602 lines
26 KiB
HTML
602 lines
26 KiB
HTML
<?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>
|
|
<!-- 2019-12-12 jeu. 11:39 -->
|
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
|
<title>Kinematics of the station</title>
|
|
<meta name="generator" content="Org mode" />
|
|
<meta name="author" content="Dehaeze Thomas" />
|
|
<style type="text/css">
|
|
<!--/*--><![CDATA[/*><!--*/
|
|
.title { text-align: center;
|
|
margin-bottom: .2em; }
|
|
.subtitle { text-align: center;
|
|
font-size: medium;
|
|
font-weight: bold;
|
|
margin-top:0; }
|
|
.todo { font-family: monospace; color: red; }
|
|
.done { font-family: monospace; color: green; }
|
|
.priority { font-family: monospace; color: orange; }
|
|
.tag { background-color: #eee; font-family: monospace;
|
|
padding: 2px; font-size: 80%; font-weight: normal; }
|
|
.timestamp { color: #bebebe; }
|
|
.timestamp-kwd { color: #5f9ea0; }
|
|
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
|
|
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
|
|
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
|
|
.underline { text-decoration: underline; }
|
|
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
|
|
p.verse { margin-left: 3%; }
|
|
pre {
|
|
border: 1px solid #ccc;
|
|
box-shadow: 3px 3px 3px #eee;
|
|
padding: 8pt;
|
|
font-family: monospace;
|
|
overflow: auto;
|
|
margin: 1.2em;
|
|
}
|
|
pre.src {
|
|
position: relative;
|
|
overflow: visible;
|
|
padding-top: 1.2em;
|
|
}
|
|
pre.src:before {
|
|
display: none;
|
|
position: absolute;
|
|
background-color: white;
|
|
top: -10px;
|
|
right: 10px;
|
|
padding: 3px;
|
|
border: 1px solid black;
|
|
}
|
|
pre.src:hover:before { display: inline;}
|
|
/* Languages per Org manual */
|
|
pre.src-asymptote:before { content: 'Asymptote'; }
|
|
pre.src-awk:before { content: 'Awk'; }
|
|
pre.src-C:before { content: 'C'; }
|
|
/* pre.src-C++ doesn't work in CSS */
|
|
pre.src-clojure:before { content: 'Clojure'; }
|
|
pre.src-css:before { content: 'CSS'; }
|
|
pre.src-D:before { content: 'D'; }
|
|
pre.src-ditaa:before { content: 'ditaa'; }
|
|
pre.src-dot:before { content: 'Graphviz'; }
|
|
pre.src-calc:before { content: 'Emacs Calc'; }
|
|
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
|
|
pre.src-fortran:before { content: 'Fortran'; }
|
|
pre.src-gnuplot:before { content: 'gnuplot'; }
|
|
pre.src-haskell:before { content: 'Haskell'; }
|
|
pre.src-hledger:before { content: 'hledger'; }
|
|
pre.src-java:before { content: 'Java'; }
|
|
pre.src-js:before { content: 'Javascript'; }
|
|
pre.src-latex:before { content: 'LaTeX'; }
|
|
pre.src-ledger:before { content: 'Ledger'; }
|
|
pre.src-lisp:before { content: 'Lisp'; }
|
|
pre.src-lilypond:before { content: 'Lilypond'; }
|
|
pre.src-lua:before { content: 'Lua'; }
|
|
pre.src-matlab:before { content: 'MATLAB'; }
|
|
pre.src-mscgen:before { content: 'Mscgen'; }
|
|
pre.src-ocaml:before { content: 'Objective Caml'; }
|
|
pre.src-octave:before { content: 'Octave'; }
|
|
pre.src-org:before { content: 'Org mode'; }
|
|
pre.src-oz:before { content: 'OZ'; }
|
|
pre.src-plantuml:before { content: 'Plantuml'; }
|
|
pre.src-processing:before { content: 'Processing.js'; }
|
|
pre.src-python:before { content: 'Python'; }
|
|
pre.src-R:before { content: 'R'; }
|
|
pre.src-ruby:before { content: 'Ruby'; }
|
|
pre.src-sass:before { content: 'Sass'; }
|
|
pre.src-scheme:before { content: 'Scheme'; }
|
|
pre.src-screen:before { content: 'Gnu Screen'; }
|
|
pre.src-sed:before { content: 'Sed'; }
|
|
pre.src-sh:before { content: 'shell'; }
|
|
pre.src-sql:before { content: 'SQL'; }
|
|
pre.src-sqlite:before { content: 'SQLite'; }
|
|
/* additional languages in org.el's org-babel-load-languages alist */
|
|
pre.src-forth:before { content: 'Forth'; }
|
|
pre.src-io:before { content: 'IO'; }
