_pos<span style="color: #BFEBBF;">)</span>, leg_vectors<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
|
|
stewart.Jd = Jd;
|
|
stewart.Jd_inv = inv<span style="color: #DCDCCC;">(</span>Jd<span style="color: #DCDCCC;">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Jf = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span>;
|
|
|
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">6</span>
|
|
Jf<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span> = leg_vectors<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span>;
|
|
Jf<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">4</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span> = cross<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">001</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">(</span>stewart.Bb<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #D0BF8F;">)</span> <span style="color: #7CB8BB;">-</span> opts.Jf_pos<span style="color: #BFEBBF;">)</span>, leg_vectors<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
|
|
stewart.Jf = Jf;
|
|
stewart.Jf_inv = inv<span style="color: #DCDCCC;">(</span>Jf<span style="color: #DCDCCC;">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb3e53d1" class="outline-2">
|
|
<h2 id="orgb3e53d1"><span class="section-number-2">3</span> initializeMechanicalElements</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
</div>
|
|
|
|
<div id="outline-container-orge7f185e" class="outline-3">
|
|
<h3 id="orge7f185e"><span class="section-number-3">3.1</span> Function description</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">initializeMechanicalElements</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">stewart</span>, <span style="color: #DFAF8F;">opts_param</span><span style="color: #DCDCCC;">)</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6bd219d" class="outline-3">
|
|
<h3 id="org6bd219d"><span class="section-number-3">3.2</span> Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
<p>
|
|
Default values for opts.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">opts = struct<span style="color: #DCDCCC;">(</span><span style="text-decoration: underline;">...</span>
|
|
<span style="color: #CC9393;">'thickness'</span>, <span style="color: #BFEBBF;">10</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Thickness of the base and platform [mm]</span>
|
|
<span style="color: #CC9393;">'density'</span>, <span style="color: #BFEBBF;">1000</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Density of the material used for the hexapod [kg/m3]</span>
|
|
<span style="color: #CC9393;">'k_ax'</span>, <span style="color: #BFEBBF;">1e8</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Stiffness of each actuator [N/m]</span>
|
|
<span style="color: #CC9393;">'c_ax'</span>, <span style="color: #BFEBBF;">1000</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Damping of each actuator [N/(m/s)]</span>
|
|
<span style="color: #CC9393;">'stroke'</span>, <span style="color: #BFEBBF;">50e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span> <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Maximum stroke of each actuator [m]</span>
|
|
<span style="color: #DCDCCC;">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Populate opts with input parameters
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">if</span> exist<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'opts_param','var'</span><span style="color: #DCDCCC;">)</span>
|
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">opt</span> = <span style="color: #BFEBBF;">fieldnames</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">opts_param</span><span style="color: #DCDCCC;">)</span><span style="color: #BFEBBF;">'</span>
|
|
opts.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span> = opts_param.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8d0d9c0" class="outline-3">
|
|
<h3 id="org8d0d9c0"><span class="section-number-3">3.3</span> Bottom Plate</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
|
|
<div id="org38598b1" class="figure">
|
|
<p><img src="./figs/stewart_bottom_plate.png" alt="stewart_bottom_plate.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Schematic of the bottom plates with all the parameters</p>
|
|
</div>
|
|
|
|
<p>
|
|
The bottom plate structure is initialized.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">BP = struct<span style="color: #DCDCCC;">()</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We defined its internal radius (if there is a hole in the bottom plate) and its outer radius.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">BP.Rint = <span style="color: #BFEBBF;">0</span>; <span style="color: #7F9F7F;">% Internal Radius [mm]</span>
|
|
BP.Rext = <span style="color: #BFEBBF;">150</span>; <span style="color: #7F9F7F;">% External Radius [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We define its thickness.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">BP.H = opts.thickness; <span style="color: #7F9F7F;">% Thickness of the Bottom Plate [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We defined the density of the material of the bottom plate.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">BP.density = opts.density; <span style="color: #7F9F7F;">% Density of the material [kg/m3]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And its color.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">BP.color = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span><span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% Color [RGB]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then the profile of the bottom plate is computed and will be used by Simscape
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">BP.shape = <span style="color: #DCDCCC;">[</span>BP.Rint BP.H; BP.Rint <span style="color: #BFEBBF;">0</span>; BP.Rext <span style="color: #BFEBBF;">0</span>; BP.Rext BP.H<span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The structure is added to the stewart structure
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">stewart.BP = BP;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org23fd88c" class="outline-3">
|
|
<h3 id="org23fd88c"><span class="section-number-3">3.4</span> Top Plate</h3>
|
|
