// [[Rcpp::export]]
arma::mat MVGAUSS(Rcpp::NumericMatrix OMEGA_, int n, int seed) {
// std::srand(12523);
arma::mat OMEGA( OMEGA_.begin(), OMEGA_.nrow(), OMEGA_.ncol(), false );
arma::vec eigval;
arma::mat eigvec;
arma::eig_sym(eigval,eigvec, OMEGA);
int ncol = OMEGA.n_cols;
arma::mat X = arma::randn<arma::mat>(n,ncol);
eigval = arma::sqrt(eigval);
arma::mat Z = arma::diagmat(eigval);
X = eigvec * Z * X.t();
return(X.t());
}
/**
* Recursive Newton-Euler algorithm.
*
* @Note the parameter \p stride which is used to allow for input and output
* arrays which are 2-dimensional but in column-major (Matlab) order. We
* need to access rows from the arrays.
*
*/
void
newton_euler (
Robot *robot, /*!< robot object */
double *tau, /*!< returned joint torques */
double *qd, /*!< joint velocities */
double *qdd, /*!< joint accelerations */
double *fext, /*!< external force on manipulator tip */
int stride /*!< indexing stride for qd, qdd */
) {
Vect t1, t2, t3, t4;
Vect qdv, qddv;
Vect F, N;
Vect z0 = {0.0, 0.0, 1.0};
Vect zero = {0.0, 0.0, 0.0};
Vect f_tip = {0.0, 0.0, 0.0};
Vect n_tip = {0.0, 0.0, 0.0};
register int j;
double t;
Link *links = robot->links;
/*
* angular rate and acceleration vectors only have finite
* z-axis component
*/
qdv = qddv = zero;
/* setup external force/moment vectors */
if (fext) {
f_tip.x = fext[0];
f_tip.y = fext[1];
f_tip.z = fext[2];
n_tip.x = fext[3];
n_tip.y = fext[4];
n_tip.z = fext[5];
}
/******************************************************************************
* forward recursion --the kinematics
******************************************************************************/
if (robot->dhtype == MODIFIED) {
/*
* MODIFIED D&H CONVENTIONS
*/
for (j = 0; j < robot->njoints; j++) {
/* create angular vector from scalar input */
qdv.z = qd[j*stride];
qddv.z = qdd[j*stride];
switch (links[j].sigma) {
case REVOLUTE:
/*
* calculate angular velocity of link j
*/
if (j == 0)
*OMEGA(j) = qdv;
else {
rot_trans_vect_mult (&t1, ROT(j), OMEGA(j-1));
vect_add (OMEGA(j), &t1, &qdv);
}
/*
* calculate angular acceleration of link j
*/
if (j == 0)
*OMEGADOT(j) = qddv;
else {
rot_trans_vect_mult (&t3, ROT(j), OMEGADOT(j-1));
vect_cross (&t2, &t1, &qdv);
vect_add (&t1, &t2, &t3);
vect_add (OMEGADOT(j), &t1, &qddv);
}
/*
* compute acc[j]
*/
if (j == 0) {
t1 = *robot->gravity;
} else {
vect_cross(&t1, OMEGA(j-1), PSTAR(j));
vect_cross(&t2, OMEGA(j-1), &t1);
vect_cross(&t1, OMEGADOT(j-1), PSTAR(j));
vect_add(&t1, &t1, &t2);
vect_add(&t1, &t1, ACC(j-1));
}
rot_trans_vect_mult(ACC(j), ROT(j), &t1);
break;
case PRISMATIC:
/*
* calculate omega[j]
*/
if (j == 0)
*(OMEGA(j)) = qdv;
else
rot_trans_vect_mult (OMEGA(j), ROT(j), OMEGA(j-1));
/*
* calculate alpha[j]
*/
if (j == 0)
*(OMEGADOT(j)) = qddv;
else
