#include "MultiBodyTreeImpl.hpp" namespace btInverseDynamics { MultiBodyTree::MultiBodyImpl::MultiBodyImpl(int num_bodies_, int num_dofs_) : m_num_bodies(num_bodies_), m_num_dofs(num_dofs_) #if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS) , m_m3x(3, m_num_dofs) #endif { #if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS) resize(m_m3x, m_num_dofs); #endif m_body_list.resize(num_bodies_); m_parent_index.resize(num_bodies_); m_child_indices.resize(num_bodies_); m_user_int.resize(num_bodies_); m_user_ptr.resize(num_bodies_); m_world_gravity(0) = 0.0; m_world_gravity(1) = 0.0; m_world_gravity(2) = -9.8; } const char *MultiBodyTree::MultiBodyImpl::jointTypeToString(const JointType &type) const { switch (type) { case FIXED: return "fixed"; case REVOLUTE: return "revolute"; case PRISMATIC: return "prismatic"; case FLOATING: return "floating"; case SPHERICAL: return "spherical"; } return "error: invalid"; } inline void indent(const int &level) { for (int j = 0; j < level; j++) id_printf(" "); // indent } void MultiBodyTree::MultiBodyImpl::printTree() { id_printf("body %.2d[%s]: root\n", 0, jointTypeToString(m_body_list[0].m_joint_type)); printTree(0, 0); } void MultiBodyTree::MultiBodyImpl::printTreeData() { for (idArrayIdx i = 0; i < m_body_list.size(); i++) { RigidBody &body = m_body_list[i]; id_printf("body: %d\n", static_cast(i)); id_printf("type: %s\n", jointTypeToString(body.m_joint_type)); id_printf("q_index= %d\n", body.m_q_index); id_printf("Jac_JR= [%f;%f;%f]\n", body.m_Jac_JR(0), body.m_Jac_JR(1), body.m_Jac_JR(2)); id_printf("Jac_JT= [%f;%f;%f]\n", body.m_Jac_JT(0), body.m_Jac_JT(1), body.m_Jac_JT(2)); id_printf("mass = %f\n", body.m_mass); id_printf("mass * com = [%f %f %f]\n", body.m_body_mass_com(0), body.m_body_mass_com(1), body.m_body_mass_com(2)); id_printf( "I_o= [%f %f %f;\n" " %f %f %f;\n" " %f %f %f]\n", body.m_body_I_body(0, 0), body.m_body_I_body(0, 1), body.m_body_I_body(0, 2), body.m_body_I_body(1, 0), body.m_body_I_body(1, 1), body.m_body_I_body(1, 2), body.m_body_I_body(2, 0), body.m_body_I_body(2, 1), body.m_body_I_body(2, 2)); id_printf("parent_pos_parent_body_ref= [%f %f %f]\n", body.m_parent_pos_parent_body_ref(0), body.m_parent_pos_parent_body_ref(1), body.m_parent_pos_parent_body_ref(2)); } } int MultiBodyTree::MultiBodyImpl::bodyNumDoFs(const JointType &type) const { switch (type) { case FIXED: return 0; case REVOLUTE: case PRISMATIC: return 1; case FLOATING: return 6; case SPHERICAL: return 3; } bt_id_error_message("unknown joint type %d\n", type); return 0; } void MultiBodyTree::MultiBodyImpl::printTree(int index, int indentation) { // this is adapted from URDF2Bullet. // TODO: fix this and print proper graph (similar to git --log --graph) int num_children = m_child_indices[index].size(); indentation += 2; int count = 0; for (int i = 0; i < num_children; i++) { int child_index = m_child_indices[index][i]; indent(indentation); id_printf("body %.2d[%s]: %.2d is child no. %d (qi= %d .. %d) \n", index, jointTypeToString(m_body_list[index].m_joint_type), child_index, (count++) + 1, m_body_list[index].m_q_index, m_body_list[index].m_q_index + bodyNumDoFs(m_body_list[index].m_joint_type)); // first grandchild printTree(child_index, indentation); } } int MultiBodyTree::MultiBodyImpl::setGravityInWorldFrame(const vec3 &gravity) { m_world_gravity = gravity; return 0; } int MultiBodyTree::MultiBodyImpl::generateIndexSets() { m_body_revolute_list.resize(0); m_body_prismatic_list.resize(0); int q_index = 0; for (idArrayIdx i = 0; i < m_body_list.size(); i++) { RigidBody &body = m_body_list[i]; body.m_q_index = -1; switch (body.m_joint_type) { case REVOLUTE: m_body_revolute_list.push_back(i); body.m_q_index = q_index; q_index++; break; case PRISMATIC: m_body_prismatic_list.push_back(i); body.m_q_index = q_index; q_index++; break; case FIXED: // do nothing break; case FLOATING: m_body_floating_list.push_back(i); body.m_q_index = q_index; q_index += 6; break; case SPHERICAL: m_body_spherical_list.push_back(i); body.m_q_index = q_index; q_index += 3; break; default: bt_id_error_message("unsupported joint type %d\n", body.m_joint_type); return -1; } } // sanity check if (q_index != m_num_dofs) { bt_id_error_message("internal error, q_index= %d but num_dofs %d\n", q_index, m_num_dofs); return -1; } m_child_indices.resize(m_body_list.size()); for (idArrayIdx child = 1; child < m_parent_index.size(); child++) { const int &parent = m_parent_index[child]; if (parent >= 0 && parent < (static_cast(m_parent_index.size()) - 1)) { m_child_indices[parent].push_back(child); } else { if (-1 == parent) { // multiple bodies are directly linked to the environment, ie, not a single root bt_id_error_message("building index sets parent(%zu)= -1 (multiple roots)\n", child); } else { // should never happen