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Test of position/orientation of an Hexapod

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Thomas Dehaeze
2019-12-10 18:06:33 +01:00
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@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-12-06 ven. 12:04 -->
<!-- 2019-12-10 mar. 18:05 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Simscape Model</title>
@@ -258,64 +258,65 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org5c21e47">1. Simulink Project - Startup and Shutdown scripts</a></li>
<li><a href="#org5ca7221">2. Simscape Multibody - Presentation</a>
<li><a href="#org88d59ba">1. Simulink Project - Startup and Shutdown scripts</a></li>
<li><a href="#orga2206d5">2. Simscape Multibody - Presentation</a>
<ul>
<li><a href="#orga5fbe1d">2.1. Solid bodies</a></li>
<li><a href="#org8017e71">2.2. Frames</a></li>
<li><a href="#org486d9bf">2.3. Joints</a></li>
<li><a href="#org5a1378a">2.4. Measurements</a></li>
<li><a href="#orga435910">2.5. Excitation</a></li>
<li><a href="#org6b4540f">2.1. Solid bodies</a></li>
<li><a href="#orge470a34">2.2. Frames</a></li>
<li><a href="#org474edd3">2.3. Joints</a></li>
<li><a href="#org9171b40">2.4. Measurements</a></li>
<li><a href="#org7df2aef">2.5. Excitation</a></li>
</ul>
</li>
<li><a href="#org289000e">3. Simulink files and signal names</a>
<li><a href="#org803cadc">3. Simulink files and signal names</a>
<ul>
<li><a href="#orga9d8af9">3.1. List of Simscape files</a></li>
<li><a href="#org2a9705c">3.2. List of Inputs</a>
<li><a href="#orgb5c767a">3.1. List of Simscape files</a></li>
<li><a href="#org64dbd0d">3.2. List of Inputs</a>
<ul>
<li><a href="#org7fd5d25">3.2.1. Perturbations</a></li>
<li><a href="#org0337003">3.2.2. Measurement Noise</a></li>
<li><a href="#org250f869">3.2.3. Control Inputs</a></li>
<li><a href="#orgeecef4d">3.2.1. Perturbations</a></li>
<li><a href="#org4e58ed6">3.2.2. Measurement Noise</a></li>
<li><a href="#orgc9006ba">3.2.3. Control Inputs</a></li>
</ul>
</li>
<li><a href="#orge7abaa0">3.3. List of Outputs</a></li>
<li><a href="#orgeb985b0">3.3. List of Outputs</a></li>
</ul>
</li>
<li><a href="#org0fbeac7">4. Simulink Library</a>
<li><a href="#orgfd5289f">4. Simulink Library</a>
<ul>
<li><a href="#org3ec0c6f">4.1. <code>inputs</code></a></li>
<li><a href="#org0abb61d">4.2. <code>nass_library</code></a></li>
<li><a href="#org04c0eb4">4.3. <code>pos_error_wrt_nass_base</code></a></li>
<li><a href="#orgef1709b">4.4. <code>QuaternionToAngles</code></a></li>
<li><a href="#org8a40a80">4.5. <code>RotationMatrixToAngle</code></a></li>
<li><a href="#orgd1ebe0f">4.1. <code>inputs</code></a></li>
<li><a href="#org1ae1d37">4.2. <code>nass_library</code></a></li>
<li><a href="#org54e3d07">4.3. <code>pos_error_wrt_nass_base</code></a></li>
<li><a href="#orgc0f0f02">4.4. <code>QuaternionToAngles</code></a></li>
<li><a href="#orgbda19ed">4.5. <code>RotationMatrixToAngle</code></a></li>
</ul>
</li>
<li><a href="#org81a7962">5. Functions</a>
<li><a href="#org54193c9">5. Functions</a>
<ul>
<li><a href="#orge3706e5">5.1. computePsdDispl</a></li>
<li><a href="#org14a492d">5.2. computeSetpoint</a></li>
<li><a href="#org3e9a86f">5.3. converErrorBasis</a></li>
<li><a href="#org14d5b4c">5.4. generateDiagPidControl</a></li>
<li><a href="#org5876af4">5.5. identifyPlant</a></li>
<li><a href="#orgd01681b">5.6. runSimulation</a></li>
<li><a href="#orgc1f5840">5.1. computePsdDispl</a></li>
<li><a href="#org0d8e9e6">5.2. computeSetpoint</a></li>
<li><a href="#org9a191e3">5.3. converErrorBasis</a></li>
<li><a href="#org2d44efa">5.4. generateDiagPidControl</a></li>
<li><a href="#org6f7736a">5.5. identifyPlant</a></li>
<li><a href="#org32dd782">5.6. runSimulation</a></li>
</ul>
</li>
<li><a href="#orgc88bb4f">6. Initialize Elements</a>
<li><a href="#org5cc2276">6. Initialize Elements</a>
<ul>
<li><a href="#org53e8eea">6.1. Experiment</a></li>
<li><a href="#orgd101ec3">6.2. Generate Reference Signals</a></li>
<li><a href="#org15d2680">6.3. <span class="todo TODO">TODO</span> Inputs</a></li>
<li><a href="#org2b6b02d">6.4. Ground</a></li>
<li><a href="#orge2875ed">6.5. Granite</a></li>
<li><a href="#org61ee0ba">6.6. Translation Stage</a></li>
<li><a href="#orgdba0ed0">6.7. Tilt Stage</a></li>
<li><a href="#org6d74dd3">6.8. Spindle</a></li>
<li><a href="#orgde1ec20">6.9. Micro Hexapod</a></li>
<li><a href="#orgbfe4e10">6.10. Center of gravity compensation</a></li>
<li><a href="#org1c8d312">6.11. Mirror</a></li>
<li><a href="#orgf75cc87">6.12. Nano Hexapod</a></li>
<li><a href="#orgbb8d5dd">6.13. Cedrat Actuator</a></li>
<li><a href="#orgbb20f65">6.14. Sample</a></li>
<li><a href="#org664a7e3">6.1. Experiment</a></li>
<li><a href="#org89c58f8">6.2. Generate Reference Signals</a></li>
<li><a href="#org77d160f">6.3. <span class="todo TODO">TODO</span> Inputs</a></li>
<li><a href="#org962187e">6.4. Ground</a></li>
<li><a href="#org198c366">6.5. Granite</a></li>
<li><a href="#org6e967d2">6.6. Translation Stage</a></li>
<li><a href="#org6c95b53">6.7. Tilt Stage</a></li>
<li><a href="#org13271e7">6.8. Spindle</a></li>
<li><a href="#org3c482fe">6.9. Initialize Hexapod legs' length</a></li>
<li><a href="#org7c295aa">6.10. Micro Hexapod</a></li>
<li><a href="#org72492f3">6.11. Center of gravity compensation</a></li>
<li><a href="#org68d031b">6.12. Mirror</a></li>
<li><a href="#org74149ff">6.13. Nano Hexapod</a></li>
<li><a href="#org94d9a68">6.14. Cedrat Actuator</a></li>
<li><a href="#org8ceaacc">6.15. Sample</a></li>
</ul>
</li>
</ul>
@@ -326,19 +327,19 @@ for the JavaScript code in this tag.
