void ForwardDynamicsABM::calcABMPhase3()
{
const LinkTraverse& traverse = body->linkTraverse();
DyLink* root = static_cast<DyLink*>(traverse[0]);
if(root->isFreeJoint()){
// - | Ivv trans(Iwv) | * | dvo | = | pf |
// | Iwv Iww | | dw | | ptau |
Eigen::Matrix<double, 6, 6> M;
M << root->Ivv(), root->Iwv().transpose(),
root->Iwv(), root->Iww();
Eigen::Matrix<double, 6, 1> f;
f << root->pf(),
root->ptau();
f *= -1.0;
Eigen::Matrix<double, 6, 1> a(M.colPivHouseholderQr().solve(f));
root->dvo() = a.head<3>();
root->dw() = a.tail<3>();
} else {
root->dvo().setZero();
root->dw().setZero();
}
const int n = traverse.numLinks();
for(int i=1; i < n; ++i){
DyLink* link = static_cast<DyLink*>(traverse[i]);
const DyLink* parent = link->parent();
if(!link->isFixedJoint()){
link->ddq() = (link->uu() - (link->hhv().dot(parent->dvo()) + link->hhw().dot(parent->dw()))) / link->dd();
link->dvo().noalias() = parent->dvo() + link->cv() + link->sv() * link->ddq();
link->dw().noalias() = parent->dw() + link->cw() + link->sw() * link->ddq();
}else{
link->ddq() = 0.0;
link->dvo() = parent->dvo();
link->dw() = parent->dw();
}
}
}
void ForwardDynamicsABM::calcABMPhase2()
{
const LinkTraverse& traverse = body->linkTraverse();
const int n = traverse.numLinks();
for(int i = n-1; i >= 0; --i){
DyLink* link = static_cast<DyLink*>(traverse[i]);
link->pf() -= link->f_ext();
link->ptau() -= link->tau_ext();
// compute articulated inertia (Eq.(6.48) of Kajita's textbook)
for(DyLink* child = link->child(); child; child = child->sibling()){
if(child->isFixedJoint()){
link->Ivv() += child->Ivv();
link->Iwv() += child->Iwv();
link->Iww() += child->Iww();
}else{
const Vector3 hhv_dd = child->hhv() / child->dd();
link->Ivv().noalias() += child->Ivv() - child->hhv() * hhv_dd.transpose();
link->Iwv().noalias() += child->Iwv() - child->hhw() * hhv_dd.transpose();
link->Iww().noalias() += child->Iww() - child->hhw() * (child->hhw() / child->dd()).transpose();
}
link->pf() .noalias() += child->Ivv() * child->cv() + child->Iwv().transpose() * child->cw() + child->pf();
link->ptau().noalias() += child->Iwv() * child->cv() + child->Iww() * child->cw() + child->ptau();
if(!child->isFixedJoint()){
const double uu_dd = child->uu() / child->dd();
link->pf() += uu_dd * child->hhv();
link->ptau() += uu_dd * child->hhw();
}
}
if(i > 0){
if(!link->isFixedJoint()){
// hh = Ia * s
link->hhv().noalias() = link->Ivv() * link->sv() + link->Iwv().transpose() * link->sw();
link->hhw().noalias() = link->Iwv() * link->sv() + link->Iww() * link->sw();
// dd = Ia * s * s^T
link->dd() = link->sv().dot(link->hhv()) + link->sw().dot(link->hhw()) + link->Jm2();
// uu = u - hh^T*c + s^T*pp
link->uu() = link->u() -
(link->hhv().dot(link->cv()) + link->hhw().dot(link->cw()) +
link->sv().dot(link->pf()) + link->sw().dot(link->ptau()));
}
}
}
}
// A part of phase 2 (inbound loop) that can be calculated before external forces are given
void ForwardDynamicsABM::calcABMPhase2Part1()
{
const LinkTraverse& traverse = body->linkTraverse();
const int n = traverse.numLinks();
for(int i = n-1; i >= 0; --i){
DyLink* link = static_cast<DyLink*>(traverse[i]);
for(DyLink* child = link->child(); child; child = child->sibling()){
if(child->isFixedJoint()){
link->Ivv() += child->Ivv();
link->Iwv() += child->Iwv();
link->Iww() += child->Iww();
}else{
const Vector3 hhv_dd = child->hhv() / child->dd();
link->Ivv().noalias() += child->Ivv() - child->hhv() * hhv_dd.transpose();
link->Iwv().noalias() += child->Iwv() - child->hhw() * hhv_dd.transpose();
link->Iww().noalias() += child->Iww() - child->hhw() * (child->hhw() / child->dd()).transpose();
}
link->pf() .noalias() += child->Ivv() * child->cv() + child->Iwv().transpose() * child->cw();
link->ptau().noalias() += child->Iwv() * child->cv() + child->Iww() * child->cw();
}
if(i > 0){
if(!link->isFixedJoint()){
link->hhv().noalias() = link->Ivv() * link->sv() + link->Iwv().transpose() * link->sw();
link->hhw().noalias() = link->Iwv() * link->sv() + link->Iww() * link->sw();
link->dd() = link->sv().dot(link->hhv()) + link->sw().dot(link->hhw()) + link->Jm2();
link->uu() = -(link->hhv().dot(link->cv()) + link->hhw().dot(link->cw()));
}
}
}
}
/**
\note v, dv, dw are not used in the forward dynamics, but are calculated
for forward dynamics users.
