2019-03-22 12:03:59 +01:00
<?xml version="1.0" encoding="utf-8"?>
2020-01-27 17:42:09 +01:00
<?xml version="1.0" encoding="utf-8"?>
2019-03-22 12:03:59 +01:00
< !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 >
2020-03-03 15:53:02 +01:00
<!-- 2020 - 03 - 02 lun. 17:57 -->
2019-03-22 12:03:59 +01:00
< meta http-equiv = "Content-Type" content = "text/html;charset=utf-8" / >
< meta name = "viewport" content = "width=device-width, initial-scale=1" / >
2019-08-26 11:58:44 +02:00
< title > Stewart Platforms< / title >
2019-03-22 12:03:59 +01:00
< meta name = "generator" content = "Org mode" / >
2020-01-27 17:42:09 +01:00
< meta name = "author" content = "Dehaeze Thomas" / >
2019-03-22 12:03:59 +01:00
< 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 >
2019-12-20 08:55:55 +01:00
< link rel = "stylesheet" type = "text/css" href = "./css/htmlize.css" / >
< link rel = "stylesheet" type = "text/css" href = "./css/readtheorg.css" / >
< script src = "./js/jquery.min.js" > < / script >
< script src = "./js/bootstrap.min.js" > < / script >
< script src = "./js/jquery.stickytableheaders.min.js" > < / script >
< script src = "./js/readtheorg.js" > < / script >
2019-03-22 12:03:59 +01:00
< script type = "text/javascript" >
2020-03-03 15:53:02 +01:00
// @license magnet:?xt=urn:btih:1f739d935676111cfff4b4693e3816e664797050& dn=gpl-3.0.txt GPL-v3-or-Later
2019-03-22 12:03:59 +01:00
<!-- /* --> <![CDATA[/*> <!-- */
2020-03-03 15:53:02 +01:00
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;
}
/*]]>*///-->
// @license-end
2019-03-22 12:03:59 +01:00
< / script >
< / head >
< body >
2020-02-11 18:04:45 +01:00
< 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" >
2019-08-26 11:58:44 +02:00
< h1 class = "title" > Stewart Platforms< / h1 >
2020-01-30 11:11:56 +01:00
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
2020-02-11 15:50:52 +01:00
< li > < a href = "#orgff0bfd7" > 1. Simulink Project (link)< / a > < / li >
< li > < a href = "#org38b9089" > 2. Stewart Platform Architecture Definition (link)< / a > < / li >
< li > < a href = "#orgf1c7b3b" > 3. Simscape Model of the Stewart Platform (link)< / a > < / li >
< li > < a href = "#org369c8bb" > 4. Kinematic Analysis (link)< / a > < / li >
< li > < a href = "#org2e3169e" > 5. Identification of the Stewart Dynamics (link)< / a > < / li >
< li > < a href = "#orgc3a4c87" > 6. Active Damping (link)< / a > < / li >
< li > < a href = "#org5b4e9b0" > 7. Motion Control of the Stewart Platform (link)< / a > < / li >
< li > < a href = "#org1f468b1" > 8. Cubic Configuration (link)< / a > < / li >
2020-01-30 11:11:56 +01:00
< / ul >
< / div >
< / div >
2019-03-22 12:03:59 +01:00
2019-12-20 08:55:55 +01:00
< p >
2020-01-28 13:39:47 +01:00
The goal of this project is to provide a Matlab/Simscape Toolbox to study Stewart platforms.
2019-12-20 08:55:55 +01:00
< / p >
2020-01-28 13:39:47 +01:00
< p >
The project is divided into several section listed below.
