// add a node at a pose
// <pos> is x,y,th, with th in radians
// returns node position
int SysSPA2d::addNode(const Vector3d &pos, int id)
{
Node2d nd;
nd.nodeId = id;
nd.arot = pos(2);
nd.trans.head(2) = pos.head(2);
nd.trans(2) = 1.0;
// add in to system
nd.setTransform(); // set up world2node transform
nd.setDr();
int ndi = nodes.size();
nodes.push_back(nd);
return ndi;
}
// add a constraint
// <nd0>, <nd1> are node id's
// <mean> is x,y,th, with th in radians
// <prec> is a 3x3 precision matrix (inverse covariance
// returns true if nodes are found
// TODO: make node lookup more efficient
bool SysSPA2d::addConstraint(int ndi0, int ndi1, const Vector3d &mean,
const Matrix3d &prec)
{
int ni0 = -1, ni1 = -1;
for (int i=0; i<(int)nodes.size(); i++)
{
if (nodes[i].nodeId == ndi0)
ni0 = i;
if (nodes[i].nodeId == ndi1)
ni1 = i;
}
if (ni0 < 0 || ni1 < 0) return false;
Con2dP2 con;
con.ndr = ni0;
con.nd1 = ni1;
con.tmean = mean.head(2);
con.amean = mean(2);
con.prec = prec;
p2cons.push_back(con);
return true;
}
// Set up sparse linear system for Delayed Sparse Information Filter
void SysSPA2d::setupSparseDSIF(int newnode)
{
cout << "[SetupDSIF] at " << newnode << endl;
// set matrix sizes and clear
// assumes scales vars are all free
int nFree = nodes.size() - nFixed;
// long long t0, t1, t2, t3;
// t0 = utime();
// don't erase old stuff here, the delayed filter just grows in size
csp.setupBlockStructure(nFree,false); // initialize CSparse structures
// t1 = utime();
// loop over P2 constraints
for(size_t pi=0; pi<p2cons.size(); pi++)
{
Con2dP2 &con = p2cons[pi];
// don't consider old constraints
if (con.ndr < newnode && con.nd1 < newnode)
continue;
con.setJacobians(nodes);
// add in 4 blocks of A; actually just need upper triangular
int i0 = con.ndr-nFixed; // will be negative if fixed
int i1 = con.nd1-nFixed; // will be negative if fixed
if (i0 != i1-1) continue; // just sequential nodes for now
if (i0>=0)
{
Matrix<double,3,3> m = con.J0t*con.prec*con.J0;
csp.addDiagBlock(m,i0);
}
if (i1>=0)
{
Matrix<double,3,3> m = con.J1t*con.prec*con.J1;
csp.addDiagBlock(m,i1);
if (i0>=0)
{
Matrix<double,3,3> m2 = con.J0t*con.prec*con.J1;
if (i1 < i0)
{
m = m2.transpose();
csp.addOffdiagBlock(m,i1,i0);
}
else
{
csp.addOffdiagBlock(m2,i0,i1);
}
}
}
// add in 2 blocks of B
// (J u + e)^T G J
if (i0>=0)
{
Vector3d u;
u.head(2) = nodes[con.ndr].trans.head(2);
u(2) = nodes[con.ndr].arot;
Vector3d bm = con.err + con.J0 * u;
csp.B.block<3,1>(i0*3,0) += (bm.transpose() * con.prec * con.J0).transpose();
}
if (i1>=0)
{
Vector3d u;
u.head(2) = nodes[con.nd1].trans.head(2);
u(2) = nodes[con.nd1].arot;
Vector3d bm = con.err + con.J1 * u;
csp.B.block<3,1>(i1*3,0) += (bm.transpose() * con.prec * con.J1).transpose();
}
} // finish P2 constraints
// t2 = utime();
csp.Bprev = csp.B; // save for next iteration
// set up sparse matrix structure from blocks
csp.setupCSstructure(1.0,true);
// t3 = utime();
// printf("\n[SetupSparseSys] Block: %0.1f Cons: %0.1f CS: %0.1f\n",
// (t1-t0)*.001, (t2-t1)*.001, (t3-t2)*.001);
}
/// Run the Delayed Sparse Information Filter (Eustice et al.)
