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%JACOBN Compute manipulator Jacobian in end-effector frame % % JN = JACOBN(ROBOT, Q) % % Returns a Jacobian matrix for the robot ROBOT in pose Q. % % The manipulator Jacobian matrix maps differential changes in joint space % to differential Cartesian motion of the end-effector (end-effector coords). % dX = J dQ % % This function uses the technique of % Paul, Shimano, Mayer % Differential Kinematic Control Equations for Simple Manipulators % IEEE SMC 11(6) 1981 % pp. 456-460 % % For an n-axis manipulator the Jacobian is a 6 x n matrix. % % See also: JACOB0, DIFF2TR, TR2DIFF % Copyright (C) 1999-2008, by Peter I. Corke % % This file is part of The Robotics Toolbox for Matlab (RTB). % % RTB is free software: you can redistribute it and/or modify % it under the terms of the GNU Lesser General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % RTB is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU Lesser General Public License for more details. % % You should have received a copy of the GNU Leser General Public License % along with RTB. If not, see <http://www.gnu.org/licenses/>. function J = jacobn(robot, q) n = robot.n; L = robot.link; % get the links J = []; U = robot.tool; for j=n:-1:1, if robot.mdh == 0, % standard DH convention U = L{j}( q(j) ) * U; end if L{j}.RP == 'R', % revolute axis d = [ -U(1,1)*U(2,4)+U(2,1)*U(1,4) -U(1,2)*U(2,4)+U(2,2)*U(1,4) -U(1,3)*U(2,4)+U(2,3)*U(1,4)]; delta = U(3,1:3)'; % nz oz az else % prismatic axis d = U(3,1:3)'; % nz oz az delta = zeros(3,1); % 0 0 0 end J = [[d; delta] J]; if robot.mdh ~= 0, % modified DH convention U = L{j}( q(j) ) * U; end end