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473 lines
11 KiB
473 lines
11 KiB
/**
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* \file ne.c
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* \author Peter Corke
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* \brief Compute the recursive Newton-Euler formulation
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*/
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/*
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* Copyright (C) 1999-2008, 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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*/
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/*
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* Compute the inverse dynamics via the recursive Newton-Euler formulation
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*
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* Requires: qd current joint velocities
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* qdd current joint accelerations
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* f applied tip force or load
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* grav the gravitational constant
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*
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* Returns: tau vector of bias torques
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*/
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#include "frne.h"
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#include "vmath.h"
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/*
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#define DEBUG
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*/
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/*
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* Bunch of macros to make the main code easier to read. Dereference vectors
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* from the Link structures for the manipulator.
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*
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* Note that they return pointers (except for M(j) which is a scalar)
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*/
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#undef N
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#define OMEGA(j) (&links[j].omega) /* angular velocity */
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#define OMEGADOT(j) (&links[j].omega_d) /* angular acceleration */
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#define ACC(j) (&links[j].acc) /* linear acceleration */
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#define ACC_COG(j) (&links[j].abar) /* linear acceln of COG */
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#define f(j) (&links[j].f) /* force on link j due to link j-1 */
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#define n(j) (&links[j].n) /* torque on link j due to link j-1 */
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#define ROT(j) (&links[j].R) /* link rotation matrix */
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#define M(j) (links[j].m) /* link mass */
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#define PSTAR(j) (&links[j].r) /* offset link i from link (j-1) */
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#define R_COG(j) (links[j].rbar) /* COG link j wrt link j */
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#define INERTIA(j) (links[j].I) /* inertia of link about COG */
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/**
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* Recursive Newton-Euler algorithm.
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*
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* @Note the parameter \p stride which is used to allow for input and output
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* arrays which are 2-dimensional but in column-major (Matlab) order. We
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* need to access rows from the arrays.
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*
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*/
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void
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newton_euler (
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Robot *robot, /*!< robot object */
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double *tau, /*!< returned joint torques */
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double *qd, /*!< joint velocities */
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double *qdd, /*!< joint accelerations */
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double *fext, /*!< external force on manipulator tip */
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int stride /*!< indexing stride for qd, qdd */
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) {
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Vect t1, t2, t3, t4;
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Vect qdv, qddv;
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Vect F, N;
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Vect z0 = {0.0, 0.0, 1.0};
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Vect zero = {0.0, 0.0, 0.0};
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Vect f_tip = {0.0, 0.0, 0.0};
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Vect n_tip = {0.0, 0.0, 0.0};
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register int j;
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double t;
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Link *links = robot->links;
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/*
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* angular rate and acceleration vectors only have finite
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* z-axis component
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*/
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qdv = qddv = zero;
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/* setup external force/moment vectors */
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if (fext) {
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f_tip.x = fext[0];
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f_tip.y = fext[1];
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f_tip.z = fext[2];
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n_tip.x = fext[3];
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n_tip.y = fext[4];
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n_tip.z = fext[5];
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}
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/******************************************************************************
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* forward recursion --the kinematics
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******************************************************************************/
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if (robot->dhtype == MODIFIED) {
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/*
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* MODIFIED D&H CONVENTIONS
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*/
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for (j = 0; j < robot->njoints; j++) {
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/* create angular vector from scalar input */
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qdv.z = qd[j*stride];
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qddv.z = qdd[j*stride];
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switch (links[j].sigma) {
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case REVOLUTE:
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/*
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* calculate angular velocity of link j
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*/
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if (j == 0)
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*OMEGA(j) = qdv;
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else {
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rot_trans_vect_mult (&t1, ROT(j), OMEGA(j-1));
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vect_add (OMEGA(j), &t1, &qdv);
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}
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/*
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* calculate angular acceleration of link j
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*/
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if (j == 0)
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*OMEGADOT(j) = qddv;
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else {
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rot_trans_vect_mult (&t3, ROT(j), OMEGADOT(j-1));
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vect_cross (&t2, &t1, &qdv);
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vect_add (&t1, &t2, &t3);
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vect_add (OMEGADOT(j), &t1, &qddv);
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}
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/*
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* compute acc[j]
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*/
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if (j == 0) {
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t1 = *robot->gravity;
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} else {
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vect_cross(&t1, OMEGA(j-1), PSTAR(j));
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vect_cross(&t2, OMEGA(j-1), &t1);
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vect_cross(&t1, OMEGADOT(j-1), PSTAR(j));
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vect_add(&t1, &t1, &t2);