/// <newnode> is the index of the first new node added since the last iteration
/// <useCSparse> is true for sparse Cholesky.
void SysSPA2d::doDSIF(int newnode, bool useCSparse)
{
// number of nodes
int nnodes = nodes.size();
// set number of constraints
int ncons = p2cons.size();
// check for fixed frames
if (nFixed <= 0)
{
cout << "[doDSIF] No fixed frames" << endl;
return;
}
// check for newnode being ok
if (newnode >= nnodes)
{
cout << "[doDSIF] no new nodes to add" << endl;
return;
}
nFixed = 0;
for (int i=0; i<nnodes; i++)
{
Node2d &nd = nodes[i];
if (i >= nFixed)
nd.isFixed = false;
else
nd.isFixed = true;
nd.setTransform(); // set up world-to-node transform for cost calculation
nd.setDr(); // always use local angles
}
// initialize vars
double cost = calcCost();
if (verbose)
cout << " Initial squared cost: " << cost << " which is "
<< sqrt(cost/ncons) << " rms error" << endl;
if (newnode == 1)
{
// set up first system with node 0
csp.setupBlockStructure(1,false); // initialize CSparse structures
Matrix3d m;
m.setIdentity();
m = m*1000000;
csp.addDiagBlock(m,0);
Vector3d u;
u.head(2) = nodes[0].trans.head(2);
u(2) = nodes[0].arot;
csp.B.head(3) = u*1000000;
csp.Bprev = csp.B; // save for next iteration
cout << "[doDSIF] B = " << csp.B.transpose() << endl;
}
// set up and solve linear system
// NOTE: shouldn't need to redo all calcs in setupSys if we
// got here from a bad update
long long t0, t1, t2, t3;
t0 = utime();
if (useCSparse)
setupSparseDSIF(newnode); // set up sparse linear system
else
{}
#if 1
cout << "[doDSIF] B = " << csp.B.transpose() << endl;
csp.uncompress(A);
cout << "[doDSIF] A = " << endl << A << endl;
#endif
// cout << "[SPA] Solving...";
t1 = utime();
if (useCSparse)
{
bool ok = csp.doChol();
if (!ok)
cout << "[doDSIF] Sparse Cholesky failed!" << endl;
}
else
A.ldlt().solveInPlace(B); // Cholesky decomposition and solution
t2 = utime();
// cout << "solved" << endl;
// get correct result vector
VectorXd &BB = useCSparse ? csp.B : B;
cout << "[doDSIF] RES = " << BB.transpose() << endl;
// update the frames
int ci = 0;
for(int i=0; i < nnodes; i++)
{
Node2d &nd = nodes[i];
if (nd.isFixed) continue; // not to be updated
nd.trans.head<2>() = BB.segment<2>(ci);
nd.arot = BB(ci+2);
nd.normArot();
nd.setTransform(); // set up projection matrix for cost calculation
nd.setDr(); // set rotational derivatives
ci += 3; // advance B index
}
// new cost
double newcost = calcCost();
if (verbose)
cout << " Updated squared cost: " << newcost << " which is "
<< sqrt(newcost/ncons) << " rms error" << endl;
t3 = utime();
}
// Set up sparse linear system for Delayed Sparse Information Filter
void SysSPA2d::setupSparseDSIF(int newnode)
{
cout << "[SetupDSIF] at " << newnode << endl;
// set matrix sizes and clear
// assumes scales vars are all free
int nFree = nodes.size() - nFixed;
// long long t0, t1, t2, t3;
// t0 = utime();
// don't erase old stuff here, the delayed filter just grows in size
csp.setupBlockStructure(nFree,false); // initialize CSparse structures
// t1 = utime();
// loop over P2 constraints
for(size_t pi=0; pi<p2cons.size(); pi++)
{
Con2dP2 &con = p2cons[pi];
// don't consider old constraints
if (con.ndr < newnode && con.nd1 < newnode)
continue;
con.setJacobians(nodes);
Matrix3d J;
J.setIdentity();
