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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 maniplty</title> <meta name="keywords" content="maniplty"> <meta name="description" content="MANIPLTY Manipulability measure"> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="generator" content="m2html © 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> > <a href="index.html">.</a> > maniplty.m</div><!--<table width="100%"><tr><td align="left"><a href="./index.html"><img alt="<" border="0" src="./left.png"> Master index</a></td><td align="right"><a href="index.html">Index for . <img alt=">" border="0" src="./right.png"></a></td></tr></table>--><h1>maniplty</h1><h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="./up.png"></a></h2><div class="box"><strong>MANIPLTY Manipulability measure</strong></div><h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="./up.png"></a></h2><div class="box"><strong>function w = maniplty(robot, q, which) </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">MANIPLTY Manipulability measure M = MANIPLTY(ROBOT, Q) M = MANIPLTY(ROBOT, Q, WHICH) Computes the manipulability index for the manipulator at the given pose. For an n-axis manipulator Q may be an n-element vector, or an m x n joint space trajectory. If Q is a vector MANIPLTY returns a scalar manipulability index. If Q is a matrix MANIPLTY returns a column vector of manipulability indices for each pose specified by Q. The argument WHICH can be either 'yoshikawa' (default) or 'asada' and selects one of two manipulability measures. Yoshikawa's manipulability measure gives an indication of how far the manipulator is from singularities and thus able to move and exert forces uniformly in all directions. Asada's manipulability measure is based on the manipulator's Cartesian inertia matrix. An n-dimensional inertia ellipsoid X' M(q) X = 1 gives an indication of how well the manipulator can accelerate in each of the Cartesian directions. The scalar measure computed here is the ratio of the smallest/largest ellipsoid axis. Ideally the ellipsoid would be spherical, giving a ratio of 1, but in practice will be less than 1. See also: <a href="inertia.html" class="code" title="function M = inertia(robot, q)">INERTIA</a>, <a href="jacob0.html" class="code" title="function J0 = jacob0(robot, q)">JACOB0</a>.</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)"><li><a href="inertia.html" class="code" title="function M = inertia(robot, q)">inertia</a> INERTIA Compute the manipulator inertia matrix</li><li><a href="jacob0.html" class="code" title="function J0 = jacob0(robot, q)">jacob0</a> JACOB0 Compute manipulator Jacobian in world coordinates</li></ul>This function is called by:<ul style="list-style-image:url(./matlabicon.gif)"></ul><!-- crossreference --><h2><a name="_subfunctions"></a>SUBFUNCTIONS <a href="#_top"><img alt="^" border="0" src="./up.png"></a></h2><ul style="list-style-image:url(./matlabicon.gif)"><li><a href="#_sub1" class="code">function m = yoshi(robot, q)</a></li><li><a href="#_sub2" class="code">function m = asada(robot, q)</a></li></ul><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">%MANIPLTY Manipulability measure</span>0002 <span class="comment">%</span>0003 <span class="comment">% M = MANIPLTY(ROBOT, Q)</span>0004 <span class="comment">% M = MANIPLTY(ROBOT, Q, WHICH)</span>0005 <span class="comment">%</span>0006 <span class="comment">% Computes the manipulability index for the manipulator at the given pose.</span>0007 <span class="comment">%</span>0008 <span class="comment">% For an n-axis manipulator Q may be an n-element vector, or an m x n</span>0009 <span class="comment">% joint space trajectory.</span>0010 <span class="comment">%</span>0011 <span class="comment">% If Q is a vector MANIPLTY returns a scalar manipulability index.</span>0012 <span class="comment">% If Q is a matrix MANIPLTY returns a column vector of manipulability</span>0013 <span class="comment">% indices for each pose specified by Q.</span>0014 <span class="comment">%</span>0015 <span class="comment">% The argument WHICH can be either 'yoshikawa' (default) or 'asada' and</span>0016 <span class="comment">% selects one of two manipulability measures.