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

function grav = GravityForces(thetalist, g, Mlist, Glist, Slist)
% Takes thetalist: A list of joint variables,
%       g: 3-vector for gravitational acceleration,
%       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 grav: The joint forces/torques required to overcome gravity at 
%               thetalist
% This function calls InverseDynamics with Ftip = 0, dthetalist = 0, and 
% ddthetalist = 0.
% Example Input (3 Link Robot):
%{
  clear; clc;
  thetalist = [0.1; 0.1; 0.1];
  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(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]];
  grav = GravityForces(thetalist, g, Mlist, Glist, Slist)
%}
% Output:
% grav =
%   28.4033
%  -37.6409
%   -5.4416

n = size(thetalist, 1);
grav = InverseDynamics(thetalist, zeros(n, 1), zeros(n, 1) ,g, ...
                       [0; 0; 0; 0; 0; 0], Mlist, Glist, Slist);
end