bt_id_error_message( "building index sets. parent_index[%zu]= %d, but m_parent_index.size()= %d\n", child, parent, static_cast(m_parent_index.size())); } return -1; } } return 0; } void MultiBodyTree::MultiBodyImpl::calculateStaticData() { // relative kinematics that are not a function of q, u, dot_u for (idArrayIdx i = 0; i < m_body_list.size(); i++) { RigidBody &body = m_body_list[i]; switch (body.m_joint_type) { case REVOLUTE: body.m_parent_vel_rel(0) = 0; body.m_parent_vel_rel(1) = 0; body.m_parent_vel_rel(2) = 0; body.m_parent_acc_rel(0) = 0; body.m_parent_acc_rel(1) = 0; body.m_parent_acc_rel(2) = 0; body.m_parent_pos_parent_body = body.m_parent_pos_parent_body_ref; break; case PRISMATIC: body.m_body_T_parent = body.m_body_T_parent_ref; body.m_parent_Jac_JT = body.m_body_T_parent_ref.transpose() * body.m_Jac_JT; body.m_body_ang_vel_rel(0) = 0; body.m_body_ang_vel_rel(1) = 0; body.m_body_ang_vel_rel(2) = 0; body.m_body_ang_acc_rel(0) = 0; body.m_body_ang_acc_rel(1) = 0; body.m_body_ang_acc_rel(2) = 0; break; case FIXED: body.m_parent_pos_parent_body = body.m_parent_pos_parent_body_ref; body.m_body_T_parent = body.m_body_T_parent_ref; body.m_body_ang_vel_rel(0) = 0; body.m_body_ang_vel_rel(1) = 0; body.m_body_ang_vel_rel(2) = 0; body.m_parent_vel_rel(0) = 0; body.m_parent_vel_rel(1) = 0; body.m_parent_vel_rel(2) = 0; body.m_body_ang_acc_rel(0) = 0; body.m_body_ang_acc_rel(1) = 0; body.m_body_ang_acc_rel(2) = 0; body.m_parent_acc_rel(0) = 0; body.m_parent_acc_rel(1) = 0; body.m_parent_acc_rel(2) = 0; break; case FLOATING: // no static data break; case SPHERICAL: //todo: review body.m_parent_pos_parent_body = body.m_parent_pos_parent_body_ref; body.m_parent_vel_rel(0) = 0; body.m_parent_vel_rel(1) = 0; body.m_parent_vel_rel(2) = 0; body.m_parent_acc_rel(0) = 0; body.m_parent_acc_rel(1) = 0; body.m_parent_acc_rel(2) = 0; break; } // resize & initialize jacobians to zero. #if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS) body.m_body_dot_Jac_T_u(0) = 0.0; body.m_body_dot_Jac_T_u(1) = 0.0; body.m_body_dot_Jac_T_u(2) = 0.0; body.m_body_dot_Jac_R_u(0) = 0.0; body.m_body_dot_Jac_R_u(1) = 0.0; body.m_body_dot_Jac_R_u(2) = 0.0; resize(body.m_body_Jac_T, m_num_dofs); resize(body.m_body_Jac_R, m_num_dofs); body.m_body_Jac_T.setZero(); body.m_body_Jac_R.setZero(); #endif // } } int MultiBodyTree::MultiBodyImpl::calculateInverseDynamics(const vecx &q, const vecx &u, const vecx &dot_u, vecx *joint_forces) { if (q.size() != m_num_dofs || u.size() != m_num_dofs || dot_u.size() != m_num_dofs || joint_forces->size() != m_num_dofs) { bt_id_error_message( "wrong vector dimension. system has %d DOFs,\n" "but dim(q)= %d, dim(u)= %d, dim(dot_u)= %d, dim(joint_forces)= %d\n", m_num_dofs, static_cast(q.size()), static_cast(u.size()), static_cast(dot_u.size()), static_cast(joint_forces->size())); return -1; } // 1. relative kinematics if (-1 == calculateKinematics(q, u, dot_u, POSITION_VELOCITY_ACCELERATION)) { bt_id_error_message("error in calculateKinematics\n"); return -1; } // 2. update contributions to equations of motion for every body. for (idArrayIdx i = 0; i < m_body_list.size(); i++) { RigidBody &body = m_body_list[i]; // 3.4 update dynamic terms (rate of change of angular & linear momentum) body.m_eom_lhs_rotational = body.m_body_I_body * body.m_body_ang_acc + body.m_body_mass_com.cross(body.m_body_acc) + body.m_body_ang_vel.cross(body.m_body_I_body * body.m_body_ang_vel) - body.m_body_moment_user; body.m_eom_lhs_translational = body.m_body_ang_acc.cross(body.m_body_mass_com) + body.m_mass * body.m_body_acc + body.m_body_ang_vel.cross(body.m_body_ang_vel.cross(body.m_body_mass_com)) - body.m_body_force_user; } // 3. calculate full set of forces at parent joint // (not directly calculating the joint force along the free direction // simplifies inclusion of fixed joints. // An alternative would be to fuse bodies in a pre-processing step, // but that would make changing masses online harder (eg, payload masses // added with fixed joints to a gripper) // Also, this enables adding zero weight bodies as a way to calculate frame poses // for force elements, etc. for (int body_idx = m_body_list.size() - 1; body_idx >= 0; body_idx--) { // sum of forces and moments acting on this body from its children vec3 sum_f_children; vec3 sum_m_children; setZero(sum_f_children); setZero(sum_m_children); for (idArrayIdx child_list_idx = 0; child_list_idx < m_child_indices[body_idx].size(); child_list_idx++) { const RigidBody &child = m_body_list[m_child_indices[body_idx][child_list_idx]]; vec3 child_joint_force_in_this_frame = child.m_body_T_parent.transpose() * child.m_force_at_joint; sum_f_children -= child_joint_force_in_this_frame; sum_m_children -= child.m_body_T_parent.transpose() * child.m_moment_at_joint + child.m_parent_pos_parent_body.cross(child_joint_force_in_this_frame); } RigidBody &body = m_body_list[body_idx]; body.m_force_at_joint = body.m_eom_lhs_translational - sum_f_children; body.m_moment_at_joint = body.m_eom_lhs_rotational - sum_m_children; } // 4. Calculate Joint forces. // These are the components of force_at_joint/moment_at_joint // in the free directions given by Jac_JT/Jac_JR // 4.1 revolute joints for (idArrayIdx i = 0; i < m_body_revolute_list.size(); i++) { RigidBody &body = m_body_list[m_body_revolute_list[i]]; // (*joint_forces)(body.m_q_index) = body.m_Jac_JR.transpose() * body.m_moment_at_joint; (*joint_forces)(body.m_q_index) = body.m_Jac_JR.dot(body.m_moment_at_joint); } // 4.2 for prismatic joints for (idArrayIdx i = 0; i < m_body_prismatic_list.size(); i++) { RigidBody &body = m_body_list[m_body_prismatic_list[i]]; // (*joint_forces)(body.m_q_index) = body.m_Jac_JT.transpose() * body.m_force_at_joint; (*joint_forces)(body.m_q_index) = body.m_Jac_JT.dot(body.m_force_at_joint); } // 4.3 floating bodies (6-DoF joints) for (idArrayIdx i = 0; i < m_body_floating_list.size(); i++) { RigidBody &body = m_body_list[m_body_floating_list[i]]; (*joint_forces)(body.m_q_index + 0) = body.m_moment_at_joint(0); (*joint_forces)(body.m_q_index + 1) = body.m_moment_at_joint(1); (*joint_forces)(body.m_q_index + 2) = body.m_moment_at_joint(2); (*joint_forces)(body.m_q_index + 3) = body.m_force_at_joint(0); (*joint_forces)(body.m_q_index + 4) = body.m_force_at_joint(1); (*joint_forces)(body.m_q_index + 5) = body.m_force_at_joint(2); } // 4.4 spherical bodies (3-DoF joints) for (idArrayIdx i = 0; i < m_body_spherical_list.size(); i++) { //todo: review RigidBody &body = m_body_list[m_body_spherical_list[i]]; (*joint_forces)(body.m_q_index + 0) = body.m_moment_at_joint(0); (*joint_forces)(body.m_q_index + 1) = body.m_moment_at_joint(1); (*joint_forces)(body.m_q_index + 2) = body.m_moment_at_joint(2); } return 0; } int MultiBodyTree::MultiBodyImpl::calculateKinematics(const vecx &q, const vecx &u, const vecx &dot_u, const KinUpdateType type) { if (q.size() != m_num_dofs || u.size() != m_num_dofs || dot_u.size() != m_num_dofs) { bt_id_error_message( "wrong vector dimension. system has %d DOFs,\n" "but dim(q)= %d, dim(u)= %d, dim(dot_u)= %d\n", m_num_dofs, static_cast(q.size()), static_cast(u.size()), static_cast(dot_u.size())); return -1; } if (type != POSITION_ONLY && type != POSITION_VELOCITY && type != POSITION_VELOCITY_ACCELERATION) { bt_id_error_message("invalid type %d\n", type); return -1; } // 1. update relative kinematics // 1.1 for revolute for (idArrayIdx i = 0; i < m_body_revolute_list.size(); i++) { RigidBody &body = m_body_list[m_body_revolute_list[i]]; mat33 T; bodyTParentFromAxisAngle(body.m_Jac_JR, q(body.m_q_index), &T); body.m_body_T_parent = T * body.m_body_T_parent_ref; if (type >= POSITION_VELOCITY) { body.m_body_ang_vel_rel = body.m_Jac_JR * u(body.m_q_index); } if (type >= POSITION_VELOCITY_ACCELERATION) { body.m_body_ang_acc_rel = body.m_Jac_JR * dot_u(body.m_q_index); } } // 1.2 for prismatic for (idArrayIdx i = 0; i < m_body_prismatic_list.size(); i++) { RigidBody &body = m_body_list[m_body_prismatic_list[i]]; body.m_parent_pos_parent_body = body.m_parent_pos_parent_body_ref + body.m_parent_Jac_JT * q(body.m_q_index); if (type >= POSITION_VELOCITY) { body.m_parent_vel_rel = body.m_body_T_parent_ref.transpose() * body.m_Jac_JT * u(body.m_q_index); } if (type >= POSITION_VELOCITY_ACCELERATION) { body.m_parent_acc_rel = body.m_parent_Jac_JT * dot_u(body.m_q_index); } } // 1.3 fixed joints: nothing to do // 1.4 6dof joints: for (idArrayIdx i = 0; i < m_body_floating_list.size(); i++) { RigidBody &body = m_body_list[m_body_floating_list[i]]; body.m_body_T_parent = transformZ(q(body.m_q_index + 2)) * transformY(q(body.m_q_index + 1)) * transformX(q(body.m_q_index)); body.m_parent_pos_parent_body(0) = q(body.m_q_index + 3); body.m_parent_pos_parent_body(1) = q(body.m_q_index + 4); body.m_parent_pos_parent_body(2) = q(body.m_q_index + 5); body.m_parent_pos_parent_body = body.m_body_T_parent * body.m_parent_pos_parent_body; if (type >= POSITION_VELOCITY) { body.m_body_ang_vel_rel(0) = u(body.m_q_index + 0); body.m_body_ang_vel_rel(1) = u(body.m_q_index + 1); body.m_body_ang_vel_rel(2) = u(body.m_q_index + 2); body.m_parent_vel_rel(0) = u(body.m_q_index + 3); body.m_parent_vel_rel(1) = u(body.m_q_index + 4); body.m_parent_vel_rel(2) = u(body.m_q_index + 5); body.m_parent_vel_rel = body.m_body_T_parent.transpose() * body.m_parent_vel_rel; } if (type >= POSITION_VELOCITY_ACCELERATION) { body.m_body_ang_acc_rel(0) = dot_u(body.m_q_index + 0); body.m_body_ang_acc_rel(1) = dot_u(body.m_q_index + 1); body.m_body_ang_acc_rel(2) = dot_u(body.m_q_index + 2); body.m_parent_acc_rel(0) = dot_u(body.m_q_index + 3); body.m_parent_acc_rel(1) = dot_u(body.m_q_index + 4); body.m_parent_acc_rel(2) = dot_u(body.m_q_index + 5); body.m_parent_acc_rel = body.m_body_T_parent.transpose() * body.m_parent_acc_rel; } } for (idArrayIdx i = 0; i < m_body_spherical_list.size(); i++) { //todo: review RigidBody &body = m_body_list[m_body_spherical_list[i]]; mat33 T; T = transformX(q(body.m_q_index)) * transformY(q(body.m_q_index + 1)) * transformZ(q(body.m_q_index + 2)); body.m_body_T_parent = T * body.m_body_T_parent_ref; body.m_parent_pos_parent_body(0)=0; body.m_parent_pos_parent_body(1)=0; body.m_parent_pos_parent_body(2)=0; body.m_parent_pos_parent_body = body.m_body_T_parent * body.m_parent_pos_parent_body; if (type >= POSITION_VELOCITY) { body.m_body_ang_vel_rel(0) = u(body.m_q_index + 0); body.m_body_ang_vel_rel(1) = u(body.m_q_index + 1); body.m_body_ang_vel_rel(2) = u(body.m_q_index + 2); body.m_parent_vel_rel = body.m_body_T_parent.transpose() * body.m_parent_vel_rel; } if (type >= POSITION_VELOCITY_ACCELERATION) { body.m_body_ang_acc_rel(0) = dot_u(body.m_q_index + 0); body.m_body_ang_acc_rel(1) = dot_u(body.m_q_index + 1); body.m_body_ang_acc_rel(2) = dot_u(body.m_q_index + 2); body.m_parent_acc_rel = body.m_body_T_parent.transpose() * body.m_parent_acc_rel; } } // 2. absolute kinematic quantities (vector valued) // NOTE: this should be optimized by specializing for different body types // (e.g., relative rotation is always zero for prismatic joints, etc.) // calculations for root body { RigidBody &body = m_body_list[0]; // 3.1 update absolute positions and orientations: // will be required if we add force elements (eg springs between bodies, // or contacts) // not required right now, added here for debugging purposes body.m_body_pos = body.m_body_T_parent * body.m_parent_pos_parent_body; body.m_body_T_world = body.m_body_T_parent; if (type >= POSITION_VELOCITY) { // 3.2 update absolute velocities body.m_body_ang_vel = body.m_body_ang_vel_rel; body.m_body_vel = body.m_parent_vel_rel; } if (type >= POSITION_VELOCITY_ACCELERATION) { // 3.3 update absolute accelerations // NOTE: assumption: dot(J_JR) = 0; true here, but not for general joints body.m_body_ang_acc = body.m_body_ang_acc_rel; body.m_body_acc = body.m_body_T_parent * body.m_parent_acc_rel; // add gravitational acceleration to root body // this is an efficient way to add gravitational terms, // but it does mean that the kinematics are no longer // correct at the acceleration level // NOTE: To get correct acceleration kinematics, just set world_gravity to zero body.m_body_acc = body.m_body_acc - body.m_body_T_parent * m_world_gravity; } } for (idArrayIdx i = 1; i < m_body_list.size(); i++) { RigidBody &body = m_body_list[i]; RigidBody &parent = m_body_list[m_parent_index[i]]; // 2.1 update absolute positions and orientations: // will be required if we add force elements (eg springs between bodies, // or contacts) not required right now added here for debugging purposes body.m_body_pos = body.m_body_T_parent * (parent.m_body_pos + body.m_parent_pos_parent_body); body.m_body_T_world = body.m_body_T_parent * parent.m_body_T_world; if (type >= POSITION_VELOCITY) { // 2.2 update absolute velocities body.m_body_ang_vel = body.m_body_T_parent * parent.m_body_ang_vel + body.m_body_ang_vel_rel; body.m_body_vel = body.m_body_T_parent * (parent.m_body_vel + parent.m_body_ang_vel.cross(body.m_parent_pos_parent_body) + body.m_parent_vel_rel); } if (type >= POSITION_VELOCITY_ACCELERATION) { // 2.3 update absolute accelerations // NOTE: assumption: dot(J_JR) = 0; true here, but not for general joints body.m_body_ang_acc = body.m_body_T_parent * parent.m_body_ang_acc - body.m_body_ang_vel_rel.cross(body.m_body_T_parent * parent.m_body_ang_vel) + body.m_body_ang_acc_rel; body.m_body_acc = body.m_body_T_parent * (parent.m_body_acc + parent.m_body_ang_acc.cross(body.m_parent_pos_parent_body) + parent.m_body_ang_vel.cross(parent.m_body_ang_vel.cross(body.m_parent_pos_parent_body)) + 2.0 * parent.m_body_ang_vel.cross(body.m_parent_vel_rel) + body.m_parent_acc_rel); } } return 0; } #if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS) void MultiBodyTree::MultiBodyImpl::addRelativeJacobianComponent(RigidBody &body) { const int &idx = body.m_q_index; switch (body.m_joint_type) { case FIXED: break; case REVOLUTE: setMat3xElem(0, idx, body.m_Jac_JR(0), &body.m_body_Jac_R); setMat3xElem(1, idx, body.m_Jac_JR(1), &body.m_body_Jac_R); setMat3xElem(2, idx, body.m_Jac_JR(2), &body.m_body_Jac_R); break; case PRISMATIC: setMat3xElem(0, idx, body.m_body_T_parent_ref(0, 0) * body.m_Jac_JT(0) + body.m_body_T_parent_ref(1, 0) * body.m_Jac_JT(1) + body.m_body_T_parent_ref(2, 0) * body.m_Jac_JT(2), &body.m_body_Jac_T); setMat3xElem(1, idx, body.m_body_T_parent_ref(0, 1) * body.m_Jac_JT(0) + body.m_body_T_parent_ref(1, 1) * body.m_Jac_JT(1) + body.m_body_T_parent_ref(2, 