<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <head> <!-- 2021-01-08 ven. 15:30 --> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <title>Stewart Platforms</title> <meta name="generator" content="Org mode" /> <meta name="author" content="Dehaeze Thomas" /> <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/> <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script> </head> <body> <div id="org-div-home-and-up"> <a accesskey="h" href="https://research.tdehaeze.xyz/"> UP </a> | <a accesskey="H" href="https://research.tdehaeze.xyz/"> HOME </a> </div><div id="content"> <h1 class="title">Stewart Platforms</h1> <div id="table-of-contents"> <h2>Table of Contents</h2> <div id="text-table-of-contents"> <ul> <li><a href="#orgad01eeb">1. Simulink Project (link)</a></li> <li><a href="#orgf0936f9">2. Stewart Platform Architecture Definition (link)</a></li> <li><a href="#org4bef8ba">3. Simscape Model of the Stewart Platform (link)</a></li> <li><a href="#orgfd134cc">4. Kinematic Analysis (link)</a></li> <li><a href="#org2e5eede">5. Identification of the Stewart Dynamics (link)</a></li> <li><a href="#orgb272d52">6. Control</a></li> <li><a href="#org7c7008e">7. Cubic Configuration (link)</a></li> <li><a href="#org1f2f2c6">8. Bibliography (link)</a></li> </ul> </div> </div> <p> The goal of this project is to provide a Matlab/Simscape Toolbox to study Stewart platforms. The project is divided into several section listed below. The git repository of the project is accessible <a href="https://git.tdehaeze.xyz/tdehaeze/stewart-simscape">here</a>. </p> <div id="outline-container-orgad01eeb" class="outline-2"> <h2 id="orgad01eeb"><span class="section-number-2">1</span> Simulink Project (<a href="simulink-project.html">link</a>)</h2> <div class="outline-text-2" id="text-1"> <p> The project is managed with a <b>Simulink Project</b>. Such project is briefly presented <a href="simulink-project.html">here</a>. </p> </div> </div> <div id="outline-container-orgf0936f9" class="outline-2"> <h2 id="orgf0936f9"><span class="section-number-2">2</span> Stewart Platform Architecture Definition (<a href="stewart-architecture.html">link</a>)</h2> <div class="outline-text-2" id="text-2"> <p> The way the Stewart Platform is defined is explained <a href="stewart-architecture.html">here</a>. </p> <p> All the geometrical parameters are defined including: </p> <ul class="org-ul"> <li>Definition of the location of the frames</li> <li>Location/orientation of the limbs</li> <li>Size/inertia of the platforms and the limbs</li> </ul> <p> Other parameters are also defined such as: </p> <ul class="org-ul"> <li>Stiffness and damping of the struts</li> <li>Rest position of the Stewart platform</li> </ul> </div> </div> <div id="outline-container-org4bef8ba" class="outline-2"> <h2 id="org4bef8ba"><span class="section-number-2">3</span> Simscape Model of the Stewart Platform (<a href="simscape-model.html">link</a>)</h2> <div class="outline-text-2" id="text-3"> <p> The Stewart Platform is then modeled using <a href="https://www.mathworks.com/products/simscape.html">Simscape</a>. </p> <p> The way to model is build and works is explained <a href="simscape-model.html">here</a>. </p> </div> </div> <div id="outline-container-orgfd134cc" class="outline-2"> <h2 id="orgfd134cc"><span class="section-number-2">4</span> Kinematic Analysis (<a href="kinematic-study.html">link</a>)</h2> <div class="outline-text-2" id="text-4"> <p> From the defined geometry of the Stewart platform, we can perform static analysis such as: </p> <ul class="org-ul"> <li><b>Jacobian Analysis</b> that links the velocity of each limb to the velocity of the mobile platform</li> <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> </ul> <p> 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. </p> <p> All these analysis are described <a href="kinematic-study.html">here</a>. </p> </div> </div> <div id="outline-container-org2e5eede" class="outline-2"> <h2 id="org2e5eede"><span class="section-number-2">5</span> Identification of the Stewart Dynamics (<a href="identification.html">link</a>)</h2> <div class="outline-text-2" id="text-5"> <p> The Dynamics of the Stewart platform can be identified using the Simscape model. </p> <p> It is possible to: </p> <ul class="org-ul"> <li>Determine the dynamics from the actuators to the various sensors included in the Stewart platform</li> <li>Extract State Space models for further analysis / control synthesis</li> <li>Extract the Resonant Frequencies, Modal Damping, and associated Mode Shapes</li> </ul> <p> The code that is used for identification is explained <a href="identification.html">here</a>. </p> </div> </div> <div id="outline-container-orgb272d52" class="outline-2"> <h2 id="orgb272d52"><span class="section-number-2">6</span> Control</h2> <div class="outline-text-2" id="text-6"> <p> The use of active control for Stewart platforms is a wide subject. Many aspect can be studied. </p> <p> The sensors used is of primary important. We can have: </p> <ul class="org-ul"> <li>Sensors located in each strut: relative motion, force sensor, inertial sensor</li> <li>Sensors measuring the relative motion between the fixed base and the mobile platform</li> <li>Inertial sensors located on the mobile platform</li> </ul> <p> The control objective can also vary: </p> <ul class="org-ul"> <li>Reference Tracking</li> <li>Active Damping</li> <li>Vibration Isolation</li> </ul> <p> The Control for Stewart platforms is here studied in the following files: </p> <ul class="org-ul"> <li><b>Active Damping</b> (<a href="control-active-damping.html">link</a>). The use of different sensors are compared for active damping: <ul class="org-ul"> <li>Inertial Sensor in each strut or fixed to the mobile platform</li> <li>Force Sensor in each strut</li> <li>Relative Motion Sensor in each strut</li> </ul></li> <li><b>Motion Control</b> (<a href="control-tracking.html">link</a>). Different control architectures (centralized and decentralized) are compared for the position control of the Stewart platform.</li> <li><b>Vibration Isolation</b> (<a href="control-vibration-isolation.html">link</a>)</li> </ul> </div> </div> <div id="outline-container-org7c7008e" class="outline-2"> <h2 id="org7c7008e"><span class="section-number-2">7</span> Cubic Configuration (<a href="cubic-configuration.html">link</a>)</h2> <div class="outline-text-2" id="text-7"> <p> The cubic configuration is a special class of Stewart platform that has interesting properties. </p> <p> These properties are studied in <a href="cubic-configuration.html">this</a> document. </p> </div> </div> <div id="outline-container-org1f2f2c6" class="outline-2"> <h2 id="org1f2f2c6"><span class="section-number-2">8</span> Bibliography (<a href="bibliography.html">link</a>)</h2> <div class="outline-text-2" id="text-8"> <p> Many text books, PhD thesis and articles related to parallel robots and Stewart platforms are gathered in <a href="bibliography.html">this</a> document. </p> </div> </div> </div> <div id="postamble" class="status"> <p class="author">Author: Dehaeze Thomas</p> <p class="date">Created: 2021-01-08 ven. 15:30</p> </div> </body> </html>