Vector2d dRdth = nodes[con.ndr].dRdx.transpose() * con.tmean;
J(0,2) = dRdth(0);
J(1,2) = dRdth(1);
Matrix3d Jt = J.transpose();
Vector3d u;
u.head(2) = nodes[con.ndr].trans.head(2);
u(2) = nodes[con.ndr].arot;
Vector3d f;
f.head(2) = u.head(2) + nodes[con.ndr].w2n.transpose().block<2,2>(0,0) * con.tmean;
f(2) = u(2) + con.amean;
if (f(2) > M_PI) f(2) -= 2.0*M_PI;
if (f(2) < M_PI) f(2) += 2.0*M_PI;
cout << "[SetupDSIF] u = " << u.transpose() << endl;
cout << "[SetupDSIF] f = " << f.transpose() << endl;
cout << "[SetupDSIF] fo = " << nodes[con.nd1].trans.transpose() << endl;
// add in 4 blocks of A; actually just need upper triangular
int i0 = con.ndr-nFixed; // will be negative if fixed
int i1 = con.nd1-nFixed; // will be negative if fixed
if (i0 != i1-1) continue; // just sequential nodes for now
if (i0>=0)
{
Matrix<double,3,3> m = Jt*con.prec*J;
csp.addDiagBlock(m,i0);
}
if (i1>=0)
{
Matrix<double,3,3> m = con.prec;
csp.addDiagBlock(m,i1);
if (i0>=0)
{
Matrix<double,3,3> m2 = -con.prec * J;
if (i1 < i0)
{
m = m2.transpose();
csp.addOffdiagBlock(m,i1,i0);
}
else
{
csp.addOffdiagBlock(m2,i0,i1);
}
}
}
// add in 2 blocks of B
// Jt Gamma (J u - e)
Vector3d Juf = J*u - f;
if (Juf(2) > M_PI) Juf(2) -= 2.0*M_PI;
if (Juf(2) < M_PI) Juf(2) += 2.0*M_PI;
if (i0>=0)
{
csp.B.block<3,1>(i0*3,0) += Jt * con.prec * Juf;
}
if (i1>=0)
{
csp.B.block<3,1>(i1*3,0) -= con.prec * Juf;
}
} // finish P2 constraints
// t2 = utime();
csp.Bprev = csp.B; // save for next iteration
// set up sparse matrix structure from blocks
csp.setupCSstructure(1.0,true);
// t3 = utime();
// printf("\n[SetupSparseSys] Block: %0.1f Cons: %0.1f CS: %0.1f\n",
// (t1-t0)*.001, (t2-t1)*.001, (t3-t2)*.001);
}
int main(int argc, char **argv)
{
char *fin;
if (argc < 2)
{
cout << "Arguments are: <input filename> [<number of nodes to use>]" << endl;
return -1;
}
// number of nodes to use
int nnodes = 0;
if (argc > 2)
nnodes = atoi(argv[2]);
int doiters = 10;
if (argc > 3)
doiters = atoi(argv[3]);
fin = argv[1];
// node translation
std::vector< Eigen::Vector2d, Eigen::aligned_allocator<Eigen::Vector2d> > ntrans;
// node rotation
std::vector< double > arots;
// constraint indices
std::vector< Eigen::Vector2i, Eigen::aligned_allocator<Eigen::Vector2i> > cind;
// constraint local translation
std::vector< Eigen::Vector2d, Eigen::aligned_allocator<Eigen::Vector2d> > ctrans;
// constraint local rotation as quaternion
std::vector< double > carot;
// constraint precision
std::vector< Eigen::Matrix<double,3,3>, Eigen::aligned_allocator<Eigen::Matrix<double,3,3> > > cvar;
// scans
std::vector< std::vector< Eigen::Vector2d, Eigen::aligned_allocator<Eigen::Vector2d> > > scans;
ReadSPA2dFile(fin,ntrans,arots,cind,ctrans,carot,cvar,scans);
cout << "# [ReadSPA2dFile] Found " << (int)ntrans.size() << " nodes and "
<< (int)cind.size() << " constraints" << endl;
// system
SysSPA2d spa;
spa.verbose=false;
spa.print_iros_stats=false;
// spa.useCholmod(false);
spa.useCholmod(true);
// use max nodes if we haven't specified it
if (nnodes == 0) nnodes = ntrans.size();
if (nnodes > (int)ntrans.size()) nnodes = ntrans.size();
// add first node
Node2d nd;
// rotation
nd.arot = arots[0];
// translation
Vector3d v;
v.head(2) = ntrans[0];
v(2) = 1.0;
nd.trans = v;
double cumtime = 0.0;