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vect_add(&t1, &t1, ACC(j-1));
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}
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rot_trans_vect_mult(ACC(j), ROT(j), &t1);
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break;
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case PRISMATIC:
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/*
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* calculate omega[j]
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*/
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if (j == 0)
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*(OMEGA(j)) = qdv;
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else
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rot_trans_vect_mult (OMEGA(j), ROT(j), OMEGA(j-1));
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/*
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* calculate alpha[j]
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*/
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if (j == 0)
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*(OMEGADOT(j)) = qddv;
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else
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rot_trans_vect_mult (OMEGADOT(j), ROT(j), OMEGADOT(j-1));
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/*
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* compute acc[j]
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*/
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if (j == 0) {
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*ACC(j) = *robot->gravity;
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} else {
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vect_cross(&t1, OMEGADOT(j-1), PSTAR(j));
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vect_cross(&t3, OMEGA(j-1), PSTAR(j));
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vect_cross(&t2, OMEGA(j-1), &t3);
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vect_add(&t1, &t1, &t2);
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vect_add(&t1, &t1, ACC(j-1));
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rot_trans_vect_mult(ACC(j), ROT(j), &t1);
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rot_trans_vect_mult(&t2, ROT(j), OMEGA(j-1));
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vect_cross(&t1, &t2, &qdv);
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scal_mult(&t1, &t1, 2.0);
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vect_add(ACC(j), ACC(j), &t1);
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vect_add(ACC(j), ACC(j), &qddv);
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}
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break;
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}
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/*
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* compute abar[j]
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*/
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vect_cross(&t1, OMEGADOT(j), R_COG(j));
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vect_cross(&t2, OMEGA(j), R_COG(j));
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vect_cross(&t3, OMEGA(j), &t2);
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vect_add(ACC_COG(j), &t1, &t3);
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vect_add(ACC_COG(j), ACC_COG(j), ACC(j));
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#ifdef DEBUG
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vect_print("w", OMEGA(j));
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vect_print("wd", OMEGADOT(j));
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vect_print("acc", ACC(j));
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vect_print("abar", ACC_COG(j));
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#endif
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}
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} else {
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/*
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* STANDARD D&H CONVENTIONS
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*/
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for (j = 0; j < robot->njoints; j++) {
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/* create angular vector from scalar input */
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qdv.z = qd[j*stride];
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qddv.z = qdd[j*stride];
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switch (links[j].sigma) {
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case REVOLUTE:
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/*
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* calculate omega[j]
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*/
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if (j == 0)
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t1 = qdv;
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else
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vect_add (&t1, OMEGA(j-1), &qdv);
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rot_trans_vect_mult (OMEGA(j), ROT(j), &t1);
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/*
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* calculate alpha[j]
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*/
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if (j == 0)
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t3 = qddv;
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else {
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vect_add (&t1, OMEGADOT(j-1), &qddv);
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vect_cross (&t2, OMEGA(j-1), &qdv);
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vect_add (&t3, &t1, &t2);
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}
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rot_trans_vect_mult (OMEGADOT(j), ROT(j), &t3);
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/*
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* compute acc[j]
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*/
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vect_cross(&t1, OMEGADOT(j), PSTAR(j));
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vect_cross(&t2, OMEGA(j), PSTAR(j));
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vect_cross(&t3, OMEGA(j), &t2);
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vect_add(ACC(j), &t1, &t3);
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if (j == 0) {
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rot_trans_vect_mult(&t1, ROT(j), robot->gravity);
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} else
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rot_trans_vect_mult(&t1, ROT(j), ACC(j-1));
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vect_add(ACC(j), ACC(j), &t1);
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break;
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case PRISMATIC:
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/*
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* calculate omega[j]
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*/
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if (j == 0)
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*(OMEGA(j)) = zero;
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else
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rot_trans_vect_mult (OMEGA(j), ROT(j), OMEGA(j-1));
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/*
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* calculate alpha[j]
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*/
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if (j == 0)
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*(OMEGADOT(j)) = zero;
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else
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rot_trans_vect_mult (OMEGADOT(j), ROT(j), OMEGADOT(j-1));
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/*
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* compute acc[j]
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*/
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if (j == 0) {
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vect_add(&qddv, &qddv, robot->gravity);
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rot_trans_vect_mult(ACC(j), ROT(j), &qddv);
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} else {
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vect_add(&t1, &qddv, ACC(j-1));
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rot_trans_vect_mult(ACC(j), ROT(j), &t1);
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}
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vect_cross(&t1, OMEGADOT(j), PSTAR(j));
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vect_add(ACC(j), ACC(j), &t1);
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rot_trans_vect_mult(&t1, ROT(j), &qdv);
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vect_cross(&t2, OMEGA(j), &t1);
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scal_mult(&t2, &t2, 2.0);
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vect_add(ACC(j), ACC(j), &t2);
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vect_cross(&t2, OMEGA(j), PSTAR(j));
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vect_cross(&t3, OMEGA(j), &t2);
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vect_add(ACC(j), ACC(j), &t3);
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break;
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}
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/*
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* compute abar[j]
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*/
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vect_cross(&t1, OMEGADOT(j), R_COG(j));
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vect_cross(&t2, OMEGA(j), R_COG(j));
