80 lines
3.3 KiB
Matlab
80 lines
3.3 KiB
Matlab
%*** CHAPTER 8: DYNAMICS OF OPEN CHAINS ***
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function taumat ...
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= InverseDynamicsTrajectory(thetamat, dthetamat, ddthetamat, ...
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g, Ftipmat, Mlist, Glist, Slist)
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% Takes thetamat: An N x n matrix of robot joint variables,
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% dthetamat: An N x n matrix of robot joint velocities,
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% ddthetamat: An N x n matrix of robot joint accelerations,
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% g: Gravity vector g,
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% Ftipmat: An N x 6 matrix of spatial forces applied by the
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% end-effector (If there are no tip forces, the user should
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% input a zero and a zero matrix will be used),
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% Mlist: List of link frames i relative to i-1 at the home position,
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% Glist: Spatial inertia matrices Gi of the links,
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% Slist: Screw axes Si of the joints in a space frame, in the format
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% of a matrix with the screw axes as the columns.
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% Returns taumat: The N x n matrix of joint forces/torques for the
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% specified trajectory, where each of the N rows is the
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% vector of joint forces/torques at each time step.
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% This function uses InverseDynamics to calculate the joint forces/torques
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% required to move the serial chain along the given trajectory.
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% Example Inputs (3 Link Robot)
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%{
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clc; clear;
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%Create a trajectory to follow using functions from Chapter 9
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thetastart = [0; 0; 0];
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thetaend = [pi / 2; pi / 2; pi / 2];
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Tf = 3;
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N= 1000;
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method = 5 ;
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traj = JointTrajectory(thetastart, thetaend, Tf, N, method);
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thetamat = traj;
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dthetamat = zeros(1000, 3);
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ddthetamat = zeros(1000, 3);
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dt = Tf / (N - 1);
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for i = 1: N - 1
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dthetamat(i + 1, :) = (thetamat(i + 1, :) - thetamat(i, :)) / dt;
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ddthetamat(i + 1, :) = (dthetamat(i + 1, :) - dthetamat(i, :)) / dt;
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end
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%Initialise robot descripstion (Example with 3 links)
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g = [0; 0; -9.8];
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Ftipmat = ones(N, 6);
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M01 = [[1, 0, 0, 0]; [0, 1, 0, 0]; [0, 0, 1, 0.089159]; [0, 0, 0, 1]];
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M12 = [[0, 0, 1, 0.28]; [0, 1, 0, 0.13585]; [-1, 0 ,0, 0]; [0, 0, 0, 1]];
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M23 = [[1, 0, 0, 0]; [0, 1, 0, -0.1197]; [0, 0, 1, 0.395]; [0, 0, 0, 1]];
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M34 = [[1, 0, 0, 0]; [0, 1, 0, 0]; [0, 0, 1, 0.14225]; [0, 0, 0, 1]];
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G1 = diag([0.010267, 0.010267, 0.00666, 3.7, 3.7, 3.7]);
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G2 = diag([0.22689, 0.22689, 0.0151074, 8.393, 8.393, 8.393]);
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G3 = diag([0.0494433, 0.0494433, 0.004095, 2.275, 2.275, 2.275]);
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Glist = cat(3, G1, G2, G3);
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Mlist = cat(3, M01, M12, M23, M34);
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Slist = [[1; 0; 1; 0; 1; 0], ...
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[0; 1; 0; -0.089; 0; 0], ...
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[0; 1; 0; -0.089; 0; 0.425]];
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taumat = InverseDynamicsTrajectory(thetamat, dthetamat, ddthetamat, ...
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g, Ftipmat, Mlist, Glist, Slist);
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%Output using matplotlib to plot the joint forces/torques
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time=0: dt: Tf;
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plot(time, taumat(:, 1), 'b')
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hold on
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plot(time, taumat(:, 2), 'g')
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plot(time, taumat(:, 3), 'r')
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title('Plot for Torque Trajectories')
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xlabel('Time')
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ylabel('Torque')
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legend('Tau1', 'Tau2', 'Tau3')
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%}
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thetamat = thetamat';
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dthetamat = dthetamat';
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ddthetamat = ddthetamat';
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Ftipmat = Ftipmat';
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taumat = thetamat;
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for i = 1: size(thetamat, 2)
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taumat(:, i) ...
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= InverseDynamics(thetamat(:, i), dthetamat(:, i), ddthetamat(:, i), ...
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g, Ftipmat(:, i), Mlist, Glist, Slist);
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end
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taumat = taumat';
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end |