<div class="outline-text-3" id="text-3-4">
|
|
<p>
|
|
The top plate structure is initialized.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">TP = struct<span style="color: #DCDCCC;">()</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We defined the internal and external radius of the top plate.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">TP.Rint = <span style="color: #BFEBBF;">0</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
|
TP.Rext = <span style="color: #BFEBBF;">100</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The thickness of the top plate.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">TP.H = <span style="color: #BFEBBF;">10</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The density of its material.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">TP.density = opts.density; <span style="color: #7F9F7F;">% Density of the material [kg/m3]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Its color.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">TP.color = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span><span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% Color [RGB]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then the shape of the top plate is computed
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">TP.shape = <span style="color: #DCDCCC;">[</span>TP.Rint TP.H; TP.Rint <span style="color: #BFEBBF;">0</span>; TP.Rext <span style="color: #BFEBBF;">0</span>; TP.Rext TP.H<span style="color: #DCDCCC;">]</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The structure is added to the stewart structure
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">stewart.TP = TP;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org96d7dab" class="outline-3">
|
|
<h3 id="org96d7dab"><span class="section-number-3">3.5</span> Legs</h3>
|
|
<div class="outline-text-3" id="text-3-5">
|
|
|
|
<div id="orga9ade83" class="figure">
|
|
<p><img src="./figs/stewart_legs.png" alt="stewart_legs.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Schematic for the legs of the Stewart platform</p>
|
|
</div>
|
|
|
|
<p>
|
|
The leg structure is initialized.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Leg = struct<span style="color: #DCDCCC;">()</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The maximum Stroke of each leg is defined.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Leg.stroke = opts.stroke; <span style="color: #7F9F7F;">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The stiffness and damping of each leg are defined
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Leg.k_ax = opts.k_ax; <span style="color: #7F9F7F;">% Stiffness of each leg [N/m]</span>
|
|
Leg.c_ax = opts.c_ax; <span style="color: #7F9F7F;">% Damping of each leg [N/(m/s)]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The radius of the legs are defined
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Leg.Rtop = <span style="color: #BFEBBF;">10</span>; <span style="color: #7F9F7F;">% Radius of the cylinder of the top part of the leg[mm]</span>
|
|
Leg.Rbot = <span style="color: #BFEBBF;">12</span>; <span style="color: #7F9F7F;">% Radius of the cylinder of the bottom part of the leg [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The density of its material.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Leg.density = opts.density; <span style="color: #7F9F7F;">% Density of the material used for the legs [kg/m3]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Its color.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Leg.color = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">5</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">5</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">5</span><span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% Color of the top part of the leg [RGB]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The radius of spheres representing the ball joints are defined.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Leg.R = <span style="color: #BFEBBF;">1</span>.<span style="color: #BFEBBF;">3</span><span style="color: #7CB8BB;">*</span>Leg.Rbot; <span style="color: #7F9F7F;">% Size of the sphere at the extremity of the leg [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We estimate the length of the legs.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">legs = stewart.Ab <span style="color: #7CB8BB;">-</span> stewart.Aa;
|
|
Leg.lenght = norm<span style="color: #DCDCCC;">(</span>legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>,<span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">1</span>.<span style="color: #BFEBBF;">5</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then the shape of the bottom leg is estimated
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Leg.shape.bot = <span style="text-decoration: underline;">...</span>
|
|
<span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span>; <span style="text-decoration: underline;">...</span>
|
|
Leg.Rbot <span style="color: #BFEBBF;">0</span>; <span style="text-decoration: underline;">...</span>
|
|
Leg.Rbot Leg.lenght; <span style="text-decoration: underline;">...</span>
|
|
Leg.Rtop Leg.lenght; <span style="text-decoration: underline;">...</span>
|
|
Leg.Rtop <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span>Leg.lenght; <span style="text-decoration: underline;">...</span>
|
|
<span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span>Leg.lenght<span style="color: #DCDCCC;">]</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The structure is added to the stewart structure
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">stewart.Leg = Leg;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org66df86f" class="outline-3">
|
|
<h3 id="org66df86f"><span class="section-number-3">3.6</span> Ball Joints</h3>
|
|
<div class="outline-text-3" id="text-3-6">
|
|
|
|
<div id="org250b20b" class="figure">
|
|
<p><img src="./figs/stewart_ball_joints.png" alt="stewart_ball_joints.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Schematic of the support for the ball joints</p>
|
|
</div>
|
|
|
|
<p>
|
|
<code>SP</code> is the structure representing the support for the ball joints at the extremity of each leg.