This file is used to explain how this Simscape Model works.
</p>
<ul class="org-ul">
<li>In section <a href="#org041c0e9">1</a>, the simulink project with the associated scripts are presented</li>
<li>In section <a href="#orgd5bef84">2</a>, an introduction to Simscape Multibody is done</li>
<li>In section <a href="#orgfff3010">3</a>, each simscape files are presented with the associated signal names and joint architectures</li>
<li>In section <a href="#org3c886b5">4</a>, the list of the Simulink library elements are described</li>
<li>In section <a href="#org21528cf">5</a>, a list of Matlab function that will be used are defined here</li>
<li>In section <a href="#org882f3b1">6</a>, all the functions that are used to initialize the Simscape Multibody elements are defined here. This includes the mass of all solids for instance.</li>
<li>In section <a href="#orgfd7237b">1</a>, the simulink project with the associated scripts are presented</li>
<li>In section <a href="#orgb6586ca">2</a>, an introduction to Simscape Multibody is done</li>
<li>In section <a href="#org3e8132a">3</a>, each simscape files are presented with the associated signal names and joint architectures</li>
<li>In section <a href="#orgecb3837">4</a>, the list of the Simulink library elements are described</li>
<li>In section <a href="#org94ca66a">5</a>, a list of Matlab function that will be used are defined here</li>
<li>In section <a href="#org18b2c56">6</a>, all the functions that are used to initialize the Simscape Multibody elements are defined here. This includes the mass of all solids for instance.</li>
</ul>
<div id="outline-container-org5c21e47" class="outline-2">
<h2 id="org5c21e47"><span class="section-number-2">1</span> Simulink Project - Startup and Shutdown scripts</h2>
<div id="outline-container-org88d59ba" class="outline-2">
<h2 id="org88d59ba"><span class="section-number-2">1</span> Simulink Project - Startup and Shutdown scripts</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org041c0e9"></a>
<a id="orgfd7237b"></a>
</p>
<p>
@@ -400,11 +401,11 @@ The project also permits to automatically add defined folder to the path when th
</div>
</div>
<div id="outline-container-org5ca7221" class="outline-2">
<h2 id="org5ca7221"><span class="section-number-2">2</span> Simscape Multibody - Presentation</h2>
<div id="outline-container-orga2206d5" class="outline-2">
<h2 id="orga2206d5"><span class="section-number-2">2</span> Simscape Multibody - Presentation</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="orgd5bef84"></a>
<a id="orgb6586ca"></a>
</p>
<p>
@@ -416,8 +417,8 @@ A <a href="https://.mathworks.com/products/simscape.html">simscape</a> model per
</p>
</div>
<div id="outline-container-orga5fbe1d" class="outline-3">
<h3 id="orga5fbe1d"><span class="section-number-3">2.1</span> Solid bodies</h3>
<div id="outline-container-org6b4540f" class="outline-3">
<h3 id="org6b4540f"><span class="section-number-3">2.1</span> Solid bodies</h3>
<div class="outline-text-3" id="text-2-1">
<p>
Each solid body is represented by a <a href="https://mathworks.com/help/physmod/sm/ref/solid.html">solid block</a>.
@@ -426,8 +427,8 @@ The geometry of the solid body can be imported using a <code>step</code> file. T
</div>
</div>
<div id="outline-container-org8017e71" class="outline-3">
<h3 id="org8017e71"><span class="section-number-3">2.2</span> Frames</h3>
<div id="outline-container-orge470a34" class="outline-3">
<h3 id="orge470a34"><span class="section-number-3">2.2</span> Frames</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Frames are very important in simscape multibody, they defined where the forces are applied, where the joints are located and where the measurements are made.
@@ -439,8 +440,8 @@ They can be defined from the solid body geometry, or using the <a href="https://
</div>
</div>
<div id="outline-container-org486d9bf" class="outline-3">
<h3 id="org486d9bf"><span class="section-number-3">2.3</span> Joints</h3>
<div id="outline-container-org474edd3" class="outline-3">
<h3 id="org474edd3"><span class="section-number-3">2.3</span> Joints</h3>
<div class="outline-text-3" id="text-2-3">
<p>
Solid Bodies are connected with joints (between frames of the two solid bodies).
@@ -450,7 +451,7 @@ Solid Bodies are connected with joints (between frames of the two solid bodies).
There are various types of joints that are all described <a href="https://mathworks.com/help/physmod/sm/ug/joints.html">here</a>.
</p>
<table id="org14596b7" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org57b7cc8" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Degrees of freedom associated with each joint</caption>
<colgroup>
@@ -583,7 +584,7 @@ Joint blocks are assortments of joint primitives:
<li><b>Constant Velocity</b>: Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: <code>CV</code></li>
</ul>
<table id="orgc0ad582" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org75d3b05" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Joint primitives for each joint type</caption>
<colgroup>
@@ -875,8 +876,8 @@ Composite Force/Torque sensing:
</div>
</div>
<div id="outline-container-org5a1378a" class="outline-3">
<h3 id="org5a1378a"><span class="section-number-3">2.4</span> Measurements</h3>
<div id="outline-container-org9171b40" class="outline-3">
<h3 id="org9171b40"><span class="section-number-3">2.4</span> Measurements</h3>
<div class="outline-text-3" id="text-2-4">
<p>
A transform sensor block measures the spatial relationship between two frames: the base <code>B</code> and the follower <code>F</code>.
