void testDHomogTransInv(int ntests, bool check) {
Isometry3d T;
std::default_random_engine generator;
for (int testnr = 0; testnr < ntests; testnr++) {
Vector4d q = uniformlyRandomQuat(generator);
// T = Quaterniond(q(0), q(1), q(2), q(3)) * Translation3d(Vector3d::Random());
T = Quaterniond(q(0), q(1), q(2), q(3));
const int nv = 6;
const int nq = 7;
auto S = Matrix<double, 6, Dynamic>::Random(6, nv).eval();
auto qdot_to_v = MatrixXd::Random(nv, nq).eval();
auto dT = dHomogTrans(T, S, qdot_to_v).eval();
auto dTInv = dHomogTransInv(T, dT);
volatile auto vol = dTInv;
if (check) {
auto dTInvInv = dHomogTransInv(T.inverse(), dTInv);
if (!dT.matrix().isApprox(dTInvInv.matrix(), 1e-10)) {
std::cout << "dTInv:\n" << dTInv << "\n\n";
std::cout << "dT:\n" << dT << "\n\n";
std::cout << "dTInvInv:\n" << dTInvInv << "\n\n";
std::cout << "dTInvInv - dT:\n" << dTInvInv - dT << "\n\n";
throw std::runtime_error("wrong");
}
}
}
}
void computeEdgeSE3PriorGradient(Isometry3d& E,
Matrix6d& J,
const Isometry3d& Z,
const Isometry3d& X,
const Isometry3d& P){
// compute the error at the linearization point
const Isometry3d A = Z.inverse()*X;
const Isometry3d B = P;
const Matrix3d Ra = A.rotation();
const Matrix3d Rb = B.rotation();
const Vector3d tb = B.translation();
E = A*B;
const Matrix3d Re=E.rotation();
Matrix<double, 3 , 9 > dq_dR;
compute_dq_dR (dq_dR,
Re(0,0),Re(1,0),Re(2,0),
Re(0,1),Re(1,1),Re(2,1),
Re(0,2),Re(1,2),Re(2,2));
J.setZero();
// dte/dt
J.block<3,3>(0,0)=Ra;
// dte/dq =0
// dte/dqj
{
Matrix3d S;
skew(S,tb);
J.block<3,3>(0,3)=Ra*S;
}
// dre/dt =0
// dre/dq
{
double buf[27];
Map<Matrix<double, 9,3> > M(buf);
Matrix3d Sx,Sy,Sz;
skew(Sx,Sy,Sz,Rb);
Map<Matrix3d> Mx(buf); Mx = Ra*Sx;
Map<Matrix3d> My(buf+9); My = Ra*Sy;
Map<Matrix3d> Mz(buf+18); Mz = Ra*Sz;
J.block<3,3>(3,3) = dq_dR * M;
}
}
Vector6d bodySpatialMotionPD(
const RigidBodyTree &r, const DrakeRobotState &robot_state,
const int body_index, const Isometry3d &body_pose_des,
const Ref<const Vector6d> &body_v_des,
const Ref<const Vector6d> &body_vdot_des, const Ref<const Vector6d> &Kp,
const Ref<const Vector6d> &Kd, const Isometry3d &T_task_to_world) {
// @param body_pose_des desired pose in the task frame, this is the
// homogeneous transformation from desired body frame to task frame
// @param body_v_des desired [xyzdot;angular_velocity] in task frame
// @param body_vdot_des desired [xyzddot;angular_acceleration] in task
// frame
// @param Kp The gain in task frame
// @param Kd The gain in task frame
// @param T_task_to_world The homogeneous transform from task to world
// @retval twist_dot, [angular_acceleration, xyz_acceleration] in body frame
Isometry3d T_world_to_task = T_task_to_world.inverse();
KinematicsCache<double> cache = r.doKinematics(robot_state.q, robot_state.qd);
auto body_pose = r.relativeTransform(cache, 0, body_index);
const auto &body_xyz = body_pose.translation();
Vector3d body_xyz_task = T_world_to_task * body_xyz;
Vector4d body_quat = rotmat2quat(body_pose.linear());
std::vector<int> v_indices;
auto J_geometric =
r.geometricJacobian(cache, 0, body_index, body_index, true, &v_indices);
VectorXd v_compact(v_indices.size());
for (size_t i = 0; i < v_indices.size(); i++) {
v_compact(i) = robot_state.qd(v_indices[i]);
}
Vector6d body_twist = J_geometric * v_compact;
Matrix3d R_body_to_world = quat2rotmat(body_quat);
Matrix3d R_world_to_body = R_body_to_world.transpose();
Matrix3d R_body_to_task = T_world_to_task.linear() * R_body_to_world;
