% Copyright (C) 1993-2013, by Peter I. Corke
%
% This file is part of The Robotics Toolbox for MATLAB (RTB).
% 
% RTB is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
% 
% RTB is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU Lesser General Public License for more details.
% 
% You should have received a copy of the GNU Leser General Public License
% along with RTB.  If not, see <http://www.gnu.org/licenses/>.
%
% http://www.petercorke.com

%%begin

% Forward dynamics is the computation of joint accelerations given position and
% velocity state, and actuator torques.  It is useful in simulation of a robot
% control system.
%
% Consider a Puma 560 at rest in the zero angle pose, with zero applied joint 
% torques. The joint acceleration would be given by

mdl_puma560
p560.accel(qz, zeros(1,6), zeros(1,6))

% To be useful for simulation this function must be integrated.  fdyn() uses the
% MATLAB function ode45() to integrate the joint acceleration.  It also allows 
% for a user written function to compute the joint torque as a function of 
% manipulator state.
%
% To simulate the motion of the Puma 560 from rest in the zero angle pose 
% with zero applied joint torques

tic
[t q qd] = p560.nofriction().fdyn(10, [], qz);
toc

% and the resulting motion can be plotted versus time

subplot(3,1,1)
plot(t,q(:,1))
xlabel('Time (s)');
ylabel('Joint 1 (rad)')
subplot(3,1,2)
plot(t,q(:,2))
xlabel('Time (s)');
ylabel('Joint 2 (rad)')
subplot(3,1,3)
plot(t,q(:,3))
xlabel('Time (s)');
ylabel('Joint 3 (rad)')

% Clearly the robot is collapsing under gravity, but it is interesting to 
% note that rotational velocity of the upper and lower arm are exerting 
% centripetal and Coriolis torques on the waist joint, causing it to rotate.

% This can be shown in animation also
clf
p560.plot(q)