@@ -900,8 +901,8 @@ If we want to simulate an <b>inertial sensor</b>, we just have to choose <code>B
</div>
</div>
<div id="outline-container-orga435910" class="outline-3">
<h3 id="orga435910"><span class="section-number-3">2.5</span> Excitation</h3>
<div id="outline-container-org7df2aef" class="outline-3">
<h3 id="org7df2aef"><span class="section-number-3">2.5</span> Excitation</h3>
<div class="outline-text-3" id="text-2-5">
<p>
We can apply <b>external forces</b> to the model by using an <a href="https://mathworks.com/help/physmod/sm/ref/externalforceandtorque.html">external force and torque block</a>.
@@ -914,11 +915,11 @@ Internal force, acting reciprocally between base and following origins is implem
</div>
</div>
<div id="outline-container-org289000e" class="outline-2">
<h2 id="org289000e"><span class="section-number-2">3</span> Simulink files and signal names</h2>
<div id="outline-container-org803cadc" class="outline-2">
<h2 id="org803cadc"><span class="section-number-2">3</span> Simulink files and signal names</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="orgfff3010"></a>
<a id="org3e8132a"></a>
</p>
<p>
@@ -926,8 +927,8 @@ In order to "normalize" things, the names of all the signal are listed here.
</p>
</div>
<div id="outline-container-orga9d8af9" class="outline-3">
<h3 id="orga9d8af9"><span class="section-number-3">3.1</span> List of Simscape files</h3>
<div id="outline-container-orgb5c767a" class="outline-3">
<h3 id="orgb5c767a"><span class="section-number-3">3.1</span> List of Simscape files</h3>
<div class="outline-text-3" id="text-3-1">
<p>
Few different Simulink files are used:
@@ -939,7 +940,7 @@ Few different Simulink files are used:
<li>control</li>
</ul>
<table id="org768a47d" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org6eeaf61" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> List of simscape files</caption>
<colgroup>
@@ -1006,14 +1007,14 @@ Few different Simulink files are used:
</div>
</div>
<div id="outline-container-org2a9705c" class="outline-3">
<h3 id="org2a9705c"><span class="section-number-3">3.2</span> List of Inputs</h3>
<div id="outline-container-org64dbd0d" class="outline-3">
<h3 id="org64dbd0d"><span class="section-number-3">3.2</span> List of Inputs</h3>
<div class="outline-text-3" id="text-3-2">
</div>
<div id="outline-container-org7fd5d25" class="outline-4">
<h4 id="org7fd5d25"><span class="section-number-4">3.2.1</span> Perturbations</h4>
<div id="outline-container-orgeecef4d" class="outline-4">
<h4 id="orgeecef4d"><span class="section-number-4">3.2.1</span> Perturbations</h4>
<div class="outline-text-4" id="text-3-2-1">
<table id="orgcc1cb27" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org5c60a9c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 4:</span> List of Disturbances</caption>
<colgroup>
@@ -1059,10 +1060,10 @@ Few different Simulink files are used:
</div>
</div>
<div id="outline-container-org0337003" class="outline-4">
<h4 id="org0337003"><span class="section-number-4">3.2.2</span> Measurement Noise</h4>
<div id="outline-container-org4e58ed6" class="outline-4">
<h4 id="org4e58ed6"><span class="section-number-4">3.2.2</span> Measurement Noise</h4>
<div class="outline-text-4" id="text-3-2-2">
<table id="orgb37a76c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="orgdadd8d8" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 5:</span> List of Measurement Noise</caption>
<colgroup>
@@ -1094,10 +1095,10 @@ Few different Simulink files are used:
</div>
</div>
<div id="outline-container-org250f869" class="outline-4">
<h4 id="org250f869"><span class="section-number-4">3.2.3</span> Control Inputs</h4>
<div id="outline-container-orgc9006ba" class="outline-4">
<h4 id="orgc9006ba"><span class="section-number-4">3.2.3</span> Control Inputs</h4>
<div class="outline-text-4" id="text-3-2-3">
<table id="orgb342550" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="orgfc73f52" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 6:</span> List of Control Inputs</caption>
<colgroup>
@@ -1219,10 +1220,10 @@ Few different Simulink files are used:
</div>
</div>
<div id="outline-container-orge7abaa0" class="outline-3">
<h3 id="orge7abaa0"><span class="section-number-3">3.3</span> List of Outputs</h3>
<div id="outline-container-orgeb985b0" class="outline-3">
<h3 id="orgeb985b0"><span class="section-number-3">3.3</span> List of Outputs</h3>
<div class="outline-text-3" id="text-3-3">
<table id="orgbcd4e2c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org59a5204" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 7:</span> List of Outputs</caption>
<colgroup>
@@ -1338,11 +1339,11 @@ Few different Simulink files are used:
</div>
</div>
<div id="outline-container-org0fbeac7" class="outline-2">
<h2 id="org0fbeac7"><span class="section-number-2">4</span> Simulink Library</h2>
<div id="outline-container-orgfd5289f" class="outline-2">
<h2 id="orgfd5289f"><span class="section-number-2">4</span> Simulink Library</h2>
<div class="outline-text-2" id="text-4">
<p>
<a id="org3c886b5"></a>
<a id="orgecb3837"></a>
</p>
<p>
@@ -1350,8 +1351,8 @@ A simulink library is developed in order to share elements between the different
</p>
</div>
<div id="outline-container-org3ec0c6f" class="outline-3">
<h3 id="org3ec0c6f"><span class="section-number-3">4.1</span> <code>inputs</code></h3>
<div id="outline-container-orgd1ebe0f" class="outline-3">
