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65 lines
2.1 KiB
65 lines
2.1 KiB
% Copyright (C) 1993-2013, by Peter I. Corke
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%
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% This file is part of The Robotics Toolbox for MATLAB (RTB).
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%
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% RTB is free software: you can redistribute it and/or modify
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% it under the terms of the GNU Lesser General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% RTB is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU Lesser General Public License for more details.
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%
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% You should have received a copy of the GNU Leser General Public License
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% along with RTB. If not, see <http://www.gnu.org/licenses/>.
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%
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% http://www.petercorke.com
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%%begin
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% Forward dynamics is the computation of joint accelerations given position and
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% velocity state, and actuator torques. It is useful in simulation of a robot
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% control system.
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%
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% Consider a Puma 560 at rest in the zero angle pose, with zero applied joint
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% torques. The joint acceleration would be given by
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mdl_puma560
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p560.accel(qz, zeros(1,6), zeros(1,6))
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% To be useful for simulation this function must be integrated. fdyn() uses the
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% MATLAB function ode45() to integrate the joint acceleration. It also allows
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% for a user written function to compute the joint torque as a function of
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% manipulator state.
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%
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% To simulate the motion of the Puma 560 from rest in the zero angle pose
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% with zero applied joint torques
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tic
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[t q qd] = p560.nofriction().fdyn(10, [], qz);
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toc
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% and the resulting motion can be plotted versus time
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subplot(3,1,1)
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plot(t,q(:,1))
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xlabel('Time (s)');
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ylabel('Joint 1 (rad)')
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subplot(3,1,2)
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plot(t,q(:,2))
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xlabel('Time (s)');
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ylabel('Joint 2 (rad)')
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subplot(3,1,3)
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plot(t,q(:,3))
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xlabel('Time (s)');
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ylabel('Joint 3 (rad)')
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% Clearly the robot is collapsing under gravity, but it is interesting to
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% note that rotational velocity of the upper and lower arm are exerting
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% centripetal and Coriolis torques on the waist joint, causing it to rotate.
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% This can be shown in animation also
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clf
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p560.plot(q)
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