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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-01-27 lun. 17:40 -->
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<!-- 2020-01-28 mar. 13:39 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Stewart Platforms</title>
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<h1 class="title">Stewart Platforms</h1>
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<p>
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The goal here is to provide a Matlab/Simscape Toolbox to study Stewart platforms.
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The goal of this project is to provide a Matlab/Simscape Toolbox to study Stewart platforms.
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</p>
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<div id="outline-container-orgf137e1a" class="outline-2">
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<h2 id="orgf137e1a"><span class="section-number-2">1</span> Simulink Project (<a href="simulink-project.html">link</a>)</h2>
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</div>
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<div id="outline-container-org67d7b56" class="outline-2">
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<h2 id="org67d7b56"><span class="section-number-2">2</span> Stewart Platform Architecture Definition (<a href="stewart-architecture.html">link</a>)</h2>
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</div>
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<div id="outline-container-org740c1af" class="outline-2">
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<h2 id="org740c1af"><span class="section-number-2">3</span> Simscape Model of the Stewart Platform (<a href="simscape-model.html">link</a>)</h2>
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</div>
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<div id="outline-container-orgde95161" class="outline-2">
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<h2 id="orgde95161"><span class="section-number-2">4</span> Kinematic Analysis (<a href="kinematic-study.html">link</a>)</h2>
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<div class="outline-text-2" id="text-4">
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<ul class="org-ul">
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<li>Jacobian Analysis</li>
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<li>Stiffness Analysis</li>
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<li>Static Forces</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgeae2d7c" class="outline-2">
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<h2 id="orgeae2d7c"><span class="section-number-2">5</span> Identification of the Stewart Dynamics (<a href="identification.html">link</a>)</h2>
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<div class="outline-text-2" id="text-5">
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<ul class="org-ul">
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<li>Extraction of State Space models</li>
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<li>Resonant Frequencies and Modal Damping</li>
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<li>Mode Shapes</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org748e065" class="outline-2">
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<h2 id="org748e065"><span class="section-number-2">6</span> Active Damping (<a href="active-damping.html">link</a>)</h2>
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<div class="outline-text-2" id="text-6">
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<ul class="org-ul">
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<li>Inertial Sensor</li>
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<li>Force Sensor</li>
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<li>Relative Motion Sensor</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org905e69f" class="outline-2">
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<h2 id="org905e69f"><span class="section-number-2">7</span> Control of the Stewart Platform (<a href="control-study.html">link</a>)</h2>
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</div>
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<div id="outline-container-org57e9202" class="outline-2">
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<h2 id="org57e9202"><span class="section-number-2">8</span> Cubic Configuration (<a href="cubic-configuration.html">link</a>)</h2>
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</div>
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<div id="outline-container-orgb6982d7" class="outline-2">
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<h2 id="orgb6982d7"><span class="section-number-2">9</span> Architecture Optimization</h2>
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</div>
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<p>
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<a href="ref.bib">ref.bib</a>
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The project is divided into several section listed below.
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</p>
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<div id="outline-container-org2246378" class="outline-2">
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<h2 id="org2246378"><span class="section-number-2">1</span> Simulink Project (<a href="simulink-project.html">link</a>)</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The project is managed with a <b>Simulink Project</b>.
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Such project is briefly presented <a href="simulink-project.html">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-org213a021" class="outline-2">
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<h2 id="org213a021"><span class="section-number-2">2</span> Stewart Platform Architecture Definition (<a href="stewart-architecture.html">link</a>)</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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The way the Stewart Platform is defined <a href="stewart-architecture.html">here</a>.
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</p>
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<p>
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All the geometrical parameters are defined including:
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</p>
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<ul class="org-ul">
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<li>Definition of the location of the frames</li>
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<li>Size of the platforms and the limbs</li>
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<li>Location/orientation of the limbs</li>
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</ul>
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<p>
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Other parameters are also defined such as:
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</p>
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<ul class="org-ul">
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<li>Stiffness and damping of the struts</li>
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<li>Inertia of the different elements</li>
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<li>Rest position of the Stewart platform</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org43ed1d4" class="outline-2">
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<h2 id="org43ed1d4"><span class="section-number-2">3</span> Simscape Model of the Stewart Platform (<a href="simscape-model.html">link</a>)</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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The Stewart Platform is then modeled using <a href="https://www.mathworks.com/products/simscape.html">Simscape</a>.
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</p>
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<p>
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The way to model is build and works is explained <a href="simscape-model.html">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-org5851cea" class="outline-2">
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<h2 id="org5851cea"><span class="section-number-2">4</span> Kinematic Analysis (<a href="kinematic-study.html">link</a>)</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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From the defined geometry of the Stewart platform, we can perform static analysis such as:
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</p>
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<ul class="org-ul">
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<li><b>Jacobian Analysis</b> that links the velocity of each limb to the velocity of the mobile platform</li>
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<li><b>Static Forces Analysis</b> that links the forces applied by each limb to the resulting force/torque applied to the mobile platform</li>
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</ul>
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<p>
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From the strut stiffness, we can also perform a <b>Stiffness Analysis</b> that consists of determining the Stiffness matrix and Compliance matrix of the Stewart platform from the geometry.
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</p>
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<p>
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All these analysis are described <a href="kinematic-study.html">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-orgcc5dd70" class="outline-2">
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<h2 id="orgcc5dd70"><span class="section-number-2">5</span> Identification of the Stewart Dynamics (<a href="identification.html">link</a>)</h2>
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<div class="outline-text-2" id="text-5">
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<p>
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The Dynamics of the Stewart platform can be identified using the Simscape model.
