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636 lines
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<title>Stewart Platform - Simscape Model</title>
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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 - 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="#org79eeba1">1. Parameters used for the Simscape Model</a></li>
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<li><a href="#org677dd01">2. Simulation Configuration - Configuration reference</a></li>
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<li><a href="#orge89e3e7">3. Subsystem Reference</a></li>
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<li><a href="#org5f42d80">4. Subsystem - Fixed base and Mobile Platform</a></li>
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<li><a href="#orgbec2976">5. Subsystem - Struts</a></li>
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<li><a href="#org806ecc3">6. Other Elements</a>
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<ul>
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<li><a href="#orgf4bef70">6.1. Payload</a>
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<ul>
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<li><a href="#org9c0e404">Function description</a></li>
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<li><a href="#orgabc81c1">Optional Parameters</a></li>
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<li><a href="#org4ef4a9f">Add Payload Type</a></li>
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<li><a href="#org3243d76">Add Stiffness, Damping and Mass properties of the Payload</a></li>
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</ul>
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</li>
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<li><a href="#orgd9e12ef">6.2. Ground</a>
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<ul>
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<li><a href="#org920bdd0">Function description</a></li>
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<li><a href="#orgfa4bbf4">Optional Parameters</a></li>
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<li><a href="#org2d22970">Add Ground Type</a></li>
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<li><a href="#orgf76def4">Add Stiffness and Damping properties of the Ground</a></li>
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<li><a href="#orgdb67a68">Rotation Point</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#org6d3b61e">7. Initialize Disturbances</a>
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<ul>
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<li><a href="#orgf14752d">Function Declaration and Documentation</a></li>
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<li><a href="#orga64679c">Optional Parameters</a></li>
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<li><a href="#org0f7e4dd">Structure initialization</a></li>
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<li><a href="#org1a28fcd">Ground Motion</a></li>
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<li><a href="#org90b72d6">Direct Forces</a></li>
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</ul>
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</li>
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<li><a href="#org93f2d30">8. Initialize References</a>
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<ul>
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<li><a href="#orgf124972">Function Declaration and Documentation</a></li>
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<li><a href="#orgbc7950f">Optional Parameters</a></li>
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<li><a href="#org6f05adc">8.1. Compute the corresponding strut length</a></li>
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<li><a href="#orgda73a50">References</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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In this document is explained how the Simscape model of the Stewart Platform is implemented.
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</p>
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<p>
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It is divided in the following sections:
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</p>
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<ul class="org-ul">
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<li>section <a href="#orge8daba9">1</a>: is explained how the parameters of the Stewart platform are set for the Simscape model</li>
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<li>section <a href="#org11ed7ef">2</a>: the Simulink configuration (solver, simulation time, …) is shared among all the Simulink files. It is explain how this is done.</li>
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<li>section <a href="#org1a0307c">3</a>: All the elements (platforms, struts, sensors, …) are saved in separate files and imported in Simulink files using “subsystem referenced”.</li>
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<li>section <a href="#org5fac181">4</a>: The simscape model for the fixed base and mobile platform are described in this section.</li>
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<li>section <a href="#org793a5c7">5</a>: The simscape model for the Stewart platform struts is described in this section.</li>
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</ul>
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<div id="outline-container-org79eeba1" class="outline-2">
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<h2 id="org79eeba1"><span class="section-number-2">1</span> Parameters used for the Simscape Model</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orge8daba9"></a>
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The Simscape Model of the Stewart Platform is working with the <code>stewart</code> structure generated using the functions described <a href="stewart-architecture.html">here</a>.
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</p>
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<p>
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All the geometry and inertia of the mechanical elements are defined in the <code>stewart</code> structure.
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</p>
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<p>
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By updating the <code>stewart</code> structure in the workspace, the Simscape model will be automatically updated.
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</p>
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<p>
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Thus, nothing should be changed by hand inside the Simscape model.
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</p>
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<p>
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The main advantage to have all the parameters defined in one structure (and not hard-coded in some simulink blocs) it that we can easily change the Stewart architecture/parameters in a Matlab script to perform some parametric study for instance.