|
|
pre.src-J:before { content: 'J'; }
|
|
pre.src-makefile:before { content: 'Makefile'; }
|
|
pre.src-maxima:before { content: 'Maxima'; }
|
|
pre.src-perl:before { content: 'Perl'; }
|
|
pre.src-picolisp:before { content: 'Pico Lisp'; }
|
|
pre.src-scala:before { content: 'Scala'; }
|
|
pre.src-shell:before { content: 'Shell Script'; }
|
|
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
|
|
/* additional language identifiers per "defun org-babel-execute"
|
|
in ob-*.el */
|
|
pre.src-cpp:before { content: 'C++'; }
|
|
pre.src-abc:before { content: 'ABC'; }
|
|
pre.src-coq:before { content: 'Coq'; }
|
|
pre.src-groovy:before { content: 'Groovy'; }
|
|
/* additional language identifiers from org-babel-shell-names in
|
|
ob-shell.el: ob-shell is the only babel language using a lambda to put
|
|
the execution function name together. */
|
|
pre.src-bash:before { content: 'bash'; }
|
|
pre.src-csh:before { content: 'csh'; }
|
|
pre.src-ash:before { content: 'ash'; }
|
|
pre.src-dash:before { content: 'dash'; }
|
|
pre.src-ksh:before { content: 'ksh'; }
|
|
pre.src-mksh:before { content: 'mksh'; }
|
|
pre.src-posh:before { content: 'posh'; }
|
|
/* Additional Emacs modes also supported by the LaTeX listings package */
|
|
pre.src-ada:before { content: 'Ada'; }
|
|
pre.src-asm:before { content: 'Assembler'; }
|
|
pre.src-caml:before { content: 'Caml'; }
|
|
pre.src-delphi:before { content: 'Delphi'; }
|
|
pre.src-html:before { content: 'HTML'; }
|
|
pre.src-idl:before { content: 'IDL'; }
|
|
pre.src-mercury:before { content: 'Mercury'; }
|
|
pre.src-metapost:before { content: 'MetaPost'; }
|
|
pre.src-modula-2:before { content: 'Modula-2'; }
|
|
pre.src-pascal:before { content: 'Pascal'; }
|
|
pre.src-ps:before { content: 'PostScript'; }
|
|
pre.src-prolog:before { content: 'Prolog'; }
|
|
pre.src-simula:before { content: 'Simula'; }
|
|
pre.src-tcl:before { content: 'tcl'; }
|
|
pre.src-tex:before { content: 'TeX'; }
|
|
pre.src-plain-tex:before { content: 'Plain TeX'; }
|
|
pre.src-verilog:before { content: 'Verilog'; }
|
|
pre.src-vhdl:before { content: 'VHDL'; }
|
|
pre.src-xml:before { content: 'XML'; }
|
|
pre.src-nxml:before { content: 'XML'; }
|
|
/* add a generic configuration mode; LaTeX export needs an additional
|
|
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
|
|
pre.src-conf:before { content: 'Configuration File'; }
|
|
|
|
table { border-collapse:collapse; }
|
|
caption.t-above { caption-side: top; }
|
|
caption.t-bottom { caption-side: bottom; }
|
|
td, th { vertical-align:top; }
|
|
th.org-right { text-align: center; }
|
|
th.org-left { text-align: center; }
|
|
th.org-center { text-align: center; }
|
|
td.org-right { text-align: right; }
|
|
td.org-left { text-align: left; }
|
|
td.org-center { text-align: center; }
|
|
dt { font-weight: bold; }
|
|
.footpara { display: inline; }
|
|
.footdef { margin-bottom: 1em; }
|
|
.figure { padding: 1em; }
|
|
.figure p { text-align: center; }
|
|
.equation-container {
|
|
display: table;
|
|
text-align: center;
|
|
width: 100%;
|
|
}
|
|
.equation {
|
|
vertical-align: middle;
|
|
}
|
|
.equation-label {
|
|
display: table-cell;
|
|
text-align: right;
|
|
vertical-align: middle;
|
|
}
|
|
.inlinetask {
|
|
padding: 10px;
|
|
border: 2px solid gray;
|
|
margin: 10px;
|
|
background: #ffffcc;
|
|
}
|
|
#org-div-home-and-up
|
|
{ text-align: right; font-size: 70%; white-space: nowrap; }
|
|
textarea { overflow-x: auto; }
|
|
.linenr { font-size: smaller }
|
|
.code-highlighted { background-color: #ffff00; }
|
|
.org-info-js_info-navigation { border-style: none; }
|
|
#org-info-js_console-label
|
|
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
|
|
.org-info-js_search-highlight
|
|
{ background-color: #ffff00; color: #000000; font-weight: bold; }