//cout << nd.trans.transpose() << endl << endl;
// add to system
nd.setTransform(); // set up world2node transform
nd.setDr();
spa.nodes.push_back(nd);
// add in nodes
for (int i=0; i<nnodes-1; i+=doiters)
{
for (int j=0; j<doiters; j++)
addnode(spa, i+j+1, ntrans, arots, cind, ctrans, carot, cvar);
// cout << "[SysSPA2d] Using " << (int)spa.nodes.size() << " nodes and "
// << (int)spa.p2cons.size() << " constraints" << endl;
long long t0, t1;
spa.nFixed = 1; // one fixed frame
t0 = utime();
// spa.doSPA(1,1.0e-4,SBA_SPARSE_CHOLESKY);
spa.doSPA(1,1.0e-4,SBA_BLOCK_JACOBIAN_PCG,1.0e-8,15);
t1 = utime();
cumtime += t1 - t0;
if (i%100 == 0)
{
cout << "[SPA2D] iteration: " << i << " squared cost " << spa.errcost << endl;
cerr << i << " " << cumtime*.001 << " " << spa.errcost << endl;
}
}
printf("[TestSPA2D] Compute took %0.2f ms/node, total time %0.2f ms; error %0.2f\n", 0.001*(double)cumtime/(double)nnodes, cumtime*0.001, spa.errcost);
// printf("[TestSPA] Accepted iterations: %d\n", niters);
// printf("[TestSPA] Distance cost: %0.3f m rms\n", sqrt(spa.calcCost(true)/(double)spa.p2cons.size()));
// if (verbose()){
// cerr << "iteration= " << niters
// << "\t chi2= " << spa.calcCost();
// << "\t time= " << 0.0
// << "\t cumTime= " << 0.0
// << "\t kurtChi2= " << this->kurtChi2()
// << endl;
// }
#if 0
ofstream ofs("opt2d-ground.txt");
for (int i=0; i<(int)ntrans.size(); i++)
ofs << ntrans[i].transpose() << endl;
ofs.close();
ofstream ofs2("opt2d-opt.txt");
for (int i=0; i<(int)spa.nodes.size(); i++)
ofs2 << spa.nodes[i].trans.transpose().head(2) << endl;
ofs2.close();
#endif
// spa.writeSparseA("sphere-sparse.txt",true);
return 0;
}
RigidBodySystem::StateVector<double> RigidBodySystem::dynamics(const double& t, const RigidBodySystem::StateVector<double>& x, const RigidBodySystem::InputVector<double>& u) const {
using namespace std;
using namespace Eigen;
eigen_aligned_unordered_map<const RigidBody *, Matrix<double, 6, 1> > f_ext;
// todo: make kinematics cache once and re-use it (but have to make one per type)
auto nq = tree->num_positions;
auto nv = tree->num_velocities;
auto num_actuators = tree->actuators.size();
auto q = x.topRows(nq);
auto v = x.bottomRows(nv);
auto kinsol = tree->doKinematics(q,v);
// todo: preallocate the optimization problem and constraints, and simply update them then solve on each function eval.
// happily, this clunkier version seems fast enough for now
// the optimization framework should support this (though it has not been tested thoroughly yet)
OptimizationProblem prog;
auto const & vdot = prog.addContinuousVariables(nv,"vdot");
auto H = tree->massMatrix(kinsol);
Eigen::MatrixXd H_and_neg_JT = H;
{ // loop through rigid body force elements and accumulate f_ext
// todo: distinguish between AppliedForce and ConstraintForce
// todo: have AppliedForce output tau (instead of f_ext). it's more direct, and just as easy to compute.
int u_index = 0;
const NullVector<double> force_state; // todo: will have to handle this case
for (auto const & prop : props) {
RigidBodyFrame* frame = prop->getFrame();
RigidBody* body = frame->body.get();
int num_inputs = 1; // todo: generalize this
RigidBodyPropellor::InputVector<double> u_i(u.middleRows(u_index,num_inputs));
// todo: push the frame to body transform into the dynamicsBias method?
