jtraj.m

Robotics TOOLBOX The Toolbox provides many functions that are useful in robotics including such thi

%JTRAJ Compute a joint space trajectory between two points
%
%	[Q QD QDD] = JTRAJ(Q0, Q1, N)
%	[Q QD QDD] = JTRAJ(Q0, Q1, N, QD0, QD1)
%	[Q QD QDD] = JTRAJ(Q0, Q1, T)
%	[Q QD QDD] = JTRAJ(Q0, Q1, T, QD0, QD1)
%
% Returns a joint space trajectory Q from state Q0 to Q1.  The number
% of points is N or the length of the given time vector T.  A 7th
% order polynomial is used with default zero boundary conditions for
% velocity and acceleration.  Non-zero boundary velocities can be
% optionally specified as QD0 and QD1.
%
% The function can optionally return a velocity and acceleration
% trajectories as QD and QDD.
%
% Each trajectory is an mxn matrix, with one row per time step, and
% one column per joint parameter.
%
% See also: CTRAJ.

% Copyright (C) 1993-2002, by Peter I. Corke

%  MOD.HISTORY
% 1/95 add support for initial velocities as advertised
% 8/95 fix bug with initial conditions
% 8/96 fix another bug with initial conditions
% $Log: jtraj.m,v $
% Revision 1.2  2002/04/01 11:47:14  pic
% General cleanup of code: help comments, see also, copyright, remnant dh/dyn
% references, clarification of functions.
%
% $Revision: 1.2 $

function [qt,qdt,qddt] = jtraj(q0, q1, tv, qd0, qd1)
	if length(tv) > 1,
		tscal = max(tv);
		t = tv(:)/tscal;
	else
		tscal = 1;
		t = [0:(tv-1)]'/(tv-1);	% normalized time from 0 -> 1
	end

	q0 = q0(:);
	q1 = q1(:);

	if nargin == 3,
		qd0 = zeros(size(q0));
		qd1 = qd0;
	end

	% compute the polynomial coefficients
	A = 6*(q1 - q0) - 3*(qd1+qd0)*tscal;
	B = -15*(q1 - q0) + (8*qd0 + 7*qd1)*tscal;
	C = 10*(q1 - q0) - (6*qd0 + 4*qd1)*tscal;
	E = qd0*tscal; % as the t vector has been normalized
	F = q0;

	tt = [t.^5 t.^4 t.^3 t.^2 t ones(size(t))];
	c = [A B C zeros(size(A)) E F]';
	
	qt = tt*c;

	% compute optional velocity
	if nargout >= 2,
		c = [ zeros(size(A)) 5*A 4*B 3*C  zeros(size(A)) E ]';
		qdt = tt*c/tscal;
	end

	% compute optional acceleration
	if nargout == 3,
		c = [ zeros(size(A))  zeros(size(A)) 20*A 12*B 6*C  zeros(size(A))]';
		qddt = tt*c/tscal^2;
	end