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</p>
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<p>
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It is possible to:
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</p>
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<ul class="org-ul">
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<li>Determine the dynamics from the actuators to the various sensors included in the Stewart platform</li>
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<li>Extract State Space models for further analysis / control synthesis</li>
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<li>Extract the Resonant Frequencies, Modal Damping, and associated Mode Shapes</li>
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</ul>
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<p>
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The code that is used for identification is explained <a href="identification.html">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-org58fb0b9" class="outline-2">
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<h2 id="org58fb0b9"><span class="section-number-2">6</span> Active Damping (<a href="active-damping.html">link</a>)</h2>
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<div class="outline-text-2" id="text-6">
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<p>
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The use of different sensors are compared for active damping:
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</p>
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<ul class="org-ul">
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<li>Inertial Sensor in each strut</li>
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<li>Inertial Sensor fixed to the mobile platform</li>
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<li>Force Sensor in each strut</li>
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<li>Relative Motion Sensor in each strut</li>
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</ul>
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<p>
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The result of the analysis is accessible <a href="active-damping.html">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-orgb149881" class="outline-2">
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<h2 id="orgb149881"><span class="section-number-2">7</span> Motion Control of the Stewart Platform (<a href="control-study.html">link</a>)</h2>
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<div class="outline-text-2" id="text-7">
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<p>
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Some control architecture for motion control of the Stewart platform are applied on the Simscape model and compared in <a href="control-study.html">this</a> document.
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</p>
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</div>
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</div>
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<div id="outline-container-org6bf9b4a" class="outline-2">
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<h2 id="org6bf9b4a"><span class="section-number-2">8</span> Cubic Configuration (<a href="cubic-configuration.html">link</a>)</h2>
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<div class="outline-text-2" id="text-8">
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<p>
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The cubic configuration is a special class of Stewart platform that has interesting properties.
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</p>
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<p>
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These properties are studied in <a href="cubic-configuration.html">this</a> document.
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</p>
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</div>
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</div>
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</div>
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</body>
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</html>
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58
index.org
58
index.org
@ -22,37 +22,65 @@
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:END:
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* Introduction :ignore:
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The goal here is to provide a Matlab/Simscape Toolbox to study Stewart platforms.
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The goal of this project is to provide a Matlab/Simscape Toolbox to study Stewart platforms.
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The project is divided into several section listed below.
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* Simulink Project ([[file:simulink-project.org][link]])
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The project is managed with a *Simulink Project*.
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Such project is briefly presented [[file:simulink-project.org][here]].
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* Stewart Platform Architecture Definition ([[file:stewart-architecture.org][link]])
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The way the Stewart Platform is defined [[file:stewart-architecture.org][here]].
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All the geometrical parameters are defined including:
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- Definition of the location of the frames
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- Size of the platforms and the limbs
|
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- Location/orientation of the limbs
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||||
|
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Other parameters are also defined such as:
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- Stiffness and damping of the struts
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- Inertia of the different elements
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- Rest position of the Stewart platform
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* Simscape Model of the Stewart Platform ([[file:simscape-model.org][link]])
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The Stewart Platform is then modeled using [[https://www.mathworks.com/products/simscape.html][Simscape]].
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The way to model is build and works is explained [[file:simscape-model.org][here]].
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* Kinematic Analysis ([[file:kinematic-study.org][link]])
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- Jacobian Analysis
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- Stiffness Analysis
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- Static Forces
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From the defined geometry of the Stewart platform, we can perform static analysis such as:
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- *Jacobian Analysis* that links the velocity of each limb to the velocity of the mobile platform
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- *Static Forces Analysis* that links the forces applied by each limb to the resulting force/torque applied to the mobile platform
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From the strut stiffness, we can also perform a *Stiffness Analysis* that consists of determining the Stiffness matrix and Compliance matrix of the Stewart platform from the geometry.
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All these analysis are described [[file:kinematic-study.org][here]].
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||||
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* Identification of the Stewart Dynamics ([[file:identification.org][link]])
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- Extraction of State Space models
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- Resonant Frequencies and Modal Damping
|
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- Mode Shapes
|
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The Dynamics of the Stewart platform can be identified using the Simscape model.
|
||||
|
||||
It is possible to:
|
||||
- Determine the dynamics from the actuators to the various sensors included in the Stewart platform
|
||||
- Extract State Space models for further analysis / control synthesis
|
||||
- Extract the Resonant Frequencies, Modal Damping, and associated Mode Shapes
|
||||
|
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The code that is used for identification is explained [[file:identification.org][here]].
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||||
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* Active Damping ([[file:active-damping.org][link]])
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- Inertial Sensor
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- Force Sensor
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- Relative Motion Sensor
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The use of different sensors are compared for active damping:
|
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- Inertial Sensor in each strut
|
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- Inertial Sensor fixed to the mobile platform
|
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- Force Sensor in each strut
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- Relative Motion Sensor in each strut
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* Control of the Stewart Platform ([[file:control-study.org][link]])
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The result of the analysis is accessible [[file:active-damping.org][here]].
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* Motion Control of the Stewart Platform ([[file:control-study.org][link]])
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Some control architecture for motion control of the Stewart platform are applied on the Simscape model and compared in [[file:control-study.org][this]] document.
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* Cubic Configuration ([[file:cubic-configuration.org][link]])
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The cubic configuration is a special class of Stewart platform that has interesting properties.
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* Architecture Optimization
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These properties are studied in [[file:cubic-configuration.org][this]] document.
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* Bibliography :ignore:
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bibliographystyle:unsrt
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bibliography:ref.bib
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