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</p>
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</div>
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</div>
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<div id="outline-container-org677dd01" class="outline-2">
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<h2 id="org677dd01"><span class="section-number-2">2</span> Simulation Configuration - Configuration reference</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org11ed7ef"></a>
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As multiple simulink files will be used for simulation and tests, it is very useful to determine good simulation configuration that will be <b>shared</b> among all the simulink files.
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</p>
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<p>
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This is done using something called “<b>Configuration Reference</b>” (<a href="https://fr.mathworks.com/help/simulink/ug/more-about-configuration-references.html">documentation</a>).
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</p>
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<p>
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Basically, the configuration is stored in a mat file <code>conf_simscape.mat</code> and then loaded in the workspace for it to be accessible to all the simulink models.
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It is automatically loaded when the Simulink project is open. It can be loaded manually with the command:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"> load(<span class="org-string">'mat/conf_simscape.mat'</span>);
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</pre>
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</div>
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<p>
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It is however possible to modify specific parameters just for one simulation using the <code>set_param</code> command:
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</p>
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<div class="org-src-container">
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<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);
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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-orge89e3e7" class="outline-2">
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<h2 id="orge89e3e7"><span class="section-number-2">3</span> Subsystem Reference</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="org1a0307c"></a>
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Several Stewart platform models are used, for instance one is use to study the dynamics while the other is used to apply active damping techniques.
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</p>
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<p>
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However, all the Simscape models share some subsystems using the <b>Subsystem Reference</b> Simulink block (<a href="https://fr.mathworks.com/help/simulink/ug/referenced-subsystem-1.html">documentation</a>).
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</p>
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<p>
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These shared subsystems are:
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</p>
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<ul class="org-ul">
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<li><code>Fixed_Based.slx</code> - Fixed base of the Stewart Platform</li>
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<li><code>Mobile_Platform.slx</code> - Mobile platform of the Stewart Platform</li>
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<li><code>stewart_strut.slx</code> - One strut containing two spherical/universal joints, the actuator as well as the included sensors. A parameter <code>i</code> is initialized to determine what it the “number” of the strut.</li>
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</ul>
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<p>
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These subsystems are referenced from another subsystem called <code>Stewart_Platform.slx</code> shown in figure <a href="#org18dcfb1">1</a>, that basically connect them correctly.
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This subsystem is then referenced in other simulink models for various purposes (control, analysis, simulation, …).
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</p>
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<div id="org18dcfb1" class="figure">
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<p><img src="figs/simscape_stewart_platform.png" alt="simscape_stewart_platform.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Simscape Subsystem of the Stewart platform. Encapsulate the Subsystems corresponding to the fixed base, mobile platform and all the struts.</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org5f42d80" class="outline-2">
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<h2 id="org5f42d80"><span class="section-number-2">4</span> Subsystem - Fixed base and Mobile Platform</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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<a id="org5fac181"></a>
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Both the fixed base and the mobile platform simscape models share many similarities.
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</p>
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<p>
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Their are both composed of:
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</p>
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<ul class="org-ul">
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<li>a solid body representing the platform</li>
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<li>6 rigid transform blocks to go from the frame \(\{F\}\) (resp. \(\{M\}\)) to the location of the joints.
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These rigid transform are using \({}^F\bm{a}_i\) (resp. \({}^M\bm{b}_i\)) for the position of the joint and \({}^F\bm{R}_{a_i}\) (resp. \({}^M\bm{R}_{b_i}\)) for the orientation of the joint.</li>
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</ul>
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<p>
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As always, the parameters that define the geometry are taken from the <code>stewart</code> structure.
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</p>
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<div id="org7b43415" class="figure">
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<p><img src="figs/simscape_fixed_base.png" alt="simscape_fixed_base.png" width="1000px" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Simscape Model of the Fixed base</p>
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</div>
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<div id="org7ed0d98" class="figure">
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<p><img src="figs/simscape_mobile_platform.png" alt="simscape_mobile_platform.png" width="800px" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Simscape Model of the Mobile platform</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgbec2976" class="outline-2">
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<h2 id="orgbec2976"><span class="section-number-2">5</span> Subsystem - Struts</h2>
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<div class="outline-text-2" id="text-5">
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<p>
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<a id="org793a5c7"></a>
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For the Stewart platform, the 6 struts are identical.
