%ACCEL Compute manipulator forward dynamics % % QDD = ACCEL(ROBOT, Q, QD, TORQUE) % QDD = ACCEL(ROBOT, [Q QD TORQUE]) % % Returns a vector of joint accelerations that result from applying the % actuator TORQUE to the manipulator ROBOT in state Q and QD. % % Uses the method 1 of Walker and Orin to compute the forward dynamics. % The accelerations of the coordinates are obtained first % with the method of Walker-Orin and, later,it is joining to obtain speed and position. % This form is useful for simulation of manipulator dynamics, in % conjunction with a numerical integration function. % % Walker and Orin is a numerical method used to obtain the acceleration of the % articular coordinates from the torque vector.For it, Newton-Euler's % algorithm uses when articular aceleration is zero % B= 0+H(q,q')+C(q); tau=D(q)q''+B; q''=inv(D(q))[tau-B] % See also: RNE, ROBOT, ODE45. % MOD HISTORY % 4/99 add object support % 1/02 copy rne code from inertia.m to here for speed % % General cleanup of code: help comments, see also, copyright, remnant dh/dyn % references, clarification of functions. % % % 1999 Peter I. Corke % 2007 Niceto Luque Sola function qdd = accel(robot, Q, qd, torque) n = robot.n; if nargin == 2, q = Q(1:n); qd = Q(n+1:2*n); torque = Q(2*n+1:3*n); else q = Q; if length(q) == robot.n, q = q(:); qd = qd(:); end end % compute current manipulator inertia % torques resulting from unit acceleration of each joint with % no gravity. M = frne(robot, ones(n,1)*q', zeros(n,n), eye(n), [0;0;0]); % compute gravity and coriolis torque % torques resulting from zero acceleration at given velocity & % with gravity acting. tau = frne(robot, q', qd', zeros(1,n)); qdd = feval(@inv, M) * (torque(:) - tau'); %using builtin function