</span>0017 <span class="comment">% Yoshikawa's manipulability measure gives an indication of how far</span>0018 <span class="comment">% the manipulator is from singularities and thus able to move and</span>0019 <span class="comment">% exert forces uniformly in all directions.</span>0020 <span class="comment">%</span>0021 <span class="comment">% Asada's manipulability measure is based on the manipulator's</span>0022 <span class="comment">% Cartesian inertia matrix. An n-dimensional inertia ellipsoid</span>0023 <span class="comment">% X' M(q) X = 1</span>0024 <span class="comment">% gives an indication of how well the manipulator can accelerate</span>0025 <span class="comment">% in each of the Cartesian directions. The scalar measure computed</span>0026 <span class="comment">% here is the ratio of the smallest/largest ellipsoid axis. Ideally</span>0027 <span class="comment">% the ellipsoid would be spherical, giving a ratio of 1, but in</span>0028 <span class="comment">% practice will be less than 1.</span>0029 <span class="comment">%</span>0030 <span class="comment">% See also: INERTIA, JACOB0.</span>0031 0032 <span class="comment">% Copyright (C) 1993-2008, by Peter I. Corke</span>0033 <span class="comment">%</span>0034 <span class="comment">% This file is part of The Robotics Toolbox for Matlab (RTB).</span>0035 <span class="comment">%</span>0036 <span class="comment">% RTB is free software: you can redistribute it and/or modify</span>0037 <span class="comment">% it under the terms of the GNU Lesser General Public License as published by</span>0038 <span class="comment">% the Free Software Foundation, either version 3 of the License, or</span>0039 <span class="comment">% (at your option) any later version.</span>0040 <span class="comment">%</span>0041 <span class="comment">% RTB is distributed in the hope that it will be useful,</span>0042 <span class="comment">% but WITHOUT ANY WARRANTY; without even the implied warranty of</span>0043 <span class="comment">% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span>0044 <span class="comment">% GNU Lesser General Public License for more details.</span>0045 <span class="comment">%</span>0046 <span class="comment">% You should have received a copy of the GNU Leser General Public License</span>0047 <span class="comment">% along with RTB. If not, see <http://www.gnu.org/licenses/>.</span>0048 0049 <a name="_sub0" href="#_subfunctions" class="code">function w = maniplty(robot, q, which)</a>0050 n = robot.n;0051 0052 <span class="keyword">if</span> nargin == 2,0053 which = <span class="string">'yoshikawa'</span>;0054 <span class="keyword">end</span>0055 0056 <span class="keyword">if</span> length(q) == robot.n,0057 q = q(:)';0058 <span class="keyword">end</span>0059 0060 w = [];0061 <span class="keyword">switch</span> which,0062 <span class="keyword">case</span> {<span class="string">'yoshikawa'</span>, <span class="string">'yoshi'</span>, <span class="string">'y'</span>}0063 <span class="keyword">for</span> Q = q',0064 w = [w; <a href="#_sub1" class="code" title="subfunction m = yoshi(robot, q)">yoshi</a>(robot, Q)];0065 <span class="keyword">end</span>0066 <span class="keyword">case</span> {<span class="string">'asada'</span>, <span class="string">'a'</span>}0067 <span class="keyword">for</span> Q = q',0068 w = [w; <a href="#_sub2" class="code" title="subfunction m = asada(robot, q)">asada</a>(robot, Q)];0069 <span class="keyword">end</span>0070 <span class="keyword">end</span>0071 0072 <a name="_sub1" href="#_subfunctions" class="code">function m = yoshi(robot, q)</a>0073 J = <a href="jacob0.html" class="code" title="function J0 = jacob0(robot, q)">jacob0</a>(robot, q);0074 m = sqrt(det(J * J'));0075 0076 <a name="_sub2" href="#_subfunctions" class="code">function m = asada(robot, q)</a>0077 J = <a href="jacob0.html" class="code" title="function J0 = jacob0(robot, q)">jacob0</a>(robot, q);0078 Ji = inv(J);0079 M = <a href="inertia.html" class="code" title="function M = inertia(robot, q)">inertia</a>(robot, q);0080 Mx = Ji' * M * Ji;0081 e = eig(Mx);0082 m = min(e) / max(e);</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> © 2003</address></body></html>⌨️ 快捷键说明
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