<h3 id="orgd1ebe0f"><span class="section-number-3">4.1</span> <code>inputs</code></h3>
<div class="outline-text-3" id="text-4-1">
<p>
<a href="../nass_library/inputs.slx">inputs.slx</a>
@@ -1359,8 +1360,8 @@ A simulink library is developed in order to share elements between the different
</div>
</div>
<div id="outline-container-org0abb61d" class="outline-3">
<h3 id="org0abb61d"><span class="section-number-3">4.2</span> <code>nass_library</code></h3>
<div id="outline-container-org1ae1d37" class="outline-3">
<h3 id="org1ae1d37"><span class="section-number-3">4.2</span> <code>nass_library</code></h3>
<div class="outline-text-3" id="text-4-2">
<p>
<a href="../nass_library/nass_library.slx">nass<sub>library.slx</sub></a>
@@ -1368,8 +1369,8 @@ A simulink library is developed in order to share elements between the different
</div>
</div>
<div id="outline-container-org04c0eb4" class="outline-3">
<h3 id="org04c0eb4"><span class="section-number-3">4.3</span> <code>pos_error_wrt_nass_base</code></h3>
<div id="outline-container-org54e3d07" class="outline-3">
<h3 id="org54e3d07"><span class="section-number-3">4.3</span> <code>pos_error_wrt_nass_base</code></h3>
<div class="outline-text-3" id="text-4-3">
<p>
<a href="../nass_library/pos_error_wrt_nass_base.slx">pos<sub>error</sub><sub>wrt</sub><sub>nass</sub><sub>base.slx</sub></a>
@@ -1377,8 +1378,8 @@ A simulink library is developed in order to share elements between the different
</div>
</div>
<div id="outline-container-orgef1709b" class="outline-3">
<h3 id="orgef1709b"><span class="section-number-3">4.4</span> <code>QuaternionToAngles</code></h3>
<div id="outline-container-orgc0f0f02" class="outline-3">
<h3 id="orgc0f0f02"><span class="section-number-3">4.4</span> <code>QuaternionToAngles</code></h3>
<div class="outline-text-3" id="text-4-4">
<p>
<a href="../nass_library/QuaternionToAngles.slx">QuaternionToAngles.slx</a>
@@ -1386,8 +1387,8 @@ A simulink library is developed in order to share elements between the different
</div>
</div>
<div id="outline-container-org8a40a80" class="outline-3">
<h3 id="org8a40a80"><span class="section-number-3">4.5</span> <code>RotationMatrixToAngle</code></h3>
<div id="outline-container-orgbda19ed" class="outline-3">
<h3 id="orgbda19ed"><span class="section-number-3">4.5</span> <code>RotationMatrixToAngle</code></h3>
<div class="outline-text-3" id="text-4-5">
<p>
<a href="../nass_library/RotationMatrixToAngle.slx">RotationMatrixToAngle.slx</a>
@@ -1396,18 +1397,18 @@ A simulink library is developed in order to share elements between the different
</div>
</div>
<div id="outline-container-org81a7962" class="outline-2">
<h2 id="org81a7962"><span class="section-number-2">5</span> Functions</h2>
<div id="outline-container-org54193c9" class="outline-2">
<h2 id="org54193c9"><span class="section-number-2">5</span> Functions</h2>
<div class="outline-text-2" id="text-5">
<p>
<a id="org21528cf"></a>
<a id="org94ca66a"></a>
</p>
</div>
<div id="outline-container-orge3706e5" class="outline-3">
<h3 id="orge3706e5"><span class="section-number-3">5.1</span> computePsdDispl</h3>
<div id="outline-container-orgc1f5840" class="outline-3">
<h3 id="orgc1f5840"><span class="section-number-3">5.1</span> computePsdDispl</h3>
<div class="outline-text-3" id="text-5-1">
<p>
<a id="org63dd43c"></a>
<a id="org46da1ed"></a>
</p>
<p>
@@ -1443,11 +1444,11 @@ This Matlab function is accessible <a href="../src/computePsdDispl.m">here</a>.
</div>
</div>
<div id="outline-container-org14a492d" class="outline-3">
<h3 id="org14a492d"><span class="section-number-3">5.2</span> computeSetpoint</h3>
<div id="outline-container-org0d8e9e6" class="outline-3">
<h3 id="org0d8e9e6"><span class="section-number-3">5.2</span> computeSetpoint</h3>
<div class="outline-text-3" id="text-5-2">
<p>
<a id="org0dcd84b"></a>
<a id="orga7c431b"></a>
</p>
<p>
@@ -1519,11 +1520,11 @@ setpoint<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-hi
</div>
</div>
<div id="outline-container-org3e9a86f" class="outline-3">
<h3 id="org3e9a86f"><span class="section-number-3">5.3</span> converErrorBasis</h3>
<div id="outline-container-org9a191e3" class="outline-3">
<h3 id="org9a191e3"><span class="section-number-3">5.3</span> converErrorBasis</h3>
<div class="outline-text-3" id="text-5-3">
<p>
<a id="org273e422"></a>
<a id="org2e6fbe8"></a>
</p>
<p>
@@ -1661,11 +1662,11 @@ error_nass = <span class="org-rainbow-delimiters-depth-1">[</span>dx; dy; dz; th
</div>
</div>
<div id="outline-container-org14d5b4c" class="outline-3">
<h3 id="org14d5b4c"><span class="section-number-3">5.4</span> generateDiagPidControl</h3>
<div id="outline-container-org2d44efa" class="outline-3">
<h3 id="org2d44efa"><span class="section-number-3">5.4</span> generateDiagPidControl</h3>
<div class="outline-text-3" id="text-5-4">
<p>
<a id="org4a60577"></a>
<a id="orgd1ce773"></a>
</p>
<p>
@@ -1695,11 +1696,11 @@ This Matlab function is accessible <a href="../src/generateDiagPidControl.m">her
</div>
</div>
</div>
<div id="outline-container-org5876af4" class="outline-3">
<h3 id="org5876af4"><span class="section-number-3">5.5</span> identifyPlant</h3>
<div id="outline-container-org6f7736a" class="outline-3">
<h3 id="org6f7736a"><span class="section-number-3">5.5</span> identifyPlant</h3>
<div class="outline-text-3" id="text-5-5">
<p>
<a id="orgff9faac"></a>
<a id="orgd69607b"></a>
</p>
<p>
@@ -1791,11 +1792,11 @@ This Matlab function is accessible <a href="../src/identifyPlant.m">here</a>.
