void ForwardDynamicsABM::integrateRungeKuttaOneStep(double r, double dt)
{
DyLink* root = body->rootLink();
if(!root->isFixedJoint()){
SE3exp(root->T(), T0, root->w(), root->vo(), dt);
root->vo().noalias() = vo0 + root->dvo() * dt;
root->w().noalias() = w0 + root->dw() * dt;
vo += r * root->vo();
w += r * root->w();
dvo += r * root->dvo();
dw += r * root->dw();
}
int n = body->numLinks();
for(int i=1; i < n; ++i){
DyLink* link = body->link(i);
link->q() = q0[i] + dt * link->dq();
link->dq() = dq0[i] + dt * link->ddq();
dq[i] += r * link->dq();
ddq[i] += r * link->ddq();
}
}
void ForwardDynamicsABM::calcMotionWithEulerMethod()
{
calcABMLastHalf();
if(!sensorHelper.forceSensors().empty()){
updateForceSensors();
}
DyLink* root = body->rootLink();
if(!root->isFixedJoint()){
root->dv() =
root->dvo() - root->p().cross(root->dw())
+ root->w().cross(root->vo() + root->w().cross(root->p()));
Position T;
SE3exp(T, root->T(), root->w(), root->vo(), timeStep);
root->T() = T;
root->vo() += root->dvo() * timeStep;
root->w() += root->dw() * timeStep;
}
int n = body->numLinks();
for(int i=1; i < n; ++i){
DyLink* link = body->link(i);
link->q() += link->dq() * timeStep;
link->dq() += link->ddq() * timeStep;
}
}
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::calcMotionWithRungeKuttaMethod()
{
DyLink* root = body->rootLink();
if(!root->isFixedJoint()){
T0 = root->T();
vo0 = root->vo();
w0 = root->w();
}
vo.setZero();
w.setZero();
dvo.setZero();
dw.setZero();
int n = body->numLinks();
for(int i=1; i < n; ++i){
DyLink* link = body->link(i);
q0[i] = link->q();
dq0[i] = link->dq();
dq[i] = 0.0;
ddq[i] = 0.0;
}
calcABMLastHalf();
if(!sensorHelper.forceSensors().empty()){
updateForceSensors();
}
integrateRungeKuttaOneStep(1.0 / 6.0, timeStep / 2.0);
calcABMPhase1();
calcABMPhase2();
calcABMPhase3();
integrateRungeKuttaOneStep(2.0 / 6.0, timeStep / 2.0);
calcABMPhase1();
calcABMPhase2();
calcABMPhase3();
integrateRungeKuttaOneStep(2.0 / 6.0, timeStep);
calcABMPhase1();
calcABMPhase2();
calcABMPhase3();
if(!root->isFixedJoint()){
SE3exp(root->T(), T0, w0, vo0, timeStep);
root->vo() = vo0 + (dvo + root->dvo() / 6.0) * timeStep;
root->w() = w0 + (dw + root->dw() / 6.0) * timeStep;
}
for(int i=1; i < n; ++i){
DyLink* link = body->link(i);
link->q() = q0[i] + ( dq[i] + link->dq() / 6.0) * timeStep;
link->dq() = dq0[i] + (ddq[i] + link->ddq() / 6.0) * timeStep;
}
}
/**
\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;
}
}