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vect_cross(&t3, OMEGA(j), &t2);
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vect_add(ACC_COG(j), &t1, &t3);
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vect_add(ACC_COG(j), ACC_COG(j), ACC(j));
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#ifdef DEBUG
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vect_print("w", OMEGA(j));
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vect_print("wd", OMEGADOT(j));
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vect_print("acc", ACC(j));
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vect_print("abar", ACC_COG(j));
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#endif
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}
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}
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/******************************************************************************
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* backward recursion part --the kinetics
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******************************************************************************/
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if (robot->dhtype == MODIFIED) {
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/*
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* MODIFIED D&H CONVENTIONS
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*/
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for (j = robot->njoints - 1; j >= 0; j--) {
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/*
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* compute F[j]
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*/
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scal_mult (&F, ACC_COG(j), M(j));
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/*
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* compute f[j]
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*/
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if (j == (robot->njoints-1))
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t1 = f_tip;
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else
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rot_vect_mult (&t1, ROT(j+1), f(j+1));
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vect_add (f(j), &t1, &F);
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/*
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* compute N[j]
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*/
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mat_vect_mult(&t2, INERTIA(j), OMEGADOT(j));
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mat_vect_mult(&t3, INERTIA(j), OMEGA(j));
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vect_cross(&t4, OMEGA(j), &t3);
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vect_add(&N, &t2, &t4);
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/*
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* compute n[j]
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*/
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if (j == (robot->njoints-1))
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t1 = n_tip;
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else {
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rot_vect_mult(&t1, ROT(j+1), n(j+1));
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rot_vect_mult(&t4, ROT(j+1), f(j+1));
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vect_cross(&t3, PSTAR(j+1), &t4);
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vect_add(&t1, &t1, &t3);
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}
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vect_cross(&t2, R_COG(j), &F);
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vect_add(&t1, &t1, &t2);
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vect_add(n(j), &t1, &N);
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#ifdef DEBUG
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vect_print("f", f(j));
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vect_print("n", n(j));
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#endif
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}
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} else {
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/*
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* STANDARD D&H CONVENTIONS
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*/
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for (j = robot->njoints - 1; j >= 0; j--) {
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/*
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* compute f[j]
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*/
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scal_mult (&t4, ACC_COG(j), M(j));
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if (j != (robot->njoints-1)) {
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rot_vect_mult (&t1, ROT(j+1), f(j+1));
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vect_add (f(j), &t4, &t1);
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} else
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vect_add (f(j), &t4, &f_tip);
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/*
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* compute n[j]
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*/
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/* cross(pstar+r,Fm(:,j)) */
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vect_add(&t2, PSTAR(j), R_COG(j));
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vect_cross(&t1, &t2, &t4);
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if (j != (robot->njoints-1)) {
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/* cross(R'*pstar,f) */
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rot_trans_vect_mult(&t2, ROT(j+1), PSTAR(j));
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vect_cross(&t3, &t2, f(j+1));
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/* nn += R*(nn + cross(R'*pstar,f)) */
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vect_add(&t3, &t3, n(j+1));
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rot_vect_mult(&t2, ROT(j+1), &t3);
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vect_add(&t1, &t1, &t2);
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} else {
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/* cross(R'*pstar,f) */
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vect_cross(&t2, PSTAR(j), &f_tip);
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/* nn += R*(nn + cross(R'*pstar,f)) */
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vect_add(&t1, &t1, &t2);
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vect_add(&t1, &t1, &n_tip);
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}
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mat_vect_mult(&t2, INERTIA(j), OMEGADOT(j));
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mat_vect_mult(&t3, INERTIA(j), OMEGA(j));
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vect_cross(&t4, OMEGA(j), &t3);
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vect_add(&t2, &t2, &t4);
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vect_add(n(j), &t1, &t2);
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#ifdef DEBUG
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vect_print("f", f(j));
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vect_print("n", n(j));
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#endif
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}
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}
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/*
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* Compute the torque total for each axis
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*
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*/
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for (j=0; j < robot->njoints; j++) {
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double t;
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Link *l = &links[j];
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if (robot->dhtype == MODIFIED)
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t1 = z0;
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else
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rot_trans_vect_mult(&t1, ROT(j), &z0);
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switch (l->sigma) {
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case REVOLUTE:
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t = vect_dot(n(j), &t1);
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break;
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case PRISMATIC:
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t = vect_dot(f(j), &t1);
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break;
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}
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/*
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* add actuator dynamics and friction
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*/
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t += l->G * l->G * l->Jm * qdd[j*stride]; // inertia
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t += l->G * l->G * l->B * qd[j*stride]; // viscous friction
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t += fabs(l->G) * (
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(qd[j*stride] > 0 ? l->Tc[0] : 0.0) + // Coulomb friction
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(qd[j*stride] < 0 ? l->Tc[1] : 0.0)
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);
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tau[j*stride] = t;
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}
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}
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