</div>
</div>
<div id="outline-container-orgd01681b" class="outline-3">
<h3 id="orgd01681b"><span class="section-number-3">5.6</span> runSimulation</h3>
<div id="outline-container-org32dd782" class="outline-3">
<h3 id="org32dd782"><span class="section-number-3">5.6</span> runSimulation</h3>
<div class="outline-text-3" id="text-5-6">
<p>
<a id="org1f4a257"></a>
<a id="org95edf73"></a>
</p>
<p>
@@ -1864,18 +1865,18 @@ This Matlab function is accessible <a href="../src/runSimulation.m">here</a>.
</div>
</div>
</div>
<div id="outline-container-orgc88bb4f" class="outline-2">
<h2 id="orgc88bb4f"><span class="section-number-2">6</span> Initialize Elements</h2>
<div id="outline-container-org5cc2276" class="outline-2">
<h2 id="org5cc2276"><span class="section-number-2">6</span> Initialize Elements</h2>
<div class="outline-text-2" id="text-6">
<p>
<a id="org882f3b1"></a>
<a id="org18b2c56"></a>
</p>
</div>
<div id="outline-container-org53e8eea" class="outline-3">
<h3 id="org53e8eea"><span class="section-number-3">6.1</span> Experiment</h3>
<div id="outline-container-org664a7e3" class="outline-3">
<h3 id="org664a7e3"><span class="section-number-3">6.1</span> Experiment</h3>
<div class="outline-text-3" id="text-6-1">
<p>
<a id="org7855770"></a>
<a id="org395aa48"></a>
</p>
<p>
@@ -1909,11 +1910,11 @@ This Matlab function is accessible <a href="../src/initializeExperiment.m">here<
</div>
</div>
<div id="outline-container-orgd101ec3" class="outline-3">
<h3 id="orgd101ec3"><span class="section-number-3">6.2</span> Generate Reference Signals</h3>
<div id="outline-container-org89c58f8" class="outline-3">
<h3 id="org89c58f8"><span class="section-number-3">6.2</span> Generate Reference Signals</h3>
<div class="outline-text-3" id="text-6-2">
<p>
<a id="org4821745"></a>
<a id="orgdda511e"></a>
</p>
<p>
@@ -1929,10 +1930,10 @@ This Matlab function is accessible <a href="../src/initializeInputs.m">here</a>.
<span class="org-string">'Dy_amplitude'</span>, <span class="org-highlight-numbers-number">0</span>, ...<span class="org-comment"> % Amplitude of the displacement [m]</span>
<span class="org-string">'Dy_period'</span>, <span class="org-highlight-numbers-number">1</span>, ...<span class="org-comment"> % Period of the displacement [s]</span>
<span class="org-string">'Ry_type'</span>, <span class="org-string">'constant'</span>, ...<span class="org-comment"> % Either "constant" / "triangular" / "sinusoidal"</span>
<span class="org-string">'Ry_amplitude'</span>, <span class="org-highlight-numbers-number">0</span>, ...<span class="org-comment"> % Amplitude [deg]</span>
<span class="org-string">'Ry_amplitude'</span>, <span class="org-highlight-numbers-number">0</span>, ...<span class="org-comment"> % Amplitude [rad]</span>
<span class="org-string">'Ry_period'</span>, <span class="org-highlight-numbers-number">10</span>, ...<span class="org-comment"> % Period of the displacement [s]</span>
<span class="org-string">'Rz_type'</span>, <span class="org-string">'constant'</span>, ...<span class="org-comment"> % Either "constant" / "rotating"</span>
<span class="org-string">'Rz_amplitude'</span>, <span class="org-highlight-numbers-number">0</span>, ...<span class="org-comment"> % Initial angle [deg]</span>
<span class="org-string">'Rz_amplitude'</span>, <span class="org-highlight-numbers-number">0</span>, ...<span class="org-comment"> % Initial angle [rad]</span>
<span class="org-string">'Rz_period'</span>, <span class="org-highlight-numbers-number">1</span>, ...<span class="org-comment"> % Period of the rotating [s]</span>
<span class="org-string">'Dh_type'</span>, <span class="org-string">'constant'</span>, ...<span class="org-comment"> % For now, only constant is implemented</span>
<span class="org-string">'Dh_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-2">]</span>, ...<span class="org-comment"> % Initial position [m,m,m,rad,rad,rad] of the top platform</span>
@@ -1976,13 +1977,13 @@ This Matlab function is accessible <a href="../src/initializeInputs.m">here</a>.