Vector3d body_angular_vel =
R_body_to_world *
body_twist.head<3>(); // body_angular velocity in world frame
Vector3d body_xyzdot =
R_body_to_world * body_twist.tail<3>(); // body_xyzdot in world frame
Vector3d body_angular_vel_task = T_world_to_task.linear() * body_angular_vel;
Vector3d body_xyzdot_task = T_world_to_task.linear() * body_xyzdot;
Vector3d body_xyz_des = body_pose_des.translation();
Vector3d body_angular_vel_des = body_v_des.tail<3>();
Vector3d body_angular_vel_dot_des = body_vdot_des.tail<3>();
Vector3d xyz_err_task = body_xyz_des - body_xyz_task;
Matrix3d R_des = body_pose_des.linear();
Matrix3d R_err_task = R_des * R_body_to_task.transpose();
Vector4d angleAxis_err_task = rotmat2axis(R_err_task);
Vector3d angular_err_task =
angleAxis_err_task.head<3>() * angleAxis_err_task(3);
Vector3d xyzdot_err_task = body_v_des.head<3>() - body_xyzdot_task;
Vector3d angular_vel_err_task = body_angular_vel_des - body_angular_vel_task;
Vector3d Kp_xyz = Kp.head<3>();
Vector3d Kd_xyz = Kd.head<3>();
Vector3d Kp_angular = Kp.tail<3>();
Vector3d Kd_angular = Kd.tail<3>();
Vector3d body_xyzddot_task =
(Kp_xyz.array() * xyz_err_task.array()).matrix() +
(Kd_xyz.array() * xyzdot_err_task.array()).matrix() +
body_vdot_des.head<3>();
Vector3d body_angular_vel_dot_task =
(Kp_angular.array() * angular_err_task.array()).matrix() +
(Kd_angular.array() * angular_vel_err_task.array()).matrix() +
body_angular_vel_dot_des;
Vector6d twist_dot = Vector6d::Zero();
Vector3d body_xyzddot = T_task_to_world.linear() * body_xyzddot_task;
Vector3d body_angular_vel_dot =
T_task_to_world.linear() * body_angular_vel_dot_task;
twist_dot.head<3>() = R_world_to_body * body_angular_vel_dot;
twist_dot.tail<3>() = R_world_to_body * body_xyzddot -
body_twist.head<3>().cross(body_twist.tail<3>());
return twist_dot;
}
Vector6d bodySpatialMotionPD(RigidBodyManipulator *r, DrakeRobotState &robot_state, const int body_index, const Isometry3d &body_pose_des, const Ref<const Vector6d> &body_v_des, const Ref<const Vector6d> &body_vdot_des, const Ref<const Vector6d> &Kp, const Ref<const Vector6d> &Kd, const Isometry3d &T_task_to_world)
{
// @param body_pose_des desired pose in the task frame, this is the homogeneous transformation from desired body frame to task frame
// @param body_v_des desired [xyzdot;angular_velocity] in task frame
// @param body_vdot_des desired [xyzddot;angular_acceleration] in task frame
// @param Kp The gain in task frame
// @param Kd The gain in task frame
// @param T_task_to_world The homogeneous transform from task to world
// @retval twist_dot, [angular_acceleration, xyz_acceleration] in body frame
if(!r->getUseNewKinsol())
{
throw std::runtime_error("bodySpatialMotionPD requires new kinsol format");
}
Isometry3d T_world_to_task = T_task_to_world.inverse();
r->doKinematicsNew(robot_state.q,robot_state.qd,false);
Vector3d origin = Vector3d::Zero();
auto body_pose = r->forwardKinNew(origin,body_index,0,2,0);
Vector3d body_xyz = body_pose.value().head<3>();
Vector3d body_xyz_task = T_world_to_task * body_xyz.colwise().homogeneous();
Vector4d body_quat = body_pose.value().tail<4>();
std::vector<int> v_indices;
auto J_geometric = r->geometricJacobian<double>(0,body_index,body_index,0,true,&v_indices);
VectorXd v_compact(v_indices.size());
for(size_t i = 0;i<v_indices.size();i++)
{
v_compact(i) = robot_state.qd(v_indices[i]);
}
Vector6d body_twist = J_geometric.value() * v_compact;
Matrix3d R_body_to_world = quat2rotmat(body_quat);
