📄 rtidemo.html

📁 Robot tool box - provides many functions that are useful in robotics including such things as kinem
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"                "http://www.w3.org/TR/REC-html40/loose.dtd"><html><head>  <title>Description of rtidemo</title>  <meta name="keywords" content="rtidemo">  <meta name="description" content="RTIDDEMO Inverse dynamics demo">  <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">  <meta name="generator" content="m2html &copy; 2003 Guillaume Flandin">  <meta name="robots" content="index, follow">  <link type="text/css" rel="stylesheet" href="../m2html.css"></head><body><a name="_top"></a><div><a href="../index.html">Home</a> &gt;  <a href="#">demos</a> &gt; rtidemo.m</div><!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png">&nbsp;Master index</a></td><td align="right"><a href="index.html">Index for ./demos&nbsp;<img alt=">" border="0" src="../right.png"></a></td></tr></table>--><h1>rtidemo</h1><h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="box"><strong>RTIDDEMO Inverse dynamics demo</strong></div><h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="box"><strong>This is a script file. </strong></div><h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="fragment"><pre class="comment">RTIDDEMO Inverse dynamics demo</pre></div><!-- crossreference --><h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>This function calls:<ul style="list-style-image:url(../matlabicon.gif)"></ul>This function is called by:<ul style="list-style-image:url(../matlabicon.gif)"></ul><!-- crossreference --><h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="fragment"><pre>0001 <span class="comment">%RTIDDEMO Inverse dynamics demo</span>0002 0003 <span class="comment">% Copyright (C) 1993-2002, by Peter I. Corke</span>0004 echo off0005 <span class="comment">% 6/99    fix syntax errors</span>0006 <span class="comment">% $Log: not supported by cvs2svn $</span>0007 <span class="comment">% Revision 1.3  2002-04-02 12:26:49  pic</span>0008 <span class="comment">% Handle figures better, control echo at end of each script.</span>0009 <span class="comment">% Fix bug in calling ctraj.</span>0010 <span class="comment">%</span>0011 <span class="comment">% Revision 1.2  2002/04/01 11:47:17  pic</span>0012 <span class="comment">% General cleanup of code: help comments, see also, copyright, remnant dh/dyn</span>0013 <span class="comment">% references, clarification of functions.</span>0014 <span class="comment">%</span>0015 <span class="comment">% $Revision: 1.1 $</span>0016 figure(2)0017 echo on0018 <span class="comment">%</span>0019 <span class="comment">% Inverse dynamics computes the joint torques required to achieve the specified</span>0020 <span class="comment">% state of joint position, velocity and acceleration.</span>0021 <span class="comment">% The recursive Newton-Euler formulation is an efficient matrix oriented</span>0022 <span class="comment">% algorithm for computing the inverse dynamics, and is implemented in the</span>0023 <span class="comment">% function rne().</span>0024 <span class="comment">%</span>0025 <span class="comment">% Inverse dynamics requires inertial and mass parameters of each link, as well</span>0026 <span class="comment">% as the kinematic parameters.  This is achieved by augmenting the kinematic</span>0027 <span class="comment">% description matrix with additional columns for the inertial and mass</span>0028 <span class="comment">% parameters for each link.</span>0029 <span class="comment">%</span>0030 <span class="comment">% For example, for a Puma 560 in the zero angle pose, with all joint velocities</span>0031 <span class="comment">% of 5rad/s and accelerations of 1rad/s/s, the joint torques required are</span>0032 <span class="comment">%</span>0033     tau = rne(p560, qz, 5*ones(1,6), ones(1,6))0034 pause <span class="comment">% any key to continue</span>0035 0036 <span class="comment">% As with other functions the inverse dynamics can be computed for each point</span>0037 <span class="comment">% on a trajectory.  Create a joint coordinate trajectory and compute velocity</span>0038 <span class="comment">% and acceleration as well</span>0039     t = [0:.056:2];         <span class="comment">% create time vector</span>0040     [q,qd,qdd] = jtraj(qz, qr, t); <span class="comment">% compute joint coordinate trajectory</span>0041     tau = rne(p560, q, qd, qdd); <span class="comment">% compute inverse dynamics</span>0042 <span class="comment">%</span>0043 <span class="comment">%  Now the joint torques can be plotted as a function of time</span>0044     plot(t, tau(:,1:3))0045     xlabel(<span class="string">'Time (s)'</span>);0046     ylabel(<span class="string">'Joint torque (Nm)'</span>)0047 pause <span class="comment">% any key to continue</span>0048 0049 <span class="comment">%</span>0050 <span class="comment">% Much of the torque on joints 2 and 3 of a Puma 560 (mounted conventionally) is</span>0051 <span class="comment">% due to gravity.  That component can be computed using gravload()</span>0052     taug = gravload(p560, q);0053     plot(t, taug(:,1:3))0054     xlabel(<span class="string">'Time (s)'</span>);0055     ylabel(<span class="string">'Gravity torque (Nm)'</span>)0056 pause <span class="comment">% any key to continue</span>0057 0058 <span class="comment">% Now lets plot that as a fraction of the total torque required over the</span>0059 <span class="comment">% trajectory</span>0060     subplot(2,1,1)0061     plot(t,[tau(:,2) taug(:,2)])0062     xlabel(<span class="string">'Time (s)'</span>);0063     ylabel(<span class="string">'Torque on joint 2 (Nm)'</span>)0064     subplot(2,1,2)0065     plot(t,[tau(:,3) taug(:,3)])0066     xlabel(<span class="string">'Time (s)'</span>);0067     ylabel(<span class="string">'Torque on joint 3 (Nm)'</span>)0068 pause <span class="comment">% any key to continue</span>0069 <span class="comment">%</span>0070 <span class="comment">% The inertia seen by the waist (joint 1) motor changes markedly with robot</span>0071 <span class="comment">% configuration.  The function inertia() computes the manipulator inertia matrix</span>0072 <span class="comment">% for any given configuration.</span>0073 <span class="comment">%</span>0074 <span class="comment">%  Let's compute the variation in joint 1 inertia, that is M(1,1), as the</span>0075 <span class="comment">% manipulator moves along the trajectory (this may take a few minutes)</span>0076     M = inertia(p560, q);0077     M11 = squeeze(M(1,1,:));0078     plot(t, M11);0079     xlabel(<span class="string">'Time (s)'</span>);0080     ylabel(<span class="string">'Inertia on joint 1 (kgms2)'</span>)0081 <span class="comment">% Clearly the inertia seen by joint 1 varies considerably over this path.</span>0082 <span class="comment">% This is one of many challenges to control design in robotics, achieving</span>0083 <span class="comment">% stability and high-performance in the face of plant variation.  In fact</span>0084 <span class="comment">% for this example the inertia varies by a factor of</span>0085     max(M11)/min(M11)0086 pause <span class="comment">% any key to continue</span>0087 echo off</pre></div><hr><address>Generated on Sun 15-Feb-2009 18:09:29 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> &copy; 2003</address></body></html>
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