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

function ddthetalist = ForwardDynamics(thetalist, dthetalist, taulist, ...
                                       g, Ftip, Mlist, Glist, Slist)
% Takes thetalist: A list of joint variables,
%       dthetalist: A list of joint rates,
%       taulist: An n-vector of joint forces/torques,
%       g: Gravity vector g,
%       Ftip: Spatial force applied by the end-effector expressed in frame 
%             {n+1},
%       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 ddthetalist: The resulting joint accelerations.
% This function computes ddthetalist by solving:
% Mlist(thetalist) * ddthetalist = taulist - c(thetalist,dthetalist) ...
%                                  - g(thetalist) - Jtr(thetalist) * Ftip
% Example Input (3 Link Robot):
%{
  clear; clc;
  thetalist = [0.1; 0.1; 0.1];
  dthetalist = [0.1; 0.2; 0.3]; 
  taulist = [0.5; 0.6; 0.7];
  g = [0; 0; -9.8];
  Ftip = [1; 1; 1; 1; 1; 1];
  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]];
  ddthetalist = ForwardDynamics(thetalist, dthetalist, taulist, g, ...
                                Ftip, Mlist, Glist, Slist)
%}
% Output:
% ddthetalist =
%   -0.9739
%   25.5847
%  -32.9150

ddthetalist = MassMatrix(thetalist, Mlist, Glist, Slist) ...
              \ (taulist - VelQuadraticForces(thetalist, dthetalist, ...
                                              Mlist, Glist, Slist) ...
                 - GravityForces(thetalist, g, Mlist, Glist, Slist) ...
                 - EndEffectorForces(thetalist, Ftip, Mlist, Glist, ...
                                     Slist));
end