< / p >
2019-03-22 12:03:59 +01:00
2020-02-11 15:27:39 +01:00
< div id = "outline-container-orgff0bfd7" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "orgff0bfd7" > < 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" >
2020-01-28 13:39:47 +01:00
< 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 >
2019-03-22 12:03:59 +01:00
< / div >
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org38b9089" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "org38b9089" > < 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" >
2020-01-28 13:39:47 +01:00
< 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 > Location/orientation of the limbs< / li >
2020-01-28 17:38:19 +01:00
< li > Size/inertia of the platforms and the limbs< / li >
2020-01-28 13:39:47 +01:00
< / ul >
2020-01-27 17:42:09 +01:00
2020-01-28 13:39:47 +01:00
< p >
Other parameters are also defined such as:
< / p >
< ul class = "org-ul" >
< li > Stiffness and damping of the struts< / li >
< li > Rest position of the Stewart platform< / li >
< / ul >
< / div >
2019-03-22 12:03:59 +01:00
< / div >
2020-01-27 17:42:09 +01:00
2020-02-11 15:27:39 +01:00
< div id = "outline-container-orgf1c7b3b" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "orgf1c7b3b" > < 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" >
2020-01-28 13:39:47 +01:00
< 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 >
2020-01-27 17:42:09 +01:00
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org369c8bb" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "org369c8bb" > < 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" >
2020-01-28 13:39:47 +01:00
< p >
From the defined geometry of the Stewart platform, we can perform static analysis such as:
< / p >
2019-10-09 11:08:42 +02:00
< ul class = "org-ul" >
2020-01-28 13:39:47 +01:00
< 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 >
2019-10-09 11:08:42 +02:00
< / ul >
2020-01-28 13:39:47 +01:00
< 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 >
2019-10-09 11:08:42 +02:00
< / div >
< / div >
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org2e3169e" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "org2e3169e" > < 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" >
2020-01-28 13:39:47 +01:00
< p >
The Dynamics of the Stewart platform can be identified using the Simscape model.
< / p >
< p >
It is possible to:
< / p >
2019-10-09 11:08:42 +02:00
< ul class = "org-ul" >
2020-01-28 13:39:47 +01:00
< 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 >
2019-10-09 11:08:42 +02:00
< / ul >
2020-01-28 13:39:47 +01:00
< p >
The code that is used for identification is explained < a href = "identification.html" > here< / a > .
< / p >
2019-10-09 11:08:42 +02:00
< / div >
< / div >
2020-02-11 15:27:39 +01:00
< div id = "outline-container-orgc3a4c87" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "orgc3a4c87" > < 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" >
2020-01-28 13:39:47 +01:00
< p >
The use of different sensors are compared for active damping:
< / p >
2019-10-09 11:08:42 +02:00
< ul class = "org-ul" >
2020-01-28 13:39:47 +01:00
< 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 >
2019-10-09 11:08:42 +02:00
< / ul >
2020-01-28 13:39:47 +01:00
< p >
The result of the analysis is accessible < a href = "active-damping.html" > here< / a > .
< / p >
2019-10-09 11:08:42 +02:00
< / div >
< / div >
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org5b4e9b0" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "org5b4e9b0" > < 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" >
2020-01-28 13:39:47 +01:00
< 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 >
2019-10-09 11:08:42 +02:00
< / div >
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org1f468b1" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "org1f468b1" > < 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" >
2019-10-09 11:08:42 +02:00
< p >
2020-01-28 13:39:47 +01:00
The cubic configuration is a special class of Stewart platform that has interesting properties.
< / p >
2019-10-09 11:08:42 +02:00
2020-01-28 13:39:47 +01:00
< p >
These properties are studied in < a href = "cubic-configuration.html" > this< / a > document.
2019-10-09 11:08:42 +02:00
< / p >
2019-03-22 12:03:59 +01:00
< / div >
2020-01-28 13:39:47 +01:00
< / div >
< / div >
2020-01-30 11:11:56 +01:00
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2020-03-03 15:53:02 +01:00
< p class = "date" > Created: 2020-03-02 lun. 17:57< / p >
2020-01-30 11:11:56 +01:00
< / div >
2019-03-22 12:03:59 +01:00
< / body >
< / html >
