Modern_Robotics/code/MATLAB/InverseDynamicsTrajectory.m

%*** CHAPTER 8: DYNAMICS OF OPEN CHAINS ***

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

thetamat = thetamat';
dthetamat = dthetamat';
ddthetamat = ddthetamat';
Ftipmat = Ftipmat';
taumat = thetamat;
for i = 1: size(thetamat, 2)
   taumat(:, i) ...
   = InverseDynamics(thetamat(:, i), dthetamat(:, i), ddthetamat(:, i), ...
                     g, Ftipmat(:, i), Mlist, Glist, Slist);
end
taumat = taumat';
end