|
|
</p>
|
|
|
|
<p>
|
|
The <code>SP</code> structure is initialized.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">SP = struct<span style="color: #DCDCCC;">()</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We can define its rotational stiffness and damping. For now, we use perfect joints.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">SP.k = <span style="color: #BFEBBF;">0</span>; <span style="color: #7F9F7F;">% [N*m/deg]</span>
|
|
SP.c = <span style="color: #BFEBBF;">0</span>; <span style="color: #7F9F7F;">% [N*m/deg]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Its height is defined
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">SP.H = stewart.Aa<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span> <span style="color: #7CB8BB;">-</span> BP.H; <span style="color: #7F9F7F;">% [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Its radius is based on the radius on the sphere at the end of the legs.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">SP.R = Leg.R; <span style="color: #7F9F7F;">% [mm]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">SP.section = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span> SP.H<span style="color: #7CB8BB;">-</span>SP.R;
|
|
<span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span>;
|
|
SP.R <span style="color: #BFEBBF;">0</span>;
|
|
SP.R SP.H<span style="color: #DCDCCC;">]</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The density of its material is defined.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">SP.density = opts.density; % [kg<span style="color: #7CB8BB;">/</span>m<span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">3</span>]
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Its color is defined.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">SP.color = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span><span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% [RGB]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The structure is added to the Hexapod structure
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">stewart.SP = SP;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf3c4474" class="outline-2">
|
|
<h2 id="orgf3c4474"><span class="section-number-2">4</span> initializeSample</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
</div>
|
|
|
|
<div id="outline-container-org1ec4152" class="outline-3">
|
|
<h3 id="org1ec4152"><span class="section-number-3">4.1</span> Function description</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[]</span> = <span style="color: #93E0E3;">initializeSample</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">opts_param</span><span style="color: #DCDCCC;">)</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcd3268d" class="outline-3">
|
|
<h3 id="orgcd3268d"><span class="section-number-3">4.2</span> Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-4-2">
|
|
<p>
|
|
Default values for opts.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample = struct<span style="color: #DCDCCC;">(</span> <span style="text-decoration: underline;">...</span>
|
|
<span style="color: #CC9393;">'radius'</span>, <span style="color: #BFEBBF;">100</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% radius of the cylinder [mm]</span>
|
|
<span style="color: #CC9393;">'height'</span>, <span style="color: #BFEBBF;">100</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% height of the cylinder [mm]</span>
|
|
<span style="color: #CC9393;">'mass'</span>, <span style="color: #BFEBBF;">10</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% mass of the cylinder [kg]</span>
|
|
<span style="color: #CC9393;">'measheight'</span>, <span style="color: #BFEBBF;">50</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% measurement point z-offset [mm]</span>
|
|
<span style="color: #CC9393;">'offset'</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span><span style="color: #BFEBBF;">]</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% offset position of the sample [mm]</span>
|
|
<span style="color: #CC9393;">'color'</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">9</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">]</span> <span style="text-decoration: underline;">...</span>
|
|
<span style="color: #DCDCCC;">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Populate opts with input parameters
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">if</span> exist<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'opts_param','var'</span><span style="color: #DCDCCC;">)</span>
|
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">opt</span> = <span style="color: #BFEBBF;">fieldnames</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">opts_param</span><span style="color: #DCDCCC;">)</span><span style="color: #BFEBBF;">'</span>
|
|
sample.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span> = opts_param.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org29ee9ed" class="outline-3">
|
|
<h3 id="org29ee9ed"><span class="section-number-3">4.3</span> Save the Sample structure</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/sample.mat', 'sample'</span><span style="color: #DCDCCC;">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Thomas Dehaeze</p>
|
|
<p class="date">Created: 2019-03-25 lun. 11:18</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|