Matrix<double,6,1> f_ext_i = transformSpatialForce(frame->transform_to_body,prop->output(t,force_state,u_i,kinsol));
if (f_ext.find(body)==f_ext.end()) f_ext[body] = f_ext_i;
else f_ext[body] = f_ext[body]+f_ext_i;
u_index += num_inputs;
}
}
VectorXd C = tree->dynamicsBiasTerm(kinsol,f_ext);
if (num_actuators > 0) C -= tree->B*u.topRows(num_actuators);
{ // apply contact forces
const bool use_multi_contact = false;
VectorXd phi;
Matrix3Xd normal, xA, xB;
vector<int> bodyA_idx, bodyB_idx;
if (use_multi_contact)
tree->potentialCollisions(kinsol,phi,normal,xA,xB,bodyA_idx,bodyB_idx);
else
tree->collisionDetect(kinsol,phi,normal,xA,xB,bodyA_idx,bodyB_idx);
for (int i=0; i<phi.rows(); i++) {
if (phi(i)<0.0) { // then i have contact
double mu = 1.0; // todo: make this a parameter
// todo: move this entire block to a shared an updated "contactJacobian" method in RigidBodyTree
auto JA = tree->transformPointsJacobian(kinsol, xA.col(i), bodyA_idx[i], 0, false);
auto JB = tree->transformPointsJacobian(kinsol, xB.col(i), bodyB_idx[i], 0, false);
Vector3d this_normal = normal.col(i);
// compute the surface tangent basis
Vector3d tangent1;
if (1.0 - this_normal(2) < EPSILON) { // handle the unit-normal case (since it's unit length, just check z)
tangent1 << 1.0, 0.0, 0.0;
} else if (1 + this_normal(2) < EPSILON) {
tangent1 << -1.0, 0.0, 0.0; //same for the reflected case
} else {// now the general case
tangent1 << this_normal(1), -this_normal(0), 0.0;
tangent1 /= sqrt(this_normal(1)*this_normal(1) + this_normal(0)*this_normal(0));
}
Vector3d tangent2 = tangent1.cross(this_normal);
Matrix3d R; // rotation into normal coordinates
R << tangent1, tangent2, this_normal;
auto J = R*(JA-JB); // J = [ D1; D2; n ]
auto relative_velocity = J*v; // [ tangent1dot; tangent2dot; phidot ]
if (false) {
// spring law for normal force: fA_normal = -k*phi - b*phidot
// and damping for tangential force: fA_tangent = -b*tangentdot (bounded by the friction cone)
double k = 150, b = k / 10; // todo: put these somewhere better... or make them parameters?
Vector3d fA;
fA(2) = -k * phi(i) - b * relative_velocity(2);
fA.head(2) = -std::min(b, mu*fA(2)/(relative_velocity.head(2).norm()+EPSILON)) * relative_velocity.head(2); // epsilon to avoid divide by zero
// equal and opposite: fB = -fA.
// tau = (R*JA)^T fA + (R*JB)^T fB = J^T fA
C -= J.transpose()*fA;
} else { // linear acceleration constraints (more expensive, but less tuning required for robot mass, etc)
// note: this does not work for the multi-contact case (it overly constrains the motion of the link). Perhaps if I made them inequality constraints...
static_assert(!use_multi_contact, "The acceleration contact constraints do not play well with multi-contact");
// phiddot = -2*alpha*phidot - alpha^2*phi // critically damped response
// tangential_velocity_dot = -2*alpha*tangential_velocity
double alpha = 20; // todo: put this somewhere better... or make them parameters?