<span class="org-keyword">switch</span> <span class="org-constant">opts.Ry_type</span>
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
Ry<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= <span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Ry_amplitude;
Ry<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= opts.Ry_amplitude;
<span class="org-keyword">case</span> <span class="org-string">'triangular'</span>
Ry<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= <span class="org-type">-</span><span class="org-highlight-numbers-number">4</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Ry_amplitude<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">4</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Ry_amplitude<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span>opts.Ry_period<span class="org-type">*</span>t;
Ry<span class="org-rainbow-delimiters-depth-1">(</span>t<span class="org-type">&lt;</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">75</span><span class="org-type">*</span>opts.Ry_period<span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Ry_amplitude<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> <span class="org-highlight-numbers-number">4</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Ry_amplitude<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span>opts.Ry_period<span class="org-type">*</span>t<span class="org-rainbow-delimiters-depth-1">(</span>t<span class="org-type">&lt;</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">75</span><span class="org-type">*</span>opts.Ry_period<span class="org-rainbow-delimiters-depth-1">)</span>;
Ry<span class="org-rainbow-delimiters-depth-1">(</span>t<span class="org-type">&lt;</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">25</span><span class="org-type">*</span>opts.Ry_period<span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-highlight-numbers-number">4</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Ry_amplitude<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span>opts.Ry_period<span class="org-type">*</span>t<span class="org-rainbow-delimiters-depth-1">(</span>t<span class="org-type">&lt;</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">25</span><span class="org-type">*</span>opts.Ry_period<span class="org-rainbow-delimiters-depth-1">)</span>;
Ry<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= <span class="org-type">-</span><span class="org-highlight-numbers-number">4</span><span class="org-type">*</span>opts.Ry_amplitude <span class="org-type">+</span> <span class="org-highlight-numbers-number">4</span><span class="org-type">*</span>opts.Ry_amplitude<span class="org-type">/</span>opts.Ry_period<span class="org-type">*</span>t;
Ry<span class="org-rainbow-delimiters-depth-1">(</span>t<span class="org-type">&lt;</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">75</span><span class="org-type">*</span>opts.Ry_period<span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>opts.Ry_amplitude <span class="org-type">-</span> <span class="org-highlight-numbers-number">4</span><span class="org-type">*</span>opts.Ry_amplitude<span class="org-type">/</span>opts.Ry_period<span class="org-type">*</span>t<span class="org-rainbow-delimiters-depth-1">(</span>t<span class="org-type">&lt;</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">75</span><span class="org-type">*</span>opts.Ry_period<span class="org-rainbow-delimiters-depth-1">)</span>;
Ry<span class="org-rainbow-delimiters-depth-1">(</span>t<span class="org-type">&lt;</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">25</span><span class="org-type">*</span>opts.Ry_period<span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-highlight-numbers-number">4</span><span class="org-type">*</span>opts.Ry_amplitude<span class="org-type">/</span>opts.Ry_period<span class="org-type">*</span>t<span class="org-rainbow-delimiters-depth-1">(</span>t<span class="org-type">&lt;</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">25</span><span class="org-type">*</span>opts.Ry_period<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">case</span> <span class="org-string">'sinusoidal'</span>
Ry<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= opts.Ry_amplitude<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>opts.Ry_period<span class="org-type">*</span>t<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">otherwise</span>
warning<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Ry_type is not set correctly'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
@@ -1994,9 +1995,9 @@ This Matlab function is accessible <a href="../src/initializeInputs.m">here</a>.
<span class="org-keyword">switch</span> <span class="org-constant">opts.Rz_type</span>
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
Rz<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= <span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Rz_amplitude;
Rz<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= opts.Rz_amplitude;
<span class="org-keyword">case</span> <span class="org-string">'rotating'</span>
Rz<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= <span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Rz_amplitude<span class="org-type">+</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>opts.Rz_period<span class="org-type">*</span>t;
Rz<span class="org-type"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-type">:</span><span class="org-type"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-type"> </span>= opts.Rz_amplitude<span class="org-type">+</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>opts.Rz_period<span class="org-type">*</span>t;
<span class="org-keyword">otherwise</span>
warning<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Rz_type is not set correctly'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
@@ -2006,8 +2007,6 @@ This Matlab function is accessible <a href="../src/initializeInputs.m">here</a>.
t = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>, Ts<span class="org-rainbow-delimiters-depth-1">]</span>;
Dh = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
opts.Dh_pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Dh_pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% convert from [deg] to [rad]</span>
<span class="org-keyword">switch</span> <span class="org-constant">opts.Dh_type</span>
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
Dh = <span class="org-rainbow-delimiters-depth-1">[</span>opts.Dh_pos, opts.Dh_pos<span class="org-rainbow-delimiters-depth-1">]</span>;
@@ -2025,8 +2024,6 @@ This Matlab function is accessible <a href="../src/initializeInputs.m">here</a>.
t = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>, Ts<span class="org-rainbow-delimiters-depth-1">]</span>;
Dn = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
opts.Dn_pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span><span class="org-type">*</span>opts.Dn_pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% convert from [deg] to [rad]</span>
<span class="org-keyword">switch</span> <span class="org-constant">opts.Dn_type</span>
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
Dn = <span class="org-rainbow-delimiters-depth-1">[</span>opts.Dn_pos, opts.Dn_pos<span class="org-rainbow-delimiters-depth-1">]</span>;
@@ -2043,11 +2040,11 @@ This Matlab function is accessible <a href="../src/initializeInputs.m">here</a>.
</div>
</div>
<div id="outline-container-org15d2680" class="outline-3">
<h3 id="org15d2680"><span class="section-number-3">6.3</span> <span class="todo TODO">TODO</span> Inputs</h3>
<div id="outline-container-org77d160f" class="outline-3">
<h3 id="org77d160f"><span class="section-number-3">6.3</span> <span class="todo TODO">TODO</span> Inputs</h3>
<div class="outline-text-3" id="text-6-3">
<p>
<a id="org2728bfe"></a>
<a id="org7501b33"></a>
</p>
<ul class="org-ul">
@@ -2239,11 +2236,11 @@ This Matlab function is accessible <a href="../src/initializeInputs.m">here</a>.
</div>
</div>
<div id="outline-container-org2b6b02d" class="outline-3">
<h3 id="org2b6b02d"><span class="section-number-3">6.4</span> Ground</h3>
<div id="outline-container-org962187e" class="outline-3">
<h3 id="org962187e"><span class="section-number-3">6.4</span> Ground</h3>
<div class="outline-text-3" id="text-6-4">
<p>
<a id="orgc97869c"></a>
<a id="org763b0ff"></a>
</p>
<p>
@@ -2267,11 +2264,11 @@ This Matlab function is accessible <a href="../src/initializeGround.m">here</a>.
</div>
</div>
<div id="outline-container-orge2875ed" class="outline-3">
<h3 id="orge2875ed"><span class="section-number-3">6.5</span> Granite</h3>
<div id="outline-container-org198c366" class="outline-3">
<h3 id="org198c366"><span class="section-number-3">6.5</span> Granite</h3>
<div class="outline-text-3" id="text-6-5">
<p>
<a id="org706d529"></a>
<a id="orgbdb5477"></a>
</p>
<p>
@@ -2337,11 +2334,11 @@ This Matlab function is accessible <a href="../src/initializeGranite.m">here</a>
</div>
</div>
<div id="outline-container-org61ee0ba" class="outline-3">
<h3 id="org61ee0ba"><span class="section-number-3">6.6</span> Translation Stage</h3>
<div id="outline-container-org6e967d2" class="outline-3">
<h3 id="org6e967d2"><span class="section-number-3">6.6</span> Translation Stage</h3>
<div class="outline-text-3" id="text-6-6">
<p>
<a id="org5407512"></a>
<a id="org2597c18"></a>
</p>
<p>
@@ -2423,11 +2420,11 @@ This Matlab function is accessible <a href="../src/initializeTy.m">here</a>.