rot_trans_vect_mult (OMEGADOT(j), ROT(j), OMEGADOT(j-1));
/*
* compute acc[j]
*/
if (j == 0) {
*ACC(j) = *robot->gravity;
} else {
vect_cross(&t1, OMEGADOT(j-1), PSTAR(j));
vect_cross(&t3, OMEGA(j-1), PSTAR(j));
vect_cross(&t2, OMEGA(j-1), &t3);
vect_add(&t1, &t1, &t2);
vect_add(&t1, &t1, ACC(j-1));
rot_trans_vect_mult(ACC(j), ROT(j), &t1);
rot_trans_vect_mult(&t2, ROT(j), OMEGA(j-1));
vect_cross(&t1, &t2, &qdv);
scal_mult(&t1, &t1, 2.0);
vect_add(ACC(j), ACC(j), &t1);
vect_add(ACC(j), ACC(j), &qddv);
}
break;
}
/*
* compute abar[j]
*/
vect_cross(&t1, OMEGADOT(j), R_COG(j));
vect_cross(&t2, OMEGA(j), R_COG(j));
vect_cross(&t3, OMEGA(j), &t2);
vect_add(ACC_COG(j), &t1, &t3);
vect_add(ACC_COG(j), ACC_COG(j), ACC(j));
#ifdef DEBUG
vect_print("w", OMEGA(j));
vect_print("wd", OMEGADOT(j));
vect_print("acc", ACC(j));
vect_print("abar", ACC_COG(j));
#endif
}
} else {
/*
* STANDARD D&H CONVENTIONS
*/
for (j = 0; j < robot->njoints; j++) {
/* create angular vector from scalar input */
qdv.z = qd[j*stride];
qddv.z = qdd[j*stride];
switch (links[j].sigma) {
case REVOLUTE:
/*
* calculate omega[j]
*/
if (j == 0)
t1 = qdv;
else
vect_add (&t1, OMEGA(j-1), &qdv);
rot_trans_vect_mult (OMEGA(j), ROT(j), &t1);
/*
* calculate alpha[j]
*/
if (j == 0)
t3 = qddv;
else {
vect_add (&t1, OMEGADOT(j-1), &qddv);
vect_cross (&t2, OMEGA(j-1), &qdv);
vect_add (&t3, &t1, &t2);
}
rot_trans_vect_mult (OMEGADOT(j), ROT(j), &t3);
/*
* compute acc[j]
*/
vect_cross(&t1, OMEGADOT(j), PSTAR(j));
vect_cross(&t2, OMEGA(j), PSTAR(j));
vect_cross(&t3, OMEGA(j), &t2);
vect_add(ACC(j), &t1, &t3);
if (j == 0) {
rot_trans_vect_mult(&t1, ROT(j), robot->gravity);
} else
rot_trans_vect_mult(&t1, ROT(j), ACC(j-1));
vect_add(ACC(j), ACC(j), &t1);
break;
case PRISMATIC:
/*
* calculate omega[j]
*/
if (j == 0)
*(OMEGA(j)) = zero;
else
rot_trans_vect_mult (OMEGA(j), ROT(j), OMEGA(j-1));
/*
* calculate alpha[j]
*/
if (j == 0)
*(OMEGADOT(j)) = zero;
else
rot_trans_vect_mult (OMEGADOT(j), ROT(j), OMEGADOT(j-1));
/*
* compute acc[j]
*/
if (j == 0) {
vect_add(&qddv, &qddv, robot->gravity);
rot_trans_vect_mult(ACC(j), ROT(j), &qddv);
} else {
vect_add(&t1, &qddv, ACC(j-1));
rot_trans_vect_mult(ACC(j), ROT(j), &t1);
}
vect_cross(&t1, OMEGADOT(j), PSTAR(j));
vect_add(ACC(j), ACC(j), &t1);
rot_trans_vect_mult(&t1, ROT(j), &qdv);
vect_cross(&t2, OMEGA(j), &t1);
scal_mult(&t2, &t2, 2.0);
vect_add(ACC(j), ACC(j), &t2);
vect_cross(&t2, OMEGA(j), PSTAR(j));
vect_cross(&t3, OMEGA(j), &t2);
vect_add(ACC(j), ACC(j), &t3);
break;
}
/*
* compute abar[j]
*/
vect_cross(&t1, OMEGADOT(j), R_COG(j));
vect_cross(&t2, OMEGA(j), R_COG(j));
vect_cross(&t3, OMEGA(j), &t2);
vect_add(ACC_COG(j), &t1, &t3);
vect_add(ACC_COG(j), ACC_COG(j), ACC(j));
#ifdef DEBUG
vect_print("w", OMEGA(j));
vect_print("wd", OMEGADOT(j));