Vector3d desired_relative_acceleration = -2*alpha*relative_velocity;
desired_relative_acceleration(2) += -alpha*alpha*phi(i);
// relative_acceleration = J*vdot + R*(JAdotv - JBdotv) // uses the standard dnormal/dq = 0 assumption
cout << "phi = " << phi << endl;
cout << "desired acceleration = " << desired_relative_acceleration.transpose() << endl;
// cout << "acceleration = " << (J*vdot + R*(JAdotv - JBdotv)).transpose() << endl;
prog.addContinuousVariables(3,"contact normal force");
auto JAdotv = tree->transformPointsJacobianDotTimesV(kinsol, xA.col(i).eval(), bodyA_idx[i], 0);
auto JBdotv = tree->transformPointsJacobianDotTimesV(kinsol, xB.col(i).eval(), bodyB_idx[i], 0);
prog.addLinearEqualityConstraint(J,desired_relative_acceleration - R*(JAdotv - JBdotv),{vdot});
H_and_neg_JT.conservativeResize(NoChange,H_and_neg_JT.cols()+3);
H_and_neg_JT.rightCols(3) = -J.transpose();
}
}
}
}
if (tree->getNumPositionConstraints()) {
int nc = tree->getNumPositionConstraints();
const double alpha = 5.0; // 1/time constant of position constraint satisfaction (see my latex rigid body notes)
prog.addContinuousVariables(nc,"position constraint force"); // don't actually need to use the decision variable reference that would be returned...
// then compute the constraint force
auto phi = tree->positionConstraints(kinsol);
auto J = tree->positionConstraintsJacobian(kinsol,false);
auto Jdotv = tree->positionConstraintsJacDotTimesV(kinsol);
// phiddot = -2 alpha phidot - alpha^2 phi (0 + critically damped stabilization term)
prog.addLinearEqualityConstraint(J,-(Jdotv + 2*alpha*J*v + alpha*alpha*phi),{vdot});
H_and_neg_JT.conservativeResize(NoChange,H_and_neg_JT.cols()+J.rows());
H_and_neg_JT.rightCols(J.rows()) = -J.transpose();
}
// add [H,-J^T]*[vdot;f] = -C
prog.addLinearEqualityConstraint(H_and_neg_JT,-C);
prog.solve();
// prog.printSolution();
StateVector<double> dot(nq+nv);
dot << kinsol.transformPositionDotMappingToVelocityMapping(Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>::Identity(nq, nq))*v, vdot.value();
return dot;
}
RigidBodySystem::StateVector<double> RigidBodySystem::dynamics(
const double& t, const RigidBodySystem::StateVector<double>& x,
const RigidBodySystem::InputVector<double>& u) const {
using namespace std;
using namespace Eigen;
eigen_aligned_unordered_map<const RigidBody*, Matrix<double, 6, 1> > f_ext;
// todo: make kinematics cache once and re-use it (but have to make one per
// type)
auto nq = tree->num_positions;
auto nv = tree->num_velocities;
auto num_actuators = tree->actuators.size();
auto q = x.topRows(nq);
auto v = x.bottomRows(nv);
auto kinsol = tree->doKinematics(q, v);
// todo: preallocate the optimization problem and constraints, and simply
// update them then solve on each function eval.
// happily, this clunkier version seems fast enough for now
// the optimization framework should support this (though it has not been
// tested thoroughly yet)
OptimizationProblem prog;
auto const& vdot = prog.AddContinuousVariables(nv, "vdot");
auto H = tree->massMatrix(kinsol);
Eigen::MatrixXd H_and_neg_JT = H;
VectorXd C = tree->dynamicsBiasTerm(kinsol, f_ext);
if (num_actuators > 0) C -= tree->B * u.topRows(num_actuators);
// loop through rigid body force elements
{
// todo: distinguish between AppliedForce and ConstraintForce
size_t u_index = 0;
for (auto const& f : force_elements) {
size_t num_inputs = f->getNumInputs();
VectorXd force_input(u.middleRows(u_index, num_inputs));
C -= f->output(t, force_input, kinsol);
u_index += num_inputs;
}
}
// apply joint limit forces
{
for (auto const& b : tree->bodies) {
if (!b->hasParent()) continue;
auto const& joint = b->getJoint();
if (joint.getNumPositions() == 1 &&
joint.getNumVelocities() ==