*/
void ForwardDynamicsABM::calcABMPhase1(bool updateNonSpatialVariables)
{
const LinkTraverse& traverse = body->linkTraverse();
const int n = traverse.numLinks();
for(int i=0; i < n; ++i){
DyLink* link = static_cast<DyLink*>(traverse[i]);
const DyLink* parent = link->parent();
if(parent){
switch(link->jointType()){
case Link::ROTATIONAL_JOINT:
{
const Vector3 arm = parent->R() * link->b();
link->R().noalias() = parent->R() * AngleAxisd(link->q(), link->a());
link->p().noalias() = arm + parent->p();
link->sw().noalias() = parent->R() * link->a();
link->sv().noalias() = link->p().cross(link->sw());
link->w().noalias() = link->dq() * link->sw() + parent->w();
if(updateNonSpatialVariables){
link->dw().noalias() =
parent->dw() + link->dq() * parent->w().cross(link->sw()) + (link->ddq() * link->sw());
link->dv().noalias() =
parent->dv() + parent->w().cross(parent->w().cross(arm)) + parent->dw().cross(arm);
}
break;
}
case Link::SLIDE_JOINT:
link->p().noalias() = parent->R() * (link->b() + link->q() * link->d()) + parent->p();
link->R() = parent->R();
link->sw().setZero();
link->sv().noalias() = parent->R() * link->d();
link->w() = parent->w();
if(updateNonSpatialVariables){
link->dw() = parent->dw();
const Vector3 arm = parent->R() * link->b();
link->dv().noalias() =
parent->dv() + parent->w().cross(parent->w().cross(arm)) + parent->dw().cross(arm)
+ 2.0 * link->dq() * parent->w().cross(link->sv()) + link->ddq() * link->sv();
}
break;
case Link::FIXED_JOINT:
default:
link->p().noalias() = parent->R() * link->b() + parent->p();
link->R() = parent->R();
link->w() = parent->w();
link->vo() = parent->vo();
link->sw().setZero();
link->sv().setZero();
link->cv().setZero();
link->cw().setZero();
if(updateNonSpatialVariables){
link->dw() = parent->dw();
const Vector3 arm = parent->R() * link->b();
link->dv().noalias() = parent->dv() +
parent->w().cross(parent->w().cross(arm)) + parent->dw().cross(arm);
}
goto COMMON_CALCS_FOR_ALL_JOINT_TYPES;
}
// Common for ROTATE and SLIDE
link->vo().noalias() = link->dq() * link->sv() + parent->vo();
const Vector3 dsv = parent->w().cross(link->sv()) + parent->vo().cross(link->sw());
const Vector3 dsw = parent->w().cross(link->sw());
link->cv() = link->dq() * dsv;
link->cw() = link->dq() * dsw;
}
COMMON_CALCS_FOR_ALL_JOINT_TYPES:
if(updateNonSpatialVariables){
link->v().noalias() = link->vo() + link->w().cross(link->p());
}
link->wc().noalias() = link->R() * link->c() + link->p();
// compute I^s (Eq.(6.24) of Kajita's textbook))
const Matrix3 Iw = link->R() * link->I() * link->R().transpose();
const double m = link->m();
const Matrix3 c_hat = hat(link->wc());
link->Iww().noalias() = m * c_hat * c_hat.transpose() + Iw;
link->Ivv() <<
m, 0.0, 0.0,
0.0, m, 0.0,
0.0, 0.0, m;
link->Iwv() = m * c_hat;
// compute P and L (Eq.(6.25) of Kajita's textbook)
const Vector3 P = m * (link->vo() + link->w().cross(link->wc()));
const Vector3 L = link->Iww() * link->w() + m * link->wc().cross(link->vo());
link->pf().noalias() = link->w().cross(P);
link->ptau().noalias() = link->vo().cross(P) + link->w().cross(L);
const Vector3 fg = m * g;
const Vector3 tg = link->wc().cross(fg);
link->pf() -= fg;
link->ptau() -= tg;
}
}