Matrix3d R_world_to_body = R_body_to_world.transpose();
Matrix3d R_body_to_task = T_world_to_task.linear() * R_body_to_world;
Vector3d body_angular_vel = R_body_to_world * body_twist.head<3>();// body_angular velocity in world frame
Vector3d body_xyzdot = R_body_to_world * body_twist.tail<3>();// body_xyzdot in world frame
Vector3d body_angular_vel_task = T_world_to_task.linear() * body_angular_vel;
Vector3d body_xyzdot_task = T_world_to_task.linear() * body_xyzdot;
Vector3d body_xyz_des = body_pose_des.translation();
Vector3d body_angular_vel_des = body_v_des.tail<3>();
Vector3d body_angular_vel_dot_des = body_vdot_des.tail<3>();
Vector3d xyz_err_task = body_xyz_des-body_xyz_task;
Matrix3d R_des = body_pose_des.linear();
Matrix3d R_err_task = R_des * R_body_to_task.transpose();
Vector4d angleAxis_err_task = rotmat2axis(R_err_task);
Vector3d angular_err_task = angleAxis_err_task.head<3>() * angleAxis_err_task(3);
Vector3d xyzdot_err_task = body_v_des.head<3>() - body_xyzdot_task;
Vector3d angular_vel_err_task = body_angular_vel_des - body_angular_vel_task;
Vector3d Kp_xyz = Kp.head<3>();
Vector3d Kd_xyz = Kd.head<3>();
Vector3d Kp_angular = Kp.tail<3>();
Vector3d Kd_angular = Kd.tail<3>();
Vector3d body_xyzddot_task = (Kp_xyz.array() * xyz_err_task.array()).matrix() + (Kd_xyz.array() * xyzdot_err_task.array()).matrix() + body_vdot_des.head<3>();
Vector3d body_angular_vel_dot_task = (Kp_angular.array() * angular_err_task.array()).matrix() + (Kd_angular.array() * angular_vel_err_task.array()).matrix() + body_angular_vel_dot_des;
Vector6d twist_dot = Vector6d::Zero();
Vector3d body_xyzddot = T_task_to_world.linear() * body_xyzddot_task;
Vector3d body_angular_vel_dot = T_task_to_world.linear() * body_angular_vel_dot_task;
twist_dot.head<3>() = R_world_to_body * body_angular_vel_dot;
twist_dot.tail<3>() = R_world_to_body * body_xyzddot - body_twist.head<3>().cross(body_twist.tail<3>());
return twist_dot;
}
void computeEdgeSE3Gradient(Isometry3d& E,
Matrix6d& Ji,
Matrix6d& Jj,
const Isometry3d& Z,
const Isometry3d& Xi,
const Isometry3d& Xj,
const Isometry3d& Pi,
const Isometry3d& Pj
){
// compute the error at the linearization point
const Isometry3d A=Z.inverse()*Pi.inverse();
const Isometry3d B=Xi.inverse()*Xj;
const Isometry3d C=Pj;
const Isometry3d AB=A*B;
const Isometry3d BC=B*C;
E=AB*C;
const Matrix3d Re=E.rotation();
const Matrix3d Ra=A.rotation();
const Matrix3d Rb=B.rotation();
const Matrix3d Rc=C.rotation();
const Vector3d tc=C.translation();
//const Vector3d tab=AB.translation();
const Matrix3d Rab=AB.rotation();
const Vector3d tbc=BC.translation();
const Matrix3d Rbc=BC.rotation();
Matrix<double, 3 , 9 > dq_dR;
compute_dq_dR (dq_dR,
Re(0,0),Re(1,0),Re(2,0),
Re(0,1),Re(1,1),Re(2,1),
Re(0,2),Re(1,2),Re(2,2));
Ji.setZero();
Jj.setZero();
// dte/dti
Ji.block<3,3>(0,0)=-Ra;
// dte/dtj
Jj.block<3,3>(0,0)=Ra*Rb;
// dte/dqi
{
Matrix3d S;
skewT(S,tbc);
Ji.block<3,3>(0,3)=Ra*S;
}
// dte/dqj
{
Matrix3d S;
skew(S,tc);
Jj.block<3,3>(0,3)=Rab*S;
}
// dre/dqi
{
double buf[27];
Map<Matrix<double, 9,3> > M(buf);
Matrix3d Sxt,Syt,Szt;
skewT(Sxt,Syt,Szt,Rbc);
Map<Matrix3d> Mx(buf); Mx = Ra*Sxt;
Map<Matrix3d> My(buf+9); My = Ra*Syt;
Map<Matrix3d> Mz(buf+18); Mz = Ra*Szt;
Ji.block<3,3>(3,3) = dq_dR * M;
}
// dre/dqj
{
double buf[27];
Map<Matrix<double, 9,3> > M(buf);
Matrix3d Sx,Sy,Sz;
skew(Sx,Sy,Sz,Rc);
Map<Matrix3d> Mx(buf); Mx = Rab*Sx;
Map<Matrix3d> My(buf+9); My = Rab*Sy;
Map<Matrix3d> Mz(buf+18); Mz = Rab*Sz;
Jj.block<3,3>(3,3) = dq_dR * M;
}
}