1) { // taking advantage of only single-axis joints having joint
// limits makes things easier/faster here
double qmin = joint.getJointLimitMin()(0),
qmax = joint.getJointLimitMax()(0);
// tau = k*(qlimit-q) - b(qdot)
if (q(b->position_num_start) < qmin)
C(b->velocity_num_start) -=
penetration_stiffness * (qmin - q(b->position_num_start)) -
penetration_damping * v(b->velocity_num_start);
else if (q(b->position_num_start) > qmax)
C(b->velocity_num_start) -=
penetration_stiffness * (qmax - q(b->position_num_start)) -
penetration_damping * v(b->velocity_num_start);
}
}
}
// apply contact forces
{
VectorXd phi;
Matrix3Xd normal, xA, xB;
vector<int> bodyA_idx, bodyB_idx;
if (use_multi_contact)
tree->potentialCollisions(kinsol, phi, normal, xA, xB, bodyA_idx,
bodyB_idx);
else
tree->collisionDetect(kinsol, phi, normal, xA, xB, bodyA_idx, bodyB_idx);
for (int i = 0; i < phi.rows(); i++) {
if (phi(i) < 0.0) { // then i have contact
// todo: move this entire block to a shared an updated "contactJacobian"
// method in RigidBodyTree
auto JA = tree->transformPointsJacobian(kinsol, xA.col(i), bodyA_idx[i],
0, false);
auto JB = tree->transformPointsJacobian(kinsol, xB.col(i), bodyB_idx[i],
0, false);
Vector3d this_normal = normal.col(i);
// compute the surface tangent basis
Vector3d tangent1;
if (1.0 - this_normal(2) < EPSILON) { // handle the unit-normal case
// (since it's unit length, just
// check z)
tangent1 << 1.0, 0.0, 0.0;
} else if (1 + this_normal(2) < EPSILON) {
tangent1 << -1.0, 0.0, 0.0; // same for the reflected case
} else { // now the general case
tangent1 << this_normal(1), -this_normal(0), 0.0;
tangent1 /= sqrt(this_normal(1) * this_normal(1) +
this_normal(0) * this_normal(0));
}
Vector3d tangent2 = this_normal.cross(tangent1);
Matrix3d R; // rotation into normal coordinates
R.row(0) = tangent1;
R.row(1) = tangent2;
R.row(2) = this_normal;
auto J = R * (JA - JB); // J = [ D1; D2; n ]
auto relative_velocity = J * v; // [ tangent1dot; tangent2dot; phidot ]
{
// spring law for normal force: fA_normal = -k*phi - b*phidot
// and damping for tangential force: fA_tangent = -b*tangentdot
// (bounded by the friction cone)
Vector3d fA;
fA(2) =
std::max<double>(-penetration_stiffness * phi(i) -
penetration_damping * relative_velocity(2),
0.0);
fA.head(2) =
-std::min<double>(
penetration_damping,
friction_coefficient * fA(2) /
(relative_velocity.head(2).norm() + EPSILON)) *
relative_velocity.head(2); // epsilon to avoid divide by zero
// equal and opposite: fB = -fA.
// tau = (R*JA)^T fA + (R*JB)^T fB = J^T fA
C -= J.transpose() * fA;
}
}
}
}
if (tree->getNumPositionConstraints()) {
int nc = tree->getNumPositionConstraints();
const double alpha = 5.0; // 1/time constant of position constraint
// satisfaction (see my latex rigid body notes)
prog.AddContinuousVariables(
nc, "position constraint force"); // don't actually need to use the
// decision variable reference that
// would be returned...
// then compute the constraint force
auto phi = tree->positionConstraints(kinsol);
auto J = tree->positionConstraintsJacobian(kinsol, false);
auto Jdotv = tree->positionConstraintsJacDotTimesV(kinsol);
// phiddot = -2 alpha phidot - alpha^2 phi (0 + critically damped
// stabilization term)
prog.AddLinearEqualityConstraint(
J, -(Jdotv + 2 * alpha * J * v + alpha * alpha * phi), {vdot});
H_and_neg_JT.conservativeResize(NoChange, H_and_neg_JT.cols() + J.rows());
H_and_neg_JT.rightCols(J.rows()) = -J.transpose();
}
// add [H,-J^T]*[vdot;f] = -C
prog.AddLinearEqualityConstraint(H_and_neg_JT, -C);
prog.Solve();
// prog.PrintSolution();
StateVector<double> dot(nq + nv);
dot << kinsol.transformPositionDotMappingToVelocityMapping(
Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>::Identity(
nq, nq)) *
v,
vdot.value();
return dot;
}