</div>
</div>
<div id="outline-container-orgdba0ed0" class="outline-3">
<h3 id="orgdba0ed0"><span class="section-number-3">6.7</span> Tilt Stage</h3>
<div id="outline-container-org6c95b53" class="outline-3">
<h3 id="org6c95b53"><span class="section-number-3">6.7</span> Tilt Stage</h3>
<div class="outline-text-3" id="text-6-7">
<p>
<a id="org22557f6"></a>
<a id="org29b1fab"></a>
</p>
<p>
@@ -2498,11 +2495,11 @@ This Matlab function is accessible <a href="../src/initializeRy.m">here</a>.
</div>
</div>
<div id="outline-container-org6d74dd3" class="outline-3">
<h3 id="org6d74dd3"><span class="section-number-3">6.8</span> Spindle</h3>
<div id="outline-container-org13271e7" class="outline-3">
<h3 id="org13271e7"><span class="section-number-3">6.8</span> Spindle</h3>
<div class="outline-text-3" id="text-6-8">
<p>
<a id="orgc1728c6"></a>
<a id="org50164cd"></a>
</p>
<p>
@@ -2569,11 +2566,49 @@ This Matlab function is accessible <a href="../src/initializeRz.m">here</a>.
</div>
</div>
<div id="outline-container-orgde1ec20" class="outline-3">
<h3 id="orgde1ec20"><span class="section-number-3">6.9</span> Micro Hexapod</h3>
<div id="outline-container-org3c482fe" class="outline-3">
<h3 id="org3c482fe"><span class="section-number-3">6.9</span> Initialize Hexapod legs' length</h3>
<div class="outline-text-3" id="text-6-9">
<p>
<a id="org3e9a594"></a>
<a id="orgee2252f"></a>
</p>
<p>
This Matlab function is accessible <a href="../src/initializeHexapodPosition.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">hexapod</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeHexapodPosition</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">hexapod</span>, <span class="org-variable-name">AP</span>, <span class="org-variable-name">ARB</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-comment">% initializeHexapodPosition -</span>
<span class="org-comment">%</span>
<span class="org-comment">% Syntax: initializeHexapodPosition(hexapod, AP, ARB)</span>
<span class="org-comment">%</span>
<span class="org-comment">% Inputs:</span>
<span class="org-comment">% - hexapod - Hexapod object containing the geometry of the hexapod</span>
<span class="org-comment">% - AP - Position vector of point OB expressed in frame {A}</span>
<span class="org-comment">% - ARB - Rotation Matrix expressed in frame {A}</span>
L0 = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">L</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
Bbi = hexapod.pos_top_tranform<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span>;
Aai = hexapod.pos_base<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span>;
L0<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = sqrt<span class="org-rainbow-delimiters-depth-1">(</span>AP<span class="org-type">'*</span>AP <span class="org-type">+</span> Bbi<span class="org-type">'*</span>Bbi <span class="org-type">+</span> Aai<span class="org-type">'*</span>Aai <span class="org-type">-</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>AP<span class="org-type">'*</span>Aai <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>AP<span class="org-type">'*</span><span class="org-rainbow-delimiters-depth-2">(</span>ARB<span class="org-type">*</span>Bbi<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>ARB<span class="org-type">*</span>Bbi<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'*</span>Aai<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
hexapod.L0 = L0;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org7c295aa" class="outline-3">
<h3 id="org7c295aa"><span class="section-number-3">6.10</span> Micro Hexapod</h3>
<div class="outline-text-3" id="text-6-10">
<p>
<a id="org9e25f5d"></a>
</p>
<p>
@@ -2583,7 +2618,11 @@ This Matlab function is accessible <a href="../src/initializeMicroHexapod.m">her
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">micro_hexapod</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeMicroHexapod</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'rigid'</span>, <span class="org-constant">false</span><span class="org-rainbow-delimiters-depth-1">)</span>;
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
<span class="org-string">'rigid'</span>, <span class="org-constant">false</span>, ...
<span class="org-string">'AP'</span>, zeros<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ...<span class="org-comment"> % Wanted position in [m] of OB with respect to frame {A}</span>
<span class="org-string">'ARB'</span>, eye<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span> ...<span class="org-comment"> % Rotation Matrix that represent the wanted orientation of frame {B} with respect to frame {A}</span>
<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
@@ -2595,7 +2634,7 @@ This Matlab function is accessible <a href="../src/initializeMicroHexapod.m">her
<span class="org-matlab-cellbreak"><span class="org-comment">%% Stewart Object</span></span>
micro_hexapod = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
micro_hexapod.h = <span class="org-highlight-numbers-number">350</span>; <span class="org-comment">% Total height of the platform [mm]</span>
micro_hexapod.jacobian = <span class="org-highlight-numbers-number">270</span>; <span class="org-comment">% Distance from the top platform to the Jacobian point [mm]</span>
micro_hexapod.jacobian = <span class="org-highlight-numbers-number">270</span>; <span class="org-comment">% Distance from the top of the mobile platform to the Jacobian point [mm]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Bottom Plate - Mechanical Design</span></span>
BP = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
@@ -2630,7 +2669,7 @@ This Matlab function is accessible <a href="../src/initializeMicroHexapod.m">her
<span class="org-keyword">else</span>
Leg.k.ax = <span class="org-highlight-numbers-number">2e7</span>; <span class="org-comment">% Stiffness of each leg [N/m]</span>
<span class="org-keyword">end</span>
Leg.ksi.ax = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>; % Modal damping ksi = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>c<span class="org-type">/</span>sqrt(km) []
Leg.ksi.ax = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>; % Modal damping ksi = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>c<span class="org-type">/</span>sqrt(km) []
Leg.rad.bottom = <span class="org-highlight-numbers-number">25</span>; <span class="org-comment">% Radius of the cylinder of the bottom part [mm]</span>
Leg.rad.top = <span class="org-highlight-numbers-number">17</span>; <span class="org-comment">% Radius of the cylinder of the top part [mm]</span>
Leg.density = <span class="org-highlight-numbers-number">8000</span>; % Density of the material [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
@@ -2676,6 +2715,9 @@ This Matlab function is accessible <a href="../src/initializeMicroHexapod.m">her
