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add real-time safe Inverse Dynamics library+test+utils

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an example for the example browser will follow.
thanks to Thomas Buschmann
This commit is contained in:
Erwin Coumans
2015-11-17 08:27:38 -08:00
parent 7d9365319c
commit aa4d119f98
41 changed files with 5233 additions and 0 deletions
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67
Extras/InverseDynamics/CoilCreator.cpp Normal file
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#include <cmath>
#include "CoilCreator.hpp"
namespace btInverseDynamics {
CoilCreator::CoilCreator(int n) : m_num_bodies(n), m_parent(n) {
for (int i = 0; i < m_num_bodies; i++) {
m_parent[i] = i - 1;
}
// DH parameters (that's what's in the paper ...)
const idScalar theta_DH = 0;
const idScalar d_DH = 0.0;
const idScalar a_DH = 1.0 / m_num_bodies;
const idScalar alpha_DH = 5.0 * M_PI / m_num_bodies;
getVecMatFromDH(theta_DH, d_DH, a_DH, alpha_DH, &m_parent_r_parent_body_ref,
&m_body_T_parent_ref);
// always z-axis
m_body_axis_of_motion(0) = 0.0;
m_body_axis_of_motion(1) = 0.0;
m_body_axis_of_motion(2) = 1.0;
m_mass = 1.0 / m_num_bodies;
m_body_r_body_com(0) = 1.0 / (2.0 * m_num_bodies);
m_body_r_body_com(1) = 0.0;
m_body_r_body_com(2) = 0.0;
m_body_I_body(0, 0) = 1e-4 / (2.0 * m_num_bodies);
m_body_I_body(0, 1) = 0.0;
m_body_I_body(0, 2) = 0.0;
m_body_I_body(1, 0) = 0.0;
m_body_I_body(1, 1) = (3e-4 + 4.0 / pow(m_num_bodies, 2)) / (12.0 * m_num_bodies);
m_body_I_body(1, 2) = 0.0;
m_body_I_body(2, 0) = 0.0;
m_body_I_body(2, 1) = 0.0;
m_body_I_body(2, 2) = m_body_I_body(1, 1);
}
CoilCreator::~CoilCreator() {}
int CoilCreator::getNumBodies(int* num_bodies) const {
*num_bodies = m_num_bodies;
return 0;
}
int CoilCreator::getBody(int body_index, int* parent_index, JointType* joint_type,
vec3* parent_r_parent_body_ref, mat33* body_T_parent_ref,
vec3* body_axis_of_motion, idScalar* mass, vec3* body_r_body_com,
mat33* body_I_body, int* user_int, void** user_ptr) const {
if (body_index < 0 || body_index >= m_num_bodies) {
error_message("invalid body index %d\n", body_index);
return -1;
}
*parent_index = m_parent[body_index];
*joint_type = REVOLUTE;
*parent_r_parent_body_ref = m_parent_r_parent_body_ref;
*body_T_parent_ref = m_body_T_parent_ref;
*body_axis_of_motion = m_body_axis_of_motion;
*mass = m_mass;
*body_r_body_com = m_body_r_body_com;
*body_I_body = m_body_I_body;
*user_int = 0;
*user_ptr = 0;
return 0;
}
}

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#ifndef COILCREATOR_HPP_
#define COILCREATOR_HPP_
#include "MultiBodyTreeCreator.hpp"
namespace btInverseDynamics {
/// Creator class for building a "coil" system as intruduced as benchmark example in
/// Featherstone (1999), "A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n))
/// Calculation of Rigid-Body Dynamics. Part 2: Trees, Loops, and Accuracy.", The International
/// Journal of Robotics Research 18 (9): 876–892. doi : 10.1177 / 02783649922066628.
///
/// This is a serial chain, with an initial configuration resembling a coil.
class CoilCreator : public MultiBodyTreeCreator {
public:
/// ctor.
/// @param n the number of bodies in the system
CoilCreator(int n);
/// dtor
~CoilCreator();
// \copydoc MultiBodyTreeCreator::getNumBodies
int getNumBodies(int* num_bodies) const;
// \copydoc MultiBodyTreeCreator::getBody
int getBody(const int body_index, int* parent_index, JointType* joint_type,
vec3* parent_r_parent_body_ref, mat33* body_T_parent_ref, vec3* body_axis_of_motion,
idScalar* mass, vec3* body_r_body_com, mat33* body_I_body, int* user_int,
void** user_ptr) const;
private:
int m_num_bodies;
std::vector<int> m_parent;
vec3 m_parent_r_parent_body_ref;
mat33 m_body_T_parent_ref;
vec3 m_body_axis_of_motion;
idScalar m_mass;
vec3 m_body_r_body_com;
mat33 m_body_I_body;
};
}
#endif

