Modern_Robotics/code/MATLAB/SimulateControl.m

%*** CHAPTER 11: ROBOT CONTROL ***

function [taumat, thetamat] ...
         = SimulateControl(thetalist,dthetalist,g,Ftipmat,Mlist,Glist, ...
                           Slist,thetamatd,dthetamatd,ddthetamatd, ...
                           gtilde,Mtildelist,Gtildelist,Kp,Ki,Kd,dt,intRes)
% Takes thetalist: n-vector of initial joint variables,
%       dthetalist: n-vector of initial joint velocities,
%       g: Actual 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: Actual list of link frames i relative to i? at the home 
%              position,
%       Glist: Actual spatial inertia matrices Gi of the links,
%       Slist: Screw axes Si of the joints in a space frame,
%       thetamatd: An Nxn matrix of desired joint variables from the 
%                  reference trajectory,
%       dthetamatd: An Nxn matrix of desired joint velocities,
%       ddthetamatd: An Nxn matrix of desired joint accelerations,
%       gtilde: The gravity vector based on the model of the actual robot
%               (actual values given above),
%       Mtildelist: The link frame locations based on the model of the 
%                   actual robot (actual values given above),
%       Gtildelist: The link spatial inertias based on the model of the 
%                   actual robot (actual values given above),
%       Kp: The feedback proportional gain (identical for each joint),
%       Ki: The feedback integral gain (identical for each joint),
%       Kd: The feedback derivative gain (identical for each joint),
%       dt: The timestep between points on the reference trajectory.
%       intRes: Integration resolution is the number of times integration 
%               (Euler) takes places between each time step. Must be an 
%               integer value greater than or equal to 1.
% Returns taumat: An Nxn matrix of the controller commanded joint 
%                 forces/torques, where each row of n forces/torques 
%                 corresponds to a single time instant,
%         thetamat: An Nxn matrix of actual joint angles.
% The end of this function plots all the actual and desired joint angles.
% Example Usage
%{
  clc;clear;
  thetalist = [0.1; 0.1; 0.1];
  dthetalist = [0.1; 0.2; 0.3];
  %Initialize robot description (Example with 3 links)
  g = [0; 0; -9.8];
  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(4,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]];
  dt = 0.01;
  %Create a trajectory to follow
  thetaend =[pi / 2; pi; 1.5 * pi];
  Tf = 1;
  N = Tf / dt;
  method = 5;
  thetamatd = JointTrajectory(thetalist,thetaend,Tf,N,method);
  dthetamatd = zeros(N,3);
  ddthetamatd = zeros(N,3);
  dt = Tf / (N-1);
  for i = 1:N - 1
      dthetamatd(i + 1,:) = (thetamatd(i + 1,:)-thetamatd(i,:)) / dt;
      ddthetamatd(i + 1,:) = (dthetamatd(i + 1,:)-dthetamatd(i,:)) / dt;
  end
  %Possibly wrong robot description (Example with 3 links)
  gtilde = [0.8; 0.2; -8.8];
  Mhat01 = [[1, 0, 0, 0]; [0, 1, 0, 0]; [0, 0, 1, 0.1]; [0, 0, 0, 1]];
  Mhat12 = [[0, 0, 1, 0.3]; [0, 1, 0, 0.2]; [-1, 0 ,0, 0]; [0, 0, 0, 1]];
  Mhat23 = [[1, 0, 0, 0]; [0, 1, 0, -0.2]; [0, 0, 1, 0.4]; [0, 0, 0, 1]];
  Mhat34 = [[1, 0, 0, 0]; [0, 1, 0, 0]; [0, 0, 1, 0.2]; [0, 0, 0, 1]];
  Ghat1 = diag([0.1, 0.1, 0.1, 4, 4, 4]);
  Ghat2 = diag([0.3, 0.3, 0.1, 9, 9, 9]);
  Ghat3 = diag([0.1, 0.1, 0.1, 3, 3, 3]);
  Gtildelist = cat(3,Ghat1,Ghat2,Ghat3);
  Mtildelist = cat(4,Mhat01,Mhat12,Mhat23,Mhat34); 
  Ftipmat = ones(N,6);
  Kp = 20;
  Ki = 10;
  Kd = 18;
  intRes = 8;
  [taumat, thetamat] ...
  = SimulateControl(thetalist,dthetalist,g,Ftipmat,Mlist,Glist,Slist, ...
                    thetamatd,dthetamatd,ddthetamatd,gtilde,Mtildelist, ...
                    Gtildelist,Kp,Ki,Kd,dt,intRes);
%}

Ftipmat = Ftipmat';
thetamatd = thetamatd';
dthetamatd = dthetamatd';
ddthetamatd = ddthetamatd';
n = size(thetamatd,2);
taumat = zeros(size(thetamatd));
thetamat = zeros(size(thetamatd));
thetacurrent = thetalist;
dthetacurrent = dthetalist;
eint = zeros(size(thetamatd,1),1);
for i=1:n
    taulist ...
    = ComputedTorque(thetacurrent,dthetacurrent,eint,gtilde,Mtildelist, ...
                     Gtildelist,Slist,thetamatd(:,i),dthetamatd(:,i), ...
                     ddthetamatd(:,i),Kp,Ki,Kd);
    for j=1:intRes
        ddthetalist ...
        = ForwardDynamics(thetacurrent,dthetacurrent,taulist,g, ...
                          Ftipmat(:,i),Mlist,Glist,Slist);    
        [thetacurrent, dthetacurrent] ...
        = EulerStep(thetacurrent,dthetacurrent,ddthetalist,(dt/intRes));
    end
    taumat(:,i) = taulist;
    thetamat(:,i) = thetacurrent;    
    eint = eint + (dt*(thetamatd(:,i) - thetacurrent));
end
%Output using matplotlib
links = size(thetamat,1);
leg = cell(1,2*links);
time=0:dt:((dt*n)-(dt));
timed=0:(dt):((dt*n)-(dt));
figure
hold on
for i=1:links
    col = rand(1,3);
    plot(time,(thetamat(i,:)'),'-','Color',col)
    plot(timed,(thetamatd(i,:)'),'.','Color',col)
    leg{(2*i)-1} = (strcat('ActualTheta', num2str(i)));
    leg{(2*i)} = (strcat('DesiredTheta', num2str(i)));
end
title('Plot of Actual and Desired Joint Angles')
xlabel('Time')
ylabel('Joint Angles')
legend(leg, 'Location', 'NorthWest')
taumat = taumat';
thetamat = thetamat';
end