|
|
.org-svg { width: 90%; }
|
|
/*]]>*/-->
|
|
</style>
|
|
<link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
|
|
<link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
|
|
<link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
|
|
<script type="text/javascript" src="../js/jquery.min.js"></script>
|
|
<script type="text/javascript" src="../js/bootstrap.min.js"></script>
|
|
<script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
|
|
<script type="text/javascript" src="../js/readtheorg.js"></script>
|
|
<script type="text/javascript">
|
|
/*
|
|
@licstart The following is the entire license notice for the
|
|
JavaScript code in this tag.
|
|
|
|
Copyright (C) 2012-2019 Free Software Foundation, Inc.
|
|
|
|
The JavaScript code in this tag is free software: you can
|
|
redistribute it and/or modify it under the terms of the GNU
|
|
General Public License (GNU GPL) as published by the Free Software
|
|
Foundation, either version 3 of the License, or (at your option)
|
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
|
|
|
As additional permission under GNU GPL version 3 section 7, you
|
|
may distribute non-source (e.g., minimized or compacted) forms of
|
|
that code without the copy of the GNU GPL normally required by
|
|
section 4, provided you include this license notice and a URL
|
|
through which recipients can access the Corresponding Source.
|
|
|
|
|
|
@licend The above is the entire license notice
|
|
for the JavaScript code in this tag.
|
|
*/
|
|
<!--/*--><![CDATA[/*><!--*/
|
|
function CodeHighlightOn(elem, id)
|
|
{
|
|
var target = document.getElementById(id);
|
|
if(null != target) {
|
|
elem.cacheClassElem = elem.className;
|
|
elem.cacheClassTarget = target.className;
|
|
target.className = "code-highlighted";
|
|
elem.className = "code-highlighted";
|
|
}
|
|
}
|
|
function CodeHighlightOff(elem, id)
|
|
{
|
|
var target = document.getElementById(id);
|
|
if(elem.cacheClassElem)
|
|
elem.className = elem.cacheClassElem;
|
|
if(elem.cacheClassTarget)
|
|
target.className = elem.cacheClassTarget;
|
|
}
|
|
/*]]>*///-->
|
|
</script>
|
|
<script type="text/x-mathjax-config">
|
|
MathJax.Hub.Config({
|
|
displayAlign: "center",
|
|
displayIndent: "0em",
|
|
|
|
"HTML-CSS": { scale: 100,
|
|
linebreaks: { automatic: "false" },
|
|
webFont: "TeX"
|
|
},
|
|
SVG: {scale: 100,
|
|
linebreaks: { automatic: "false" },
|
|
font: "TeX"},
|
|
NativeMML: {scale: 100},
|
|
TeX: { equationNumbers: {autoNumber: "AMS"},
|
|
MultLineWidth: "85%",
|
|
TagSide: "right",
|
|
TagIndent: ".8em",
|
|
Macros: {
|
|
bm: ["{\\boldsymbol #1}",1],
|
|
}
|
|
}
|
|
});
|
|
</script>
|
|
<script type="text/javascript"
|
|
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML"></script>
|
|
</head>
|
|
<body>
|
|
<div id="org-div-home-and-up">
|
|
<a accesskey="h" href="../index.html"> UP </a>
|
|
|
|
|
<a accesskey="H" href="../index.html"> HOME </a>
|
|
</div><div id="content">
|
|
<h1 class="title">Kinematics of the station</h1>
|
|
<div id="table-of-contents">
|
|
<h2>Table of Contents</h2>
|
|
<div id="text-table-of-contents">
|
|
<ul>
|
|
<li><a href="#org1c1eaea">1. Micro Hexapod</a>
|
|
<ul>
|
|
<li><a href="#orgbed4ee9">1.1. How the Symetrie Hexapod is controlled on the micro station</a></li>
|
|
<li><a href="#org3fdba3a">1.2. Control of the Micro-Hexapod using Simscape</a>
|
|
<ul>
|
|
<li><a href="#org6d226ad">1.2.1. Using Bushing Joint</a></li>
|
|
<li><a href="#orgd390910">1.2.2. Using Inverse Kinematics and Leg Actuators</a>
|
|
<ul>
|
|
<li><a href="#orgf6ea97b">1.2.2.1. Theory</a></li>
|
|
<li><a href="#org67bcb7b">1.2.2.2. Matlab Implementation</a></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<p>
|
|
In this document, we discuss the way the motion of each stage is defined.
