Matrix<Scalar, TWIST_SIZE, Dynamic> geometricJacobianTemp(
const RigidBodyTree &model, const KinematicsCache<Scalar> &cache,
int base_body_or_frame_ind, int end_effector_body_or_frame_ind,
int expressed_in_body_or_frame_ind, bool in_terms_of_qdot) {
// temporary solution. Gross v_or_qdot_indices pointer will be gone soon.
return model.geometricJacobian(
cache, base_body_or_frame_ind, end_effector_body_or_frame_ind,
expressed_in_body_or_frame_ind, in_terms_of_qdot, nullptr);
};
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;
}