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Thus, all the struts used in the Stewart platform are referring to the same subsystem called <code>stewart_strut.slx</code> and shown in Figure <a href="#org96a73eb">4</a>.
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</p>
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<p>
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This strut has the following structure:
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</p>
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<ul class="org-ul">
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<li><b>Universal Joint</b> connected on the Fixed base</li>
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<li><b>Prismatic Joint</b> for the actuator</li>
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<li><b>Spherical Joint</b> connected on the Mobile platform</li>
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</ul>
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<p>
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This configuration is called <b>UPS</b>.
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</p>
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<p>
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The other common configuration <b>SPS</b> has the disadvantage of having additional passive degrees-of-freedom corresponding to the rotation of the strut around its main axis.
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This is why the <b>UPS</b> configuration is used, but other configuration can be easily implemented.
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</p>
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<div id="org96a73eb" class="figure">
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<p><img src="figs/simscape_strut.png" alt="simscape_strut.png" width="800px" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Simscape model of the Stewart platform’s strut</p>
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</div>
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<p>
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Several sensors are included in the strut that may or may not be used for control:
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</p>
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<ul class="org-ul">
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<li>Relative Displacement sensor: gives the relative displacement of the strut.</li>
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<li>Force sensor: measure the total force applied by the force actuator, the stiffness and damping forces in the direction of the strut.</li>
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<li>Inertial sensor: measure the absolute motion (velocity) of the top part of the strut in the direction of the strut.</li>
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</ul>
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<p>
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There is two main types of inertial sensor that can be used to measure the absolute motion of the top part of the strut in the direction of the strut:
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</p>
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<ul class="org-ul">
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<li>a geophone that measures the absolute velocity above some frequency</li>
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<li>an accelerometer that measures the absolute acceleration below some frequency</li>
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</ul>
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<p>
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Both inertial sensors are described bellow.
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</p>
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</div>
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</div>
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<div id="outline-container-org806ecc3" class="outline-2">
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<h2 id="org806ecc3"><span class="section-number-2">6</span> Other Elements</h2>
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<div class="outline-text-2" id="text-6">
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</div>
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<div id="outline-container-orgf4bef70" class="outline-3">
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<h3 id="orgf4bef70"><span class="section-number-3">6.1</span> Payload</h3>
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<div class="outline-text-3" id="text-6-1">
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<p>
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<a id="orgdd9802d"></a>
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</p>
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<p>
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This Matlab function is accessible <a href="../src/initializePayload.m">here</a>.