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
micro_hexapod = initializeParameters<span class="org-rainbow-delimiters-depth-1">(</span>micro_hexapod<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Setup equilibrium position of each leg</span></span>
micro_hexapod.L0 = initializeHexapodPosition<span class="org-rainbow-delimiters-depth-1">(</span>micro_hexapod, opts.AP, opts.ARB<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'micro_hexapod'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@@ -2769,24 +2811,47 @@ This Matlab function is accessible <a href="../src/initializeMicroHexapod.m">her
stewart.J = getJacobianMatrix<span class="org-rainbow-delimiters-depth-1">(</span>leg_vectors<span class="org-type">'</span>, aa<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">function</span> <span class="org-variable-name">J</span> = <span class="org-function-name">getJacobianMatrix</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">RM</span>,<span class="org-variable-name">M_pos_base</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name">J</span> = <span class="org-function-name">getJacobianMatrix</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">RM</span>, <span class="org-variable-name">M_pos_base</span><span class="org-rainbow-delimiters-depth-1">)</span>
% RM<span class="org-type">:</span> [<span class="org-highlight-numbers-number">3x6</span>] unit vector of each leg in the fixed frame
% M_pos_base<span class="org-type">:</span> [<span class="org-highlight-numbers-number">3x6</span>] vector of the leg connection at the top platform location in the fixed frame
J = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
J<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = RM<span class="org-type">'</span>;
J<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = cross<span class="org-rainbow-delimiters-depth-1">(</span>M_pos_base, RM<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">L</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeHexapodPosition</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">hexapod</span>, <span class="org-variable-name">AP</span>, <span class="org-variable-name">ARB</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-comment">% initializeHexapodPosition - Compute the initial position of each leg to have the wanted Hexapod's position</span>
<span class="org-comment">%</span>
<span class="org-comment">% Syntax: initializeHexapodPosition(hexapod, AP, ARB)</span>
<span class="org-comment">%</span>
<span class="org-comment">% Inputs:</span>
<span class="org-comment">% - hexapod - Hexapod object containing the geometry of the hexapod</span>
<span class="org-comment">% - AP - Position vector of point OB expressed in frame {A} in [m]</span>
<span class="org-comment">% - ARB - Rotation Matrix expressed in frame {A}</span>
<span class="org-comment">% Wanted Length of the hexapod's legs [m]</span>
L = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">L</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
Bbi = hexapod.pos_top_tranform<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span> <span class="org-type">-</span> <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> ; <span class="org-highlight-numbers-number">0</span> ; hexapod.TP.thickness<span class="org-type">+</span>hexapod.Leg.sphere.top<span class="org-type">+</span>hexapod.SP.thickness.top<span class="org-type">+</span>hexapod.jacobian<span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [m]</span>
Aai = hexapod.pos_base<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> ; <span class="org-highlight-numbers-number">0</span> ; hexapod.BP.thickness<span class="org-type">+</span>hexapod.Leg.sphere.bottom<span class="org-type">+</span>hexapod.SP.thickness.bottom<span class="org-type">-</span>micro_hexapod.h<span class="org-type">-</span>hexapod.jacobian<span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [m]</span>
L<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = sqrt<span class="org-rainbow-delimiters-depth-1">(</span>AP<span class="org-type">'*</span>AP <span class="org-type">+</span> Bbi<span class="org-type">'*</span>Bbi <span class="org-type">+</span> Aai<span class="org-type">'*</span>Aai <span class="org-type">-</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>AP<span class="org-type">'*</span>Aai <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>AP<span class="org-type">'*</span><span class="org-rainbow-delimiters-depth-2">(</span>ARB<span class="org-type">*</span>Bbi<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>ARB<span class="org-type">*</span>Bbi<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'*</span>Aai<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbfe4e10" class="outline-3">
<h3 id="orgbfe4e10"><span class="section-number-3">6.10</span> Center of gravity compensation</h3>
<div class="outline-text-3" id="text-6-10">
<div id="outline-container-org72492f3" class="outline-3">
<h3 id="org72492f3"><span class="section-number-3">6.11</span> Center of gravity compensation</h3>
<div class="outline-text-3" id="text-6-11">
<p>
<a id="org3db12eb"></a>
<a id="org991aec0"></a>
</p>
<p>
@@ -2830,11 +2895,11 @@ This Matlab function is accessible <a href="../src/initializeAxisc.m">here</a>.
</div>
</div>
<div id="outline-container-org1c8d312" class="outline-3">
<h3 id="org1c8d312"><span class="section-number-3">6.11</span> Mirror</h3>
<div class="outline-text-3" id="text-6-11">
<div id="outline-container-org68d031b" class="outline-3">
<h3 id="org68d031b"><span class="section-number-3">6.12</span> Mirror</h3>
<div class="outline-text-3" id="text-6-12">
<p>
<a id="org1354fa1"></a>
<a id="org43cadec"></a>
</p>
<p>
@@ -2900,11 +2965,11 @@ This Matlab function is accessible <a href="../src/initializeMirror.m">here</a>.
</div>
</div>
<div id="outline-container-orgf75cc87" class="outline-3">
<h3 id="orgf75cc87"><span class="section-number-3">6.12</span> Nano Hexapod</h3>
<div class="outline-text-3" id="text-6-12">
<div id="outline-container-org74149ff" class="outline-3">
<h3 id="org74149ff"><span class="section-number-3">6.13</span> Nano Hexapod</h3>
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<h3 id="orgbb8d5dd"><span class="section-number-3">6.13</span> Cedrat Actuator</h3>
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<h3 id="org94d9a68"><span class="section-number-3">6.14</span> Cedrat Actuator</h3>
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<h3 id="orgbb20f65"><span class="section-number-3">6.14</span> Sample</h3>
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<h3 id="org8ceaacc"><span class="section-number-3">6.15</span> Sample</h3>
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-12-06 ven. 12:04</p>
<p class="date">Created: 2019-12-10 mar. 18:05</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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