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godot/thirdparty/bullet/BulletInverseDynamics/details/MultiBodyTreeImpl.cpp

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#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";
}
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<int>(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;
}
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;
default:
error_message("unsupported joint type %d\n", body.m_joint_type);
return -1;
}
}
// sanity check
if (q_index != m_num_dofs) {
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<int>(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
error_message("building index sets parent(%zu)= -1 (multiple roots)\n", child);
} else {
// should never happen
error_message(
"building index sets. parent_index[%zu]= %d, but m_parent_index.size()= %d\n",
child, parent, static_cast<int>(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;
}
// 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) {
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<int>(q.size()), static_cast<int>(u.size()),
static_cast<int>(dot_u.size()), static_cast<int>(joint_forces->size()));
return -1;
}
// 1. relative kinematics
if(-1 == calculateKinematics(q,u,dot_u, POSITION_VELOCITY_ACCELERATION)) {
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);
}
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 ) {
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<int>(q.size()), static_cast<int>(u.size()),
static_cast<int>(dot_u.size()));
return -1;
}
if(type != POSITION_ONLY && type != POSITION_VELOCITY && type != POSITION_VELOCITY_ACCELERATION) {
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;
}
}
// 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;
}
}
int MultiBodyTree::MultiBodyImpl::calculateJacobians(const vecx& q, const vecx& u, const KinUpdateType type) {
if (q.size() != m_num_dofs || u.size() != m_num_dofs) {
error_message("wrong vector dimension. system has %d DOFs,\n"
"but dim(q)= %d, dim(u)= %d\n",
m_num_dofs, static_cast<int>(q.size()), static_cast<int>(u.size()));
return -1;
}
if(type != POSITION_ONLY && type != POSITION_VELOCITY) {
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 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;
}
// this should never happen
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) {
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<int>(q.size()), static_cast<int>(mass_matrix->rows()),
static_cast<int>(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 (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);
}
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 (FLOATING != body.m_joint_type) {
error_message("??\n");
return -1;
}
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--) {
// 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) { \
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
}
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