lwr_server/lwrserv/matlab/rvctools/robot/@SerialLink/gravjac.m

%SerialLink.GRAVJAC Fast gravity load and Jacobian
% 
% [TAU,JAC0] = R.gravjac(Q) is the generalised joint force/torques due to
% gravity (1xN) and the manipulator Jacobian in the base frame (6xN) for
% robot pose Q (1xN), where N is the number of robot joints.
%
% [TAU,JAC0] = R.gravjac(Q,GRAV) as above but gravity is given explicitly
% by GRAV (3x1).
%
% Trajectory operation::
%
% If Q is MxN where N is the number of robot joints then a trajectory is
% assumed where each row of Q corresponds to a pose.  TAU (MxN) is the
% generalised joint torque, each row corresponding to an input pose, and
% JAC0 (6xNxM) where each plane is a Jacobian corresponding to an input pose.
%
% Notes::
% - The gravity vector is defined by the SerialLink property if not explicitly given.
% - Does not use inverse dynamics function RNE.
% - Faster than computing gravity and Jacobian separately.
%
% Author::
% Bryan Moutrie
%
% See also SerialLink.pay, SerialLink, SerialLink.gravload, SerialLink.jacob0.

% Copyright (C) Bryan Moutrie, 2013-2015
% Licensed under the GNU Lesser General Public License
% see full file for full statement
%
% LICENSE STATEMENT:
%
% This file is part of pHRIWARE.
% 
% pHRIWARE 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.
%
% pHRIWARE 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 General Public License for more details.
%
% You should have received a copy of the GNU Lesser General Public 
% License along with pHRIWARE.  If not, see <http://www.gnu.org/licenses/>.
%

function [tauB, J] = gravjac(robot, q, grav)
    
    n = robot.n;
    revolute = [robot.links(:).isrevolute];
    if ~robot.mdh
        baseAxis = robot.base(1:3,3);
        baseOrigin = robot.base(1:3,4);
    end
    
    poses = size(q, 1);
    tauB = zeros(poses, n);
    if nargout == 2, J = zeros(6, robot.n, poses); end
    
    % Forces
    force = zeros(3,n);
    if nargin < 3, grav = robot.gravity; end
    for joint = 1: n
        force(:,joint) = robot.links(joint).m * grav;
    end
    
    % Centre of masses (local frames)
    r = zeros(4,n);
    for joint = 1: n
        r(:,joint) = [robot.links(joint).r'; 1];
    end
    com_arr = zeros(3, n);
    
    for pose = 1: poses
        
        [Te, T] = robot.fkine(q(pose,:));
        
        jointOrigins = squeeze(T(1:3,4,:));
        jointAxes = squeeze(T(1:3,3,:));
        
        if ~robot.mdh
            jointOrigins = [baseOrigin, jointOrigins(:,1:end-1)];
            jointAxes = [baseAxis, jointAxes(:,1:end-1)];
        end
        
        % Backwards recursion
        for joint = n: -1: 1
            
            com = T(:,:,joint) * r(:,joint); % C.o.M. in world frame, homog
            com_arr(:,joint) = com(1:3); % Add it to the distal others
            
            t = 0;
            for link = joint: n % for all links distal to it
                if revolute(joint)
                    d = com_arr(:,link) - jointOrigins(:,joint);
                    t = t + cross3(d, force(:,link));
                    % Though r x F would give the applied torque and not the
                    % reaction torque, the gravity vector is nominally in the
                    % positive z direction, not negative, hence the force is
                    % the reaction force
                else
                    t = t + force(:,link); %force on prismatic joint
                end
            end
            
            tauB(pose,joint) = t' * jointAxes(:,joint);
        end
        
        if nargout == 2
            J(:,:,pose) = makeJ(jointOrigins,jointAxes,Te(1:3,4),revolute);
        end
        
    end
    
    
end

function J = makeJ(O,A,e,r)
    J(4:6,:) = A;
    for j = 1:length(r)
        if r(j)
            J(1:3,j) = cross3(A(:,j),e-O(:,j));
        else
            J(:,j) = J([4 5 6 1 2 3],j); %J(1:3,:) = 0;
        end
    end
end

function c = cross3(a,b)
    c(3,1) = a(1)*b(2) - a(2)*b(1);
    c(1,1) = a(2)*b(3) - a(3)*b(2);
    c(2,1) = a(3)*b(1) - a(1)*b(3);
end