1) * body.m_Jac_JT(2), &body.m_body_Jac_T); setMat3xElem(2, idx, body.m_body_T_parent_ref(0, 2) * body.m_Jac_JT(0) + body.m_body_T_parent_ref(1, 2) * body.m_Jac_JT(1) + body.m_body_T_parent_ref(2, 2) * body.m_Jac_JT(2), &body.m_body_Jac_T); break; case FLOATING: setMat3xElem(0, idx + 0, 1.0, &body.m_body_Jac_R); setMat3xElem(1, idx + 1, 1.0, &body.m_body_Jac_R); setMat3xElem(2, idx + 2, 1.0, &body.m_body_Jac_R); // body_Jac_T = body_T_parent.transpose(); setMat3xElem(0, idx + 3, body.m_body_T_parent(0, 0), &body.m_body_Jac_T); setMat3xElem(0, idx + 4, body.m_body_T_parent(1, 0), &body.m_body_Jac_T); setMat3xElem(0, idx + 5, body.m_body_T_parent(2, 0), &body.m_body_Jac_T); setMat3xElem(1, idx + 3, body.m_body_T_parent(0, 1), &body.m_body_Jac_T); setMat3xElem(1, idx + 4, body.m_body_T_parent(1, 1), &body.m_body_Jac_T); setMat3xElem(1, idx + 5, body.m_body_T_parent(2, 1), &body.m_body_Jac_T); setMat3xElem(2, idx + 3, body.m_body_T_parent(0, 2), &body.m_body_Jac_T); setMat3xElem(2, idx + 4, body.m_body_T_parent(1, 2), &body.m_body_Jac_T); setMat3xElem(2, idx + 5, body.m_body_T_parent(2, 2), &body.m_body_Jac_T); break; case SPHERICAL: //todo: review setMat3xElem(0, idx + 0, 1.0, &body.m_body_Jac_R); setMat3xElem(1, idx + 1, 1.0, &body.m_body_Jac_R); setMat3xElem(2, idx + 2, 1.0, &body.m_body_Jac_R); break; } } int MultiBodyTree::MultiBodyImpl::calculateJacobians(const vecx &q, const vecx &u, const KinUpdateType type) { if (q.size() != m_num_dofs || u.size() != m_num_dofs) { bt_id_error_message( "wrong vector dimension. system has %d DOFs,\n" "but dim(q)= %d, dim(u)= %d\n", m_num_dofs, static_cast(q.size()), static_cast(u.size())); return -1; } if (type != POSITION_ONLY && type != POSITION_VELOCITY) { bt_id_error_message("invalid type %d\n", type); return -1; } addRelativeJacobianComponent(m_body_list[0]); for (idArrayIdx i = 1; i < m_body_list.size(); i++) { RigidBody &body = m_body_list[i]; RigidBody &parent = m_body_list[m_parent_index[i]]; mul(body.m_body_T_parent, parent.m_body_Jac_R, &body.m_body_Jac_R); body.m_body_Jac_T = parent.m_body_Jac_T; mul(tildeOperator(body.m_parent_pos_parent_body), parent.m_body_Jac_R, &m_m3x); sub(body.m_body_Jac_T, m_m3x, &body.m_body_Jac_T); addRelativeJacobianComponent(body); mul(body.m_body_T_parent, body.m_body_Jac_T, &body.m_body_Jac_T); if (type >= POSITION_VELOCITY) { body.m_body_dot_Jac_R_u = body.m_body_T_parent * parent.m_body_dot_Jac_R_u - body.m_body_ang_vel_rel.cross(body.m_body_T_parent * parent.m_body_ang_vel); body.m_body_dot_Jac_T_u = body.m_body_T_parent * (parent.m_body_dot_Jac_T_u + parent.m_body_dot_Jac_R_u.cross(body.m_parent_pos_parent_body) + parent.m_body_ang_vel.cross(parent.m_body_ang_vel.cross(body.m_parent_pos_parent_body)) + 2.0 * parent.m_body_ang_vel.cross(body.m_parent_vel_rel)); } } return 0; } #endif static inline void setThreeDoFJacobians(const int dof, vec3 &Jac_JR, vec3 &Jac_JT) { switch (dof) { // rotational part case 0: Jac_JR(0) = 1; Jac_JR(1) = 0; Jac_JR(2) = 0; setZero(Jac_JT); break; case 1: Jac_JR(0) = 0; Jac_JR(1) = 1; Jac_JR(2) = 0; setZero(Jac_JT); break; case 2: Jac_JR(0) = 0; Jac_JR(1) = 0; Jac_JR(2) = 1; setZero(Jac_JT); break; } } static inline void setSixDoFJacobians(const int dof, vec3 &Jac_JR, vec3 &Jac_JT) { switch (dof) { // rotational part case 0: Jac_JR(0) = 1; Jac_JR(1) = 0; Jac_JR(2) = 0; setZero(Jac_JT); break; case 1: Jac_JR(0) = 0; Jac_JR(1) = 1; Jac_JR(2) = 0; setZero(Jac_JT); break; case 2: Jac_JR(0) = 0; Jac_JR(1) = 0; Jac_JR(2) = 1; setZero(Jac_JT); break; // translational part case 3: setZero(Jac_JR); Jac_JT(0) = 1; Jac_JT(1) = 0; Jac_JT(2) = 0; break; case 4: setZero(Jac_JR); Jac_JT(0) = 0; Jac_JT(1) = 1; Jac_JT(2) = 0; break; case 5: setZero(Jac_JR); Jac_JT(0) = 0; Jac_JT(1) = 0; Jac_JT(2) = 1; break; } } static inline int jointNumDoFs(const JointType &type) { switch (type) { case FIXED: return 0; case REVOLUTE: case PRISMATIC: return 1; case FLOATING: return 6; case SPHERICAL: return 3; } // this should never happen bt_id_error_message("invalid joint type\n"); // TODO add configurable abort/crash function abort(); return 0; } int MultiBodyTree::MultiBodyImpl::calculateMassMatrix(const vecx &q, const bool update_kinematics, const bool initialize_matrix, const bool set_lower_triangular_matrix, matxx *mass_matrix) { // This calculates the joint space mass matrix for the multibody system. // The algorithm is essentially an implementation of "method 3" // in "Efficient Dynamic Simulation of Robotic Mechanisms" (Walker and Orin, 1982) // (Later named "Composite Rigid Body Algorithm" by Featherstone). // // This implementation, however, handles branched systems and uses a formulation centered // on the origin of the body-fixed frame to avoid re-computing various quantities at the com. if (q.size() != m_num_dofs || mass_matrix->rows() != m_num_dofs || mass_matrix->cols() != m_num_dofs) { bt_id_error_message( "Dimension error. System has %d DOFs,\n" "but dim(q)= %d, dim(mass_matrix)= %d x %d\n", m_num_dofs, static_cast(q.size()), static_cast(mass_matrix->rows()), static_cast(mass_matrix->cols())); return -1; } // TODO add optimized zeroing function? if (initialize_matrix) { for (int i = 0; i < m_num_dofs; i++) { for (int j = 0; j < m_num_dofs; j++) { setMatxxElem(i, j, 0.0, mass_matrix); } } } if (update_kinematics) { // 1. update relative kinematics // 1.1 for revolute joints for (idArrayIdx i = 0; i < m_body_revolute_list.size(); i++) { RigidBody &body = m_body_list[m_body_revolute_list[i]]; // from reference orientation (q=0) of body-fixed frame to current orientation mat33 body_T_body_ref; bodyTParentFromAxisAngle(body.m_Jac_JR, q(body.m_q_index), &body_T_body_ref); body.m_body_T_parent = body_T_body_ref * body.m_body_T_parent_ref; } // 1.2 for prismatic joints for (idArrayIdx i = 0; i < m_body_prismatic_list.size(); i++) { RigidBody &body = m_body_list[m_body_prismatic_list[i]]; // body.m_body_T_parent= fixed body.m_parent_pos_parent_body = body.m_parent_pos_parent_body_ref + body.m_parent_Jac_JT * q(body.m_q_index); } // 1.3 fixed joints: nothing to do // 1.4 6dof joints: for (idArrayIdx i = 0; i < m_body_floating_list.size(); i++) { RigidBody &body = m_body_list[m_body_floating_list[i]]; body.m_body_T_parent = transformZ(q(body.m_q_index + 2)) * transformY(q(body.m_q_index + 1)) * transformX(q(body.m_q_index)); body.m_parent_pos_parent_body(0) = q(body.m_q_index + 3); body.m_parent_pos_parent_body(1) = q(body.m_q_index + 4); body.m_parent_pos_parent_body(2) = q(body.m_q_index + 5); body.m_parent_pos_parent_body = body.m_body_T_parent * body.m_parent_pos_parent_body; } for (idArrayIdx i = 0; i < m_body_spherical_list.size(); i++) { //todo: review RigidBody &body = m_body_list[m_body_spherical_list[i]]; mat33 T; T = transformX(q(body.m_q_index)) * transformY(q(body.m_q_index + 1)) * transformZ(q(body.m_q_index + 2)); body.m_body_T_parent = T * body.m_body_T_parent_ref; body.m_parent_pos_parent_body(0)=0; body.m_parent_pos_parent_body(1)=0; body.m_parent_pos_parent_body(2)=0; body.m_parent_pos_parent_body = body.m_body_T_parent * body.m_parent_pos_parent_body; } } for (int i = m_body_list.size() - 1; i >= 0; i--) { RigidBody &body = m_body_list[i]; // calculate mass, center of mass and inertia of "composite rigid body", // ie, sub-tree starting at current body body.m_subtree_mass = body.m_mass; body.m_body_subtree_mass_com = body.m_body_mass_com; body.m_body_subtree_I_body = body.m_body_I_body; for (idArrayIdx c = 0; c < m_child_indices[i].size(); c++) { RigidBody &child = m_body_list[m_child_indices[i][c]]; mat33 body_T_child = child.m_body_T_parent.transpose(); body.m_subtree_mass += child.m_subtree_mass; body.m_body_subtree_mass_com += body_T_child * child.m_body_subtree_mass_com + child.m_parent_pos_parent_body * child.m_subtree_mass; body.m_body_subtree_I_body += body_T_child * child.m_body_subtree_I_body * child.m_body_T_parent; if (child.m_subtree_mass > 0) { // Shift the reference point for the child subtree inertia using the // Huygens-Steiner ("parallel axis") theorem. // (First shift from child origin to child com, then from there to this body's // origin) vec3 r_com = body_T_child * child.m_body_subtree_mass_com / child.m_subtree_mass; mat33 tilde_r_child_com = tildeOperator(r_com); mat33 tilde_r_body_com = tildeOperator(child.m_parent_pos_parent_body + r_com); body.m_body_subtree_I_body += child.m_subtree_mass * (tilde_r_child_com * tilde_r_child_com - tilde_r_body_com * tilde_r_body_com); } } } for (int i = m_body_list.size() - 1; i >= 0; i--) { const RigidBody &body = m_body_list[i]; // determine DoF-range for body const int q_index_min = body.m_q_index; const int q_index_max = q_index_min + jointNumDoFs(body.m_joint_type) - 1; // loop over the DoFs used by this body // local joint jacobians (ok as is for 1-DoF joints) vec3 Jac_JR = body.m_Jac_JR; vec3 Jac_JT = body.m_Jac_JT; for (int col = q_index_max; col >= q_index_min; col--) { // set jacobians for 6-DoF joints if (FLOATING == body.m_joint_type) { setSixDoFJacobians(col - q_index_min, Jac_JR, Jac_JT); } if (SPHERICAL == body.m_joint_type) { //todo: review setThreeDoFJacobians(col - q_index_min, Jac_JR, Jac_JT); } vec3 body_eom_rot = body.m_body_subtree_I_body * Jac_JR + body.m_body_subtree_mass_com.cross(Jac_JT); vec3 body_eom_trans = body.m_subtree_mass * Jac_JT - body.m_body_subtree_mass_com.cross(Jac_JR); setMatxxElem(col, col, Jac_JR.dot(body_eom_rot) + Jac_JT.dot(body_eom_trans), mass_matrix); // rest of the mass matrix column upwards { // 1. for multi-dof joints, rest of the dofs of this body for (int row = col - 1; row >= q_index_min; row--) { if (SPHERICAL == body.m_joint_type) { //todo: review setThreeDoFJacobians(row - q_index_min, Jac_JR, Jac_JT); const double Mrc = Jac_JR.dot(body_eom_rot) + Jac_JT.dot(body_eom_trans); setMatxxElem(col, row, Mrc, mass_matrix); } if (FLOATING == body.m_joint_type) { setSixDoFJacobians(row - q_index_min, Jac_JR, Jac_JT); const double Mrc = Jac_JR.dot(body_eom_rot) + Jac_JT.dot(body_eom_trans); setMatxxElem(col, row, Mrc, mass_matrix); } } // 2. ancestor dofs int child_idx = i; int parent_idx = m_parent_index[i]; while (parent_idx >= 0) { const RigidBody &child_body = m_body_list[child_idx]; const RigidBody &parent_body = m_body_list[parent_idx]; const mat33 parent_T_child = child_body.m_body_T_parent.transpose(); body_eom_rot = parent_T_child * body_eom_rot; body_eom_trans = parent_T_child * body_eom_trans; body_eom_rot += child_body.m_parent_pos_parent_body.cross(body_eom_trans); const int parent_body_q_index_min = parent_body.m_q_index; const int parent_body_q_index_max = parent_body_q_index_min + jointNumDoFs(parent_body.m_joint_type) - 1; vec3 Jac_JR = parent_body.m_Jac_JR; vec3 Jac_JT = parent_body.m_Jac_JT; for (int row = parent_body_q_index_max; row >= parent_body_q_index_min; row--) { if (SPHERICAL == parent_body.m_joint_type) { //todo: review setThreeDoFJacobians(row - parent_body_q_index_min, Jac_JR, Jac_JT); } // set jacobians for 6-DoF joints if (FLOATING == parent_body.m_joint_type) { setSixDoFJacobians(row - parent_body_q_index_min, Jac_JR, Jac_JT); } const double Mrc = Jac_JR.dot(body_eom_rot) + Jac_JT.dot(body_eom_trans); setMatxxElem(col, row, Mrc, mass_matrix); } child_idx = parent_idx; parent_idx = m_parent_index[child_idx]; } } } } if (set_lower_triangular_matrix) { for (int col = 0; col < m_num_dofs; col++) { for (int row = 0; row < col; row++) { setMatxxElem(row, col, (*mass_matrix)(col, row), mass_matrix); } } } return 0; } // utility macro #define CHECK_IF_BODY_INDEX_IS_VALID(index) \ do \ { \ if (index < 0 || index >= m_num_bodies) \ { \ bt_id_error_message("invalid index %d (num_bodies= %d)\n", index, m_num_bodies); \ return -1; \ } \ } while (0) int MultiBodyTree::MultiBodyImpl::getParentIndex(const int body_index, int *p) { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *p = m_parent_index[body_index]; return 0; } int MultiBodyTree::MultiBodyImpl::getUserInt(const int body_index, int *user_int) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *user_int = m_user_int[body_index]; return 0; } int MultiBodyTree::MultiBodyImpl::getUserPtr(const int body_index, void **user_ptr) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *user_ptr = m_user_ptr[body_index]; return 0; } int MultiBodyTree::MultiBodyImpl::setUserInt(const int body_index, const int user_int) { CHECK_IF_BODY_INDEX_IS_VALID(body_index); m_user_int[body_index] = user_int; return 0; } int MultiBodyTree::MultiBodyImpl::setUserPtr(const int body_index, void *const user_ptr) { CHECK_IF_BODY_INDEX_IS_VALID(body_index); m_user_ptr[body_index] = user_ptr; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyOrigin(int body_index, vec3 *world_origin) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; *world_origin = body.m_body_T_world.transpose() * body.m_body_pos; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyCoM(int body_index, vec3 *world_com) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; if (body.m_mass > 0) { *world_com = body.m_body_T_world.transpose() * (body.m_body_pos + body.m_body_mass_com / body.m_mass); } else { *world_com = body.m_body_T_world.transpose() * (body.m_body_pos); } return 0; } int MultiBodyTree::MultiBodyImpl::getBodyTransform(int body_index, mat33 *world_T_body) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; *world_T_body = body.m_body_T_world.transpose(); return 0; } int MultiBodyTree::MultiBodyImpl::getBodyAngularVelocity(int body_index, vec3 *world_omega) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; *world_omega = body.m_body_T_world.transpose() * body.m_body_ang_vel; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyLinearVelocity(int body_index, vec3 *world_velocity) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; *world_velocity = body.m_body_T_world.transpose() * body.m_body_vel; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyLinearVelocityCoM(int body_index, vec3 *world_velocity) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; vec3 com; if (body.m_mass > 0) { com = body.m_body_mass_com / body.m_mass; } else { com(0) = 0; com(1) = 0; com(2) = 0; } *world_velocity = body.m_body_T_world.transpose() * (body.m_body_vel + body.m_body_ang_vel.cross(com)); return 0; } int MultiBodyTree::MultiBodyImpl::getBodyAngularAcceleration(int body_index, vec3 *world_dot_omega) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; *world_dot_omega = body.m_body_T_world.transpose() * body.m_body_ang_acc; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyLinearAcceleration(int body_index, vec3 *world_acceleration) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; *world_acceleration = body.m_body_T_world.transpose() * body.m_body_acc; return 0; } int MultiBodyTree::MultiBodyImpl::getJointType(const int body_index, JointType *joint_type) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *joint_type = m_body_list[body_index].m_joint_type; return 0; } int MultiBodyTree::MultiBodyImpl::getJointTypeStr(const int body_index, const char **joint_type) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *joint_type = jointTypeToString(m_body_list[body_index].m_joint_type); return 0; } int MultiBodyTree::MultiBodyImpl::getParentRParentBodyRef(const int body_index, vec3 *r) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *r = m_body_list[body_index].m_parent_pos_parent_body_ref; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyTParentRef(const int body_index, mat33 *T) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *T = m_body_list[body_index].m_body_T_parent_ref; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyAxisOfMotion(const int body_index, vec3 *axis) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); if (m_body_list[body_index].m_joint_type == REVOLUTE) { *axis = m_body_list[body_index].m_Jac_JR; return 0; } if (m_body_list[body_index].m_joint_type == PRISMATIC) { *axis = m_body_list[body_index].m_Jac_JT; return 0; } setZero(*axis); return 0; } int MultiBodyTree::MultiBodyImpl::getDoFOffset(const int body_index, int *q_index) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *q_index = m_body_list[body_index].m_q_index; return 0; } int MultiBodyTree::MultiBodyImpl::setBodyMass(const int body_index, const idScalar mass) { CHECK_IF_BODY_INDEX_IS_VALID(body_index); m_body_list[body_index].m_mass = mass; return 0; } int MultiBodyTree::MultiBodyImpl::setBodyFirstMassMoment(const int body_index, const vec3 &first_mass_moment) { CHECK_IF_BODY_INDEX_IS_VALID(body_index); m_body_list[body_index].m_body_mass_com = first_mass_moment; return 0; } int MultiBodyTree::MultiBodyImpl::setBodySecondMassMoment(const int body_index, const mat33 &second_mass_moment) { CHECK_IF_BODY_INDEX_IS_VALID(body_index); m_body_list[body_index].m_body_I_body = second_mass_moment; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyMass(const int body_index, idScalar *mass) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *mass = m_body_list[body_index].m_mass; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyFirstMassMoment(const int body_index, vec3 *first_mass_moment) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *first_mass_moment = m_body_list[body_index].m_body_mass_com; return 0; } int MultiBodyTree::MultiBodyImpl::getBodySecondMassMoment(const int body_index, mat33 *second_mass_moment) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); *second_mass_moment = m_body_list[body_index].m_body_I_body; return 0; } void MultiBodyTree::MultiBodyImpl::clearAllUserForcesAndMoments() { for (int index = 0; index < m_num_bodies; index++) { RigidBody &body = m_body_list[index]; setZero(body.m_body_force_user); setZero(body.m_body_moment_user); } } int MultiBodyTree::MultiBodyImpl::addUserForce(const int body_index, const vec3 &body_force) { CHECK_IF_BODY_INDEX_IS_VALID(body_index); m_body_list[body_index].m_body_force_user += body_force; return 0; } int MultiBodyTree::MultiBodyImpl::addUserMoment(const int body_index, const vec3 &body_moment) { CHECK_IF_BODY_INDEX_IS_VALID(body_index); m_body_list[body_index].m_body_moment_user += body_moment; return 0; } #if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS) int MultiBodyTree::MultiBodyImpl::getBodyDotJacobianTransU(const int body_index, vec3 *world_dot_jac_trans_u) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; *world_dot_jac_trans_u = body.m_body_T_world.transpose() * body.m_body_dot_Jac_T_u; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyDotJacobianRotU(const int body_index, vec3 *world_dot_jac_rot_u) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; *world_dot_jac_rot_u = body.m_body_T_world.transpose() * body.m_body_dot_Jac_R_u; return 0; } int MultiBodyTree::MultiBodyImpl::getBodyJacobianTrans(const int body_index, mat3x *world_jac_trans) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; mul(body.m_body_T_world.transpose(), body.m_body_Jac_T, world_jac_trans); return 0; } int MultiBodyTree::MultiBodyImpl::getBodyJacobianRot(const int body_index, mat3x *world_jac_rot) const { CHECK_IF_BODY_INDEX_IS_VALID(body_index); const RigidBody &body = m_body_list[body_index]; mul(body.m_body_T_world.transpose(), body.m_body_Jac_R, world_jac_rot); return 0; } #endif } // namespace btInverseDynamics