|
|
</p>
|
|
|
|
<div id="outline-container-org1c1eaea" class="outline-2">
|
|
<h2 id="org1c1eaea"><span class="section-number-2">1</span> Micro Hexapod</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
</div>
|
|
<div id="outline-container-orgbed4ee9" class="outline-3">
|
|
<h3 id="orgbed4ee9"><span class="section-number-3">1.1</span> How the Symetrie Hexapod is controlled on the micro station</h3>
|
|
<div class="outline-text-3" id="text-1-1">
|
|
<p>
|
|
For the Micro-Hexapod, the convention for the angles are defined in <code>MAN_A_Software API_4.0.150918_EN.pdf</code> on page 13 (section 2.4 - Rotation Vectors):
|
|
</p>
|
|
|
|
<blockquote>
|
|
<p>
|
|
The <b>Euler type II convention</b> is used to express the rotation vector.
|
|
This convention is mainly used in the aeronautics field (standard ISO 1151 concerning flight mechanics).
|
|
</p>
|
|
|
|
<p>
|
|
This convention uses the concepts of rotation of vehicles (ship, car and plane).
|
|
Generally, we consider that the main movement of the vehicle is following the X-axis and the Z-axis is parallel to the axis of gravity (at the initial position).
|
|
The roll rotation is around the X-axis, the pitch is around the Y-axis and yaw is the rotation around the Z-axis.
|
|
<b>The order of rotation is: Rx, Ry and then Rz.</b>
|
|
</p>
|
|
|
|
<p>
|
|
In most case, rotations are related to a reference with fixed axis; thus we say the rotations are around fixed axes.
|
|
The combination of these three rotations enables to write a rotation matrix.
|
|
This writing is unique and equal to:
|
|
\[ \bm{R} = \bm{R}_z(\gamma) \cdot \bm{R}_y(\beta) \cdot \bm{R}_x(\alpha) \]
|
|
</p>
|
|
|
|
<p>
|
|
The Euler type II convention corresponding to the <b>succession of rotations with respect to fixed axes</b>: first around X0, then Y0 and Z0.
|
|
This is equivalent to the succession of rotations with respect to mobile axes: first around Z0, then Y1' and X2'.
|
|
</p>
|
|
</blockquote>
|
|
|
|
<p>
|
|
More generally on the Control of the Micro-Hexapod:
|
|
</p>
|
|
<blockquote>
|
|
<p>
|
|
Note that for all control modes, <b>the rotation center coincides with Object coordinate system origin</b>.
|
|
Moreover, the movements are controlled with <b>translation components at first</b> (Tx, Ty, Tz) <b>then rotation components</b> (Rx, Ry, Rz).
|
|
</p>
|
|
</blockquote>
|
|
|
|
<p>
|
|
Thus, it does the translations and then the rotation around the new translated frame.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3fdba3a" class="outline-3">
|
|
<h3 id="org3fdba3a"><span class="section-number-3">1.2</span> Control of the Micro-Hexapod using Simscape</h3>
|
|
<div class="outline-text-3" id="text-1-2">
|
|
<p>
|
|
We can think of two main ways to position the Micro-Hexapod using Simscape.
|
|
</p>
|
|
|
|
<p>
|
|
The first one is to use only one Bushing Joint between the base and the mobile platform.
