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<title>Stewart Platforms</title>
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<h1 class="title">Stewart Platforms</h1>
<p>
The goal here is to provide a Matlab/Simscape Toolbox to study Stewart platforms.
The goal of this project is to provide a Matlab/Simscape Toolbox to study Stewart platforms.
</p>
<div id="outline-container-orgf137e1a" class="outline-2">
<h2 id="orgf137e1a"><span class="section-number-2">1</span> Simulink Project (<a href="simulink-project.html">link</a>)</h2>
</div>
<div id="outline-container-org67d7b56" class="outline-2">
<h2 id="org67d7b56"><span class="section-number-2">2</span> Stewart Platform Architecture Definition (<a href="stewart-architecture.html">link</a>)</h2>
</div>
<div id="outline-container-org740c1af" class="outline-2">
<h2 id="org740c1af"><span class="section-number-2">3</span> Simscape Model of the Stewart Platform (<a href="simscape-model.html">link</a>)</h2>
</div>
<div id="outline-container-orgde95161" class="outline-2">
<h2 id="orgde95161"><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">
<ul class="org-ul">
<li>Jacobian Analysis</li>
<li>Stiffness Analysis</li>
<li>Static Forces</li>
</ul>
</div>
</div>
<div id="outline-container-orgeae2d7c" class="outline-2">
<h2 id="orgeae2d7c"><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">
<ul class="org-ul">
<li>Extraction of State Space models</li>
<li>Resonant Frequencies and Modal Damping</li>
<li>Mode Shapes</li>
</ul>
</div>
</div>
<div id="outline-container-org748e065" class="outline-2">
<h2 id="org748e065"><span class="section-number-2">6</span> Active Damping (<a href="active-damping.html">link</a>)</h2>
<div class="outline-text-2" id="text-6">
<ul class="org-ul">
<li>Inertial Sensor</li>
<li>Force Sensor</li>
<li>Relative Motion Sensor</li>
</ul>
</div>
</div>
<div id="outline-container-org905e69f" class="outline-2">
<h2 id="org905e69f"><span class="section-number-2">7</span> Control of the Stewart Platform (<a href="control-study.html">link</a>)</h2>
</div>
<div id="outline-container-org57e9202" class="outline-2">
<h2 id="org57e9202"><span class="section-number-2">8</span> Cubic Configuration (<a href="cubic-configuration.html">link</a>)</h2>
</div>
<div id="outline-container-orgb6982d7" class="outline-2">
<h2 id="orgb6982d7"><span class="section-number-2">9</span> Architecture Optimization</h2>
</div>
<p>
<a href="ref.bib">ref.bib</a>
The project is divided into several section listed below.
</p>
<div id="outline-container-org2246378" class="outline-2">
<h2 id="org2246378"><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-org213a021" class="outline-2">
<h2 id="org213a021"><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 <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>Size of the platforms and the limbs</li>
<li>Location/orientation of 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>Inertia of the different elements</li>
<li>Rest position of the Stewart platform</li>
</ul>
</div>
</div>
<div id="outline-container-org43ed1d4" class="outline-2">
<h2 id="org43ed1d4"><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-org5851cea" class="outline-2">
<h2 id="org5851cea"><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-orgcc5dd70" class="outline-2">
<h2 id="orgcc5dd70"><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-org58fb0b9" class="outline-2">
<h2 id="org58fb0b9"><span class="section-number-2">6</span> Active Damping (<a href="active-damping.html">link</a>)</h2>
<div class="outline-text-2" id="text-6">
<p>
The use of different sensors are compared for active damping:
</p>
<ul class="org-ul">
<li>Inertial Sensor in each strut</li>
<li>Inertial Sensor fixed to the mobile platform</li>
<li>Force Sensor in each strut</li>
<li>Relative Motion Sensor in each strut</li>
</ul>
<p>
The result of the analysis is accessible <a href="active-damping.html">here</a>.
</p>
</div>
</div>
<div id="outline-container-orgb149881" class="outline-2">
<h2 id="orgb149881"><span class="section-number-2">7</span> Motion Control of the Stewart Platform (<a href="control-study.html">link</a>)</h2>
<div class="outline-text-2" id="text-7">
<p>
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.
</p>
</div>
</div>
<div id="outline-container-org6bf9b4a" class="outline-2">
<h2 id="org6bf9b4a"><span class="section-number-2">8</span> Cubic Configuration (<a href="cubic-configuration.html">link</a>)</h2>
<div class="outline-text-2" id="text-8">
<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>
</body>
</html>

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:END:
* Introduction :ignore:
The goal here is to provide a Matlab/Simscape Toolbox to study Stewart platforms.
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.
* Simulink Project ([[file:simulink-project.org][link]])
The project is managed with a *Simulink Project*.
Such project is briefly presented [[file:simulink-project.org][here]].
* Stewart Platform Architecture Definition ([[file:stewart-architecture.org][link]])
The way the Stewart Platform is defined [[file:stewart-architecture.org][here]].
All the geometrical parameters are defined including:
- Definition of the location of the frames
- Size of the platforms and the limbs
- Location/orientation of the limbs
Other parameters are also defined such as:
- Stiffness and damping of the struts
- Inertia of the different elements
- Rest position of the Stewart platform
* Simscape Model of the Stewart Platform ([[file:simscape-model.org][link]])
The Stewart Platform is then modeled using [[https://www.mathworks.com/products/simscape.html][Simscape]].
The way to model is build and works is explained [[file:simscape-model.org][here]].
* Kinematic Analysis ([[file:kinematic-study.org][link]])
- Jacobian Analysis
- Stiffness Analysis
- Static Forces
From the defined geometry of the Stewart platform, we can perform static analysis such as:
- *Jacobian Analysis* that links the velocity of each limb to the velocity of the mobile platform
- *Static Forces Analysis* that links the forces applied by each limb to the resulting force/torque applied to the mobile platform
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.
All these analysis are described [[file:kinematic-study.org][here]].
* Identification of the Stewart Dynamics ([[file:identification.org][link]])
- Extraction of State Space models
- Resonant Frequencies and Modal Damping
- Mode Shapes
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
The code that is used for identification is explained [[file:identification.org][here]].
* Active Damping ([[file:active-damping.org][link]])
- Inertial Sensor
- Force Sensor
- Relative Motion Sensor
The use of different sensors are compared for active damping:
- Inertial Sensor in each strut
- Inertial Sensor fixed to the mobile platform
- Force Sensor in each strut
- Relative Motion Sensor in each strut
* Control of the Stewart Platform ([[file:control-study.org][link]])
The result of the analysis is accessible [[file:active-damping.org][here]].
* Motion Control of the Stewart Platform ([[file:control-study.org][link]])
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.
* Cubic Configuration ([[file:cubic-configuration.org][link]])
The cubic configuration is a special class of Stewart platform that has interesting properties.
* Architecture Optimization
These properties are studied in [[file:cubic-configuration.org][this]] document.
* Bibliography :ignore:
bibliographystyle:unsrt
bibliography:ref.bib