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111 lines
3.5 KiB
111 lines
3.5 KiB
%SerialLink.fdyn Integrate forward dynamics
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%
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% [T,Q,QD] = R.fdyn(T1, TORQFUN) integrates the dynamics of the robot over
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% the time interval 0 to T and returns vectors of time TI, joint position Q
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% and joint velocity QD. The initial joint position and velocity are zero.
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% The torque applied to the joints is computed by the user function TORQFUN:
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%
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% [TI,Q,QD] = R.fdyn(T, TORQFUN, Q0, QD0) as above but allows the initial
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% joint position and velocity to be specified.
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%
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% The control torque is computed by a user defined function
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%
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% TAU = TORQFUN(T, Q, QD, ARG1, ARG2, ...)
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%
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% where Q and QD are the manipulator joint coordinate and velocity state
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% respectively, and T is the current time.
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%
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% [T,Q,QD] = R.fdyn(T1, TORQFUN, Q0, QD0, ARG1, ARG2, ...) allows optional
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% arguments to be passed through to the user function.
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%
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% Note::
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% - This function performs poorly with non-linear joint friction, such as
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% Coulomb friction. The R.nofriction() method can be used to set this
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% friction to zero.
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% - If TORQFUN is not specified, or is given as 0 or [], then zero torque
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% is applied to the manipulator joints.
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% - The builtin integration function ode45() is used.
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%
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% See also SerialLink.accel, SerialLink.nofriction, SerialLink.rne, ode45.
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% Copyright (C) 1993-2011, by Peter I. Corke
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%
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% This file is part of The Robotics Toolbox for Matlab (RTB).
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%
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% RTB is free software: you can redistribute it and/or modify
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% it under the terms of the GNU Lesser General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% RTB is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU Lesser General Public License for more details.
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%
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% You should have received a copy of the GNU Leser General Public License
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% along with RTB. If not, see <http://www.gnu.org/licenses/>.
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%
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% http://www.petercorke.com
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function [t, q, qd] = fdyn(robot, t1, torqfun, q0, qd0, varargin)
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% check the Matlab version, since ode45 syntax has changed
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if verLessThan('matlab', '7')
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error('fdyn now requires Matlab version >= 7');
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end
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n = robot.n;
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if nargin == 2
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torqfun = 0;
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q0 = zeros(1,n);
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qd0 = zeros(1,n);
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elseif nargin == 3
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q0 = zeros(1,n);
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qd0 = zeros(1,n);
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elseif nargin == 4
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qd0 = zeros(1,n);
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end
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% concatenate q and qd into the initial state vector
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q0 = [q0(:); qd0(:)];
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[t,y] = ode45(@fdyn2, [0 t1], q0, [], robot, torqfun, varargin{:});
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q = y(:,1:n);
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qd = y(:,n+1:2*n);
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end
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%FDYN2 private function called by FDYN
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%
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% XDD = FDYN2(T, X, FLAG, ROBOT, TORQUEFUN)
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%
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% Called by FDYN to evaluate the robot velocity and acceleration for
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% forward dynamics. T is the current time, X = [Q QD] is the state vector,
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% ROBOT is the object being integrated, and TORQUEFUN is the string name of
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% the function to compute joint torques and called as
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%
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% TAU = TORQUEFUN(T, X)
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%
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% if not given zero joint torques are assumed.
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%
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% The result is XDD = [QD QDD].
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function xd = fdyn2(t, x, robot, torqfun, varargin)
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n = robot.n;
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q = x(1:n)';
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qd = x(n+1:2*n)';
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% evaluate the torque function if one is given
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if isa(torqfun, 'function_handle')
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tau = torqfun(robot, t, q, qd, varargin{:});
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else
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tau = zeros(1,n);
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end
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qdd = robot.accel(x(1:n,1)', x(n+1:2*n,1)', tau);
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xd = [x(n+1:2*n,1); qdd];
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end
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