|
|
The advantage is that it is very easy to impose the wanted displacement, however, we loose the dynamical properties of the Hexapod.
|
|
</p>
|
|
|
|
<p>
|
|
The second way is to specify the wanted length of the legs of the Hexapod in order to have the wanted position of the mobile platform.
|
|
This require a little bit more of mathematical derivations but this is the chosen solution.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org6d226ad" class="outline-4">
|
|
<h4 id="org6d226ad"><span class="section-number-4">1.2.1</span> Using Bushing Joint</h4>
|
|
<div class="outline-text-4" id="text-1-2-1">
|
|
<p>
|
|
In the documentation of the Bushing Joint (<code>doc "Bushing Joint"</code>) that is used to position the Hexapods, it is mention that the following frame is positioned with respect to the base frame in a way shown in figure <a href="#orgb016316">1</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orgb016316" class="figure">
|
|
<p><img src="figs/bushing_joint_transform.png" alt="bushing_joint_transform.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Joint Transformation Sequence for the Bushing Joint</p>
|
|
</div>
|
|
|
|
<p>
|
|
Basically, it performs the translations, and then the rotation along the X, Y and Z axis of the moving frame.
|
|
The three rotations that we define thus corresponds to the Euler U-V-W angles.
|
|
</p>
|
|
|
|
<p>
|
|
We should have the <b>same behavior</b> for the Micro-Hexapod on Simscape (same inputs at least).
|
|
However, the Bushing Joint makes rotations around mobiles axes (X, Y' and then Z'') and not fixed axes (X, Y and Z).
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd390910" class="outline-4">
|
|
<h4 id="orgd390910"><span class="section-number-4">1.2.2</span> Using Inverse Kinematics and Leg Actuators</h4>
|
|
<div class="outline-text-4" id="text-1-2-2">
|
|
<p>
|
|
Here, we can use the Inverse Kinematic of the Hexapod to determine the length of each leg in order to obtain some defined translation and rotation of the mobile platform.
|
|
</p>
|
|
|
|
<p>
|
|
The advantages are:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>we can position the Hexapod as we want by specifying a rotation matrix</li>
|
|
<li>the hexapod keeps its full flexibility as we don't specify any wanted displacements, only leg's rest position</li>
|
|
</ul>
|
|
|
|
<p>
|
|
However:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>even though the rest position of each leg (the position where the stiffness force is zero) is set correctly, the hexapod will we deflected due to gravity</li>
|
|
</ul>
|
|
|
|
<p>
|
|
Thus, for this simulation, we <b>remove the gravity</b>.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf6ea97b" class="outline-5">
|
|
<h5 id="orgf6ea97b"><span class="section-number-5">1.2.2.1</span> Theory</h5>
|
|
<div class="outline-text-5" id="text-1-2-2-1">
|
|
<p>
|
|
For inverse kinematic analysis, it is assumed that the position \({}^A\bm{P}\) and orientation of the moving platform \({}^A\bm{R}_B\) are given and the problem is to obtain the joint variables, namely, \(\bm{L} = [l_1, l_2, \dots, l_6]^T\).
|
|
</p>
|
|
|
|
<p>
|
|
From the geometry of the manipulator, the loop closure for each limb, \(i = 1, 2, \dots, 6\) can be written as
|
|
</p>
|
|
\begin{align*}
|
|
l_i {}^A\hat{\bm{s}}_i &= {}^A\bm{A} + {}^A\bm{b}_i - {}^A\bm{a}_i \\
|
|
&= {}^A\bm{A} + {}^A\bm{R}_b {}^B\bm{b}_i - {}^A\bm{a}_i
|
|
\end{align*}
|
|
|
|
<p>
|
|
To obtain the length of each actuator and eliminate \(\hat{\bm{s}}_i\), it is sufficient to dot multiply each side by itself:
|
|
</p>
|
|
\begin{equation}
|
|
l_i^2 \left[ {}^A\hat{\bm{s}}_i^T {}^A\hat{\bm{s}}_i \right] = \left[ {}^A\bm{P} + {}^A\bm{R}_B {}^B\bm{b}_i - {}^A\bm{a}_i \right]^T \left[ {}^A\bm{P} + {}^A\bm{R}_B {}^B\bm{b}_i - {}^A\bm{a}_i \right]
|
|
\end{equation}
|
|
|
|
<p>
|
|
Hence, for \(i = 1, 2, \dots, 6\), each limb length can be uniquely determined by:
|
|
</p>
|
|
\begin{equation}
|
|
l_i = \sqrt{{}^A\bm{P}^T {}^A\bm{P} + {}^B\bm{b}_i^T {}^B\bm{b}_i + {}^A\bm{a}_i^T {}^A\bm{a}_i - 2 {}^A\bm{P}^T {}^A\bm{a}_i + 2 {}^A\bm{P}^T \left[{}^A\bm{R}_B {}^B\bm{b}_i\right] - 2 \left[{}^A\bm{R}_B {}^B\bm{b}_i\right]^T {}^A\bm{a}_i}
|
|
\end{equation}
|
|
|
|
<p>
|
|
If the position and orientation of the moving platform lie in the feasible workspace of the manipulator, one unique solution to the limb length is determined by the above equation.