vect_print("acc", ACC(j));
vect_print("abar", ACC_COG(j));
#endif
}
}
/******************************************************************************
* backward recursion part --the kinetics
******************************************************************************/
if (robot->dhtype == MODIFIED) {
/*
* MODIFIED D&H CONVENTIONS
*/
for (j = robot->njoints - 1; j >= 0; j--) {
/*
* compute F[j]
*/
scal_mult (&F, ACC_COG(j), M(j));
/*
* compute f[j]
*/
if (j == (robot->njoints-1))
t1 = f_tip;
else
rot_vect_mult (&t1, ROT(j+1), f(j+1));
vect_add (f(j), &t1, &F);
/*
* compute N[j]
*/
mat_vect_mult(&t2, INERTIA(j), OMEGADOT(j));
mat_vect_mult(&t3, INERTIA(j), OMEGA(j));
vect_cross(&t4, OMEGA(j), &t3);
vect_add(&N, &t2, &t4);
/*
* compute n[j]
*/
if (j == (robot->njoints-1))
t1 = n_tip;
else {
rot_vect_mult(&t1, ROT(j+1), n(j+1));
rot_vect_mult(&t4, ROT(j+1), f(j+1));
vect_cross(&t3, PSTAR(j+1), &t4);
vect_add(&t1, &t1, &t3);
}
vect_cross(&t2, R_COG(j), &F);
vect_add(&t1, &t1, &t2);
vect_add(n(j), &t1, &N);
#ifdef DEBUG
vect_print("f", f(j));
vect_print("n", n(j));
#endif
}
} else {
/*
* STANDARD D&H CONVENTIONS
*/
for (j = robot->njoints - 1; j >= 0; j--) {
/*
* compute f[j]
*/
scal_mult (&t4, ACC_COG(j), M(j));
if (j != (robot->njoints-1)) {
rot_vect_mult (&t1, ROT(j+1), f(j+1));
vect_add (f(j), &t4, &t1);
} else
vect_add (f(j), &t4, &f_tip);
/*
* compute n[j]
*/
/* cross(pstar+r,Fm(:,j)) */
vect_add(&t2, PSTAR(j), R_COG(j));
vect_cross(&t1, &t2, &t4);
if (j != (robot->njoints-1)) {
/* cross(R'*pstar,f) */
rot_trans_vect_mult(&t2, ROT(j+1), PSTAR(j));
vect_cross(&t3, &t2, f(j+1));
/* nn += R*(nn + cross(R'*pstar,f)) */
vect_add(&t3, &t3, n(j+1));
rot_vect_mult(&t2, ROT(j+1), &t3);
vect_add(&t1, &t1, &t2);
} else {
/* cross(R'*pstar,f) */
vect_cross(&t2, PSTAR(j), &f_tip);
/* nn += R*(nn + cross(R'*pstar,f)) */
vect_add(&t1, &t1, &t2);
vect_add(&t1, &t1, &n_tip);
}
mat_vect_mult(&t2, INERTIA(j), OMEGADOT(j));
mat_vect_mult(&t3, INERTIA(j), OMEGA(j));
vect_cross(&t4, OMEGA(j), &t3);
vect_add(&t2, &t2, &t4);
vect_add(n(j), &t1, &t2);
#ifdef DEBUG
vect_print("f", f(j));
vect_print("n", n(j));
#endif
}
}
/*
* Compute the torque total for each axis
*
*/
for (j=0; j < robot->njoints; j++) {
double t;
Link *l = &links[j];
if (robot->dhtype == MODIFIED)
t1 = z0;
else
rot_trans_vect_mult(&t1, ROT(j), &z0);
switch (l->sigma) {
case REVOLUTE:
t = vect_dot(n(j), &t1);
break;
case PRISMATIC:
t = vect_dot(f(j), &t1);
break;
}
/*
* add actuator dynamics and friction
*/
t += l->G * l->G * l->Jm * qdd[j*stride]; // inertia
t += l->G * l->G * l->B * qd[j*stride]; // viscous friction
t += fabs(l->G) * (
(qd[j*stride] > 0 ? l->Tc[0] : 0.0) + // Coulomb friction
(qd[j*stride] < 0 ? l->Tc[1] : 0.0)
);
tau[j*stride] = t;
}
}