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</p>
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</div>
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<div id="outline-container-org9c0e404" class="outline-4">
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<h4 id="org9c0e404">Function description</h4>
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<div class="outline-text-4" id="text-org9c0e404">
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<div class="org-src-container">
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<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>)
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<span class="org-comment">% initializePayload - Initialize the Payload that can then be used for simulations and analysis</span>
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<span class="org-comment">%</span>
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<span class="org-comment">% Syntax: [payload] = initializePayload(args)</span>
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<span class="org-comment">%</span>
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<span class="org-comment">% Inputs:</span>
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<span class="org-comment">% - args - Structure with the following fields:</span>
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<span class="org-comment">% - type - 'none', 'rigid', 'flexible', 'cartesian'</span>
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<span class="org-comment">% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]</span>
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<span class="org-comment">% This also the position where K and C are defined</span>
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<span class="org-comment">% - K [6x1] - Stiffness of the Payload [N/m, N/rad]</span>
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<span class="org-comment">% - C [6x1] - Damping of the Payload [N/(m/s), N/(rad/s)]</span>
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<span class="org-comment">% - m [1x1] - Mass of the Payload [kg]</span>
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<span class="org-comment">% - I [3x3] - Inertia matrix for the Payload [kg*m2]</span>
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<span class="org-comment">%</span>
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<span class="org-comment">% Outputs:</span>
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<span class="org-comment">% - payload - Struture with the following properties:</span>
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<span class="org-comment">% - type - 1 (none), 2 (rigid), 3 (flexible)</span>
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<span class="org-comment">% - h [1x1] - Height of the CoM of the payload w.r.t {M} [m]</span>
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<span class="org-comment">% - K [6x1] - Stiffness of the Payload [N/m, N/rad]</span>
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<span class="org-comment">% - C [6x1] - Stiffness of the Payload [N/(m/s), N/(rad/s)]</span>
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<span class="org-comment">% - m [1x1] - Mass of the Payload [kg]</span>
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<span class="org-comment">% - I [3x3] - Inertia matrix for the Payload [kg*m2]</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-orgabc81c1" class="outline-4">
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<h4 id="orgabc81c1">Optional Parameters</h4>
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<div class="outline-text-4" id="text-orgabc81c1">
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<div class="org-src-container">
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<pre class="src src-matlab"> <span class="org-keyword">arguments</span>
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<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>
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<span class="org-variable-name">args</span>.K (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e8<span class="org-type">*</span>ones(6,1)
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<span class="org-variable-name">args</span>.C (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1<span class="org-type">*</span>ones(6,1)
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<span class="org-variable-name">args</span>.h (1,1) double {mustBeNumeric, mustBeNonnegative} = 100e<span class="org-type">-</span>3
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<span class="org-variable-name">args</span>.m (1,1) double {mustBeNumeric, mustBeNonnegative} = 10
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<span class="org-variable-name">args</span>.I (3,3) double {mustBeNumeric, mustBeNonnegative} = 1<span class="org-type">*</span>eye(3)
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<span class="org-keyword">end</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-org4ef4a9f" class="outline-4">
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<h4 id="org4ef4a9f">Add Payload Type</h4>
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<div class="outline-text-4" id="text-org4ef4a9f">
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<div class="org-src-container">
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<pre class="src src-matlab"> <span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
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<span class="org-keyword">case</span> <span class="org-string">'none'</span>
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payload.type = 1;
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<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
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payload.type = 2;
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<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
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payload.type = 3;
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<span class="org-keyword">case</span> <span class="org-string">'cartesian'</span>
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payload.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3243d76" class="outline-4">
|
|
<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;
|
|
|
|
payload.h = args.h;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd9e12ef" class="outline-3">
|
|
<h3 id="orgd9e12ef"><span class="section-number-3">6.2</span> Ground</h3>
|
|
<div class="outline-text-3" id="text-6-2">
|
|
<p>
|
|
<a id="org140423a"></a>
|
|
</p>
|
|
|
|
<p>
|
|
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 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>
|
|
</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 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">'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>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2d22970" class="outline-4">
|
|
<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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf76def4" class="outline-4">
|
|
<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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdb67a68" class="outline-4">
|
|
<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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org6d3b61e" class="outline-2">
|
|
<h2 id="org6d3b61e"><span class="section-number-2">7</span> Initialize Disturbances</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<p>
|
|
<a id="org5c942ea"></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 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>
|
|
</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 class="org-src-container">
|
|
<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>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org0f7e4dd" class="outline-3">
|
|
<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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1a28fcd" class="outline-3">
|
|
<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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org90b72d6" class="outline-3">
|
|
<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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org93f2d30" class="outline-2">
|
|
<h2 id="org93f2d30"><span class="section-number-2">8</span> Initialize References</h2>
|
|
<div class="outline-text-2" id="text-8">
|
|
<p>
|
|
<a id="orge24eeb5"></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 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>
|
|
</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 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>.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>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6f05adc" class="outline-3">
|
|
<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));
|
|
|
|
<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> ...
|
|
[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>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgda73a50" class="outline-3">
|
|
<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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2021-01-08 ven. 15:29</p>
|
|
</div>
|
|
</body>
|
|
</html>
|