|
|
Otherwise, when the limbs' lengths derived yield complex numbers, then the position or orientation of the moving platform is not reachable.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org67bcb7b" class="outline-5">
|
|
<h5 id="org67bcb7b"><span class="section-number-5">1.2.2.2</span> Matlab Implementation</h5>
|
|
<div class="outline-text-5" id="text-1-2-2-2">
|
|
<p>
|
|
We open the Simulink file.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">open<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'kinematics/matlab/hexapod_tests.slx'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We load the configuration and set a small <code>StopTime</code>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/conf_simscape.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-matlab-simulink-keyword">set_param</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, '<span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We define the wanted position/orientation of the Hexapod under study.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">tx = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% [rad]</span>
|
|
ty = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">2</span>; <span class="org-comment">% [rad]</span>
|
|
tz = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">05</span>; <span class="org-comment">% [rad]</span>
|
|
|
|
Rx = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</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> cos<span class="org-rainbow-delimiters-depth-2">(</span>tx<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>tx<span class="org-rainbow-delimiters-depth-2">)</span>;
|
|
<span class="org-highlight-numbers-number">0</span> sin<span class="org-rainbow-delimiters-depth-2">(</span>tx<span class="org-rainbow-delimiters-depth-2">)</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>tx<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
|
|
Ry = <span class="org-rainbow-delimiters-depth-1">[</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>ty<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> sin<span class="org-rainbow-delimiters-depth-2">(</span>ty<span class="org-rainbow-delimiters-depth-2">)</span>;
|
|
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span>;
|
|
<span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>ty<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>ty<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
|
|
Rz = <span class="org-rainbow-delimiters-depth-1">[</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>tz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>tz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span>;
|
|
sin<span class="org-rainbow-delimiters-depth-2">(</span>tz<span class="org-rainbow-delimiters-depth-2">)</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>tz<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">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
|
|
ARB = Rz<span class="org-type">*</span>Ry<span class="org-type">*</span>Rx;
|
|
AP = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">01</span>; <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">02</span>; <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">03</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [m]</span>
|
|
|
|
hexapod = initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'AP'</span>, AP, <span class="org-string">'ARB'</span>, ARB<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We run the simulation.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'hexapod_tests'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we verify that we indeed succeed to go to the wanted position.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>simout.x.Data<span class="org-rainbow-delimiters-depth-2">(</span>end<span class="org-rainbow-delimiters-depth-2">)</span> ; simout.y.Data<span class="org-rainbow-delimiters-depth-2">(</span>end<span class="org-rainbow-delimiters-depth-2">)</span> ; simout.z.Data<span class="org-rainbow-delimiters-depth-2">(</span>end<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span> <span class="org-type">-</span> AP
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">1.611e-10</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">-1.3748e-10</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">8.4879e-11</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">simout.R.Data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-type">:</span>, end<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>ARB
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-right" />
|
|
|
|
<col class="org-right" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">-1.2659e-10</td>
|
|
<td class="org-right">6.5603e-11</td>
|
|
<td class="org-right">6.2183e-10</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">1.0354e-10</td>
|
|
<td class="org-right">-5.2439e-11</td>
|
|
<td class="org-right">-5.2425e-10</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">-5.9816e-10</td>
|
|
<td class="org-right">5.532e-10</td>
|
|
<td class="org-right">-1.7737e-10</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2019-12-12 jeu. 11:39</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|