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Extras/InverseDynamics/DillCreator.cpp Normal file
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#include "DillCreator.hpp"
#include <cmath>
namespace btInverseDynamics {
DillCreator::DillCreator(int level)
: m_level(level),
m_num_bodies(std::pow(2, level)),
m_parent(m_num_bodies),
m_parent_r_parent_body_ref(m_num_bodies),
m_body_T_parent_ref(m_num_bodies),
m_body_axis_of_motion(m_num_bodies),
m_mass(m_num_bodies),
m_body_r_body_com(m_num_bodies),
m_body_I_body(m_num_bodies) {
// generate names (for debugging)
for (int i = 0; i < m_num_bodies; i++) {
m_parent[i] = i - 1;
// all z-axis (DH convention)
m_body_axis_of_motion[i](0) = 0.0;
m_body_axis_of_motion[i](1) = 0.0;
m_body_axis_of_motion[i](2) = 1.0;
}
// recursively build data structures
m_current_body = 0;
const int parent = -1;
const idScalar d_DH = 0.0;
const idScalar a_DH = 0.0;
const idScalar alpha_DH = 0.0;
if (-1 == recurseDill(m_level, parent, d_DH, a_DH, alpha_DH)) {
error_message("recurseDill failed\n");
abort();
}
}
DillCreator::~DillCreator() {}
int DillCreator::getNumBodies(int* num_bodies) const {
*num_bodies = m_num_bodies;
return 0;
}
int DillCreator::getBody(int body_index, int* parent_index, JointType* joint_type,
vec3* parent_r_parent_body_ref, mat33* body_T_parent_ref,
vec3* body_axis_of_motion, idScalar* mass, vec3* body_r_body_com,
mat33* body_I_body, int* user_int, void** user_ptr) const {
if (body_index < 0 || body_index >= m_num_bodies) {
error_message("invalid body index %d\n", body_index);
return -1;
}
*parent_index = m_parent[body_index];
*joint_type = REVOLUTE;
*parent_r_parent_body_ref = m_parent_r_parent_body_ref[body_index];
*body_T_parent_ref = m_body_T_parent_ref[body_index];
*body_axis_of_motion = m_body_axis_of_motion[body_index];
*mass = m_mass[body_index];
*body_r_body_com = m_body_r_body_com[body_index];
*body_I_body = m_body_I_body[body_index];
*user_int = 0;
*user_ptr = 0;
return 0;
}
int DillCreator::recurseDill(const int level, const int parent, const idScalar d_DH_in,
const idScalar a_DH_in, const idScalar alpha_DH_in) {
if (level < 0) {
error_message("invalid level parameter (%d)\n", level);
return -1;
}
if (m_current_body >= m_num_bodies || m_current_body < 0) {
error_message("invalid body parameter (%d, num_bodies: %d)\n", m_current_body,
m_num_bodies);
return -1;
}
idScalar size = std::max(level, 1);
const int body = m_current_body;
// length = 0.1 * size;
// with = 2 * 0.01 * size;
/// these parameters are from the paper ...
/// TODO: add proper citation
m_parent[body] = parent;
m_mass[body] = 0.1 * std::pow(size, 3);
m_body_r_body_com[body](0) = 0.05 * size;
m_body_r_body_com[body](1) = 0;
m_body_r_body_com[body](2) = 0;
// initialization
for (int i = 0; i < 3; i++) {
m_parent_r_parent_body_ref[body](i) = 0;
for (int j = 0; j < 3; j++) {
m_body_I_body[body](i, j) = 0.0;
m_body_T_parent_ref[body](i, j) = 0.0;
}
}
const idScalar size_5 = pow(size, 5);
m_body_I_body[body](0, 0) = size_5 / 0.2e6;
m_body_I_body[body](1, 1) = size_5 * 403 / 1.2e6;
m_body_I_body[body](2, 2) = m_body_I_body[body](1, 1);
getVecMatFromDH(0, 0, a_DH_in, alpha_DH_in, &m_parent_r_parent_body_ref[body],
&m_body_T_parent_ref[body]);
// attach "level" Dill systems of levels 1...level
for (int i = 1; i <= level; i++) {
idScalar d_DH = 0.01 * size;
if (i == level) {
d_DH = 0.0;
}
const idScalar a_DH = i * 0.1;
const idScalar alpha_DH = i * M_PI / 3.0;
m_current_body++;
recurseDill(i - 1, body, d_DH, a_DH, alpha_DH);
}
return 0; // ok!
}
}

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#ifndef DILLCREATOR_HPP_
#define DILLCREATOR_HPP_
#include "MultiBodyTreeCreator.hpp"
namespace btInverseDynamics {
/// Creator class for building a "Dill" system as intruduced as benchmark example in
/// Featherstone (1999), "A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n))
/// Calculation of Rigid-Body Dynamics. Part 2: Trees, Loops, and Accuracy.", The International
/// Journal of Robotics Research 18 (9): 876–892. doi : 10.1177 / 02783649922066628.
///
/// This is a self-similar branched tree, somewhat resembling a dill plant
class DillCreator : public MultiBodyTreeCreator {
public:
/// ctor
/// @param levels the number of dill levels
DillCreator(int levels);
/// dtor
~DillCreator();
///\copydoc MultiBodyTreeCreator::getNumBodies
int getNumBodies(int* num_bodies) const;
///\copydoc MultiBodyTreeCreator::getBody
int getBody(int body_index, int* parent_index, JointType* joint_type,
vec3* parent_r_parent_body_ref, mat33* body_T_parent_ref, vec3* body_axis_of_motion,
idScalar* mass, vec3* body_r_body_com, mat33* body_I_body, int* user_int,
void** user_ptr) const;
private:
/// recursively generate dill bodies.
/// TODO better documentation
int recurseDill(const int levels, const int parent, const idScalar d_DH_in,
const idScalar a_DH_in, const idScalar alpha_DH_in);
int m_level;
int m_num_bodies;
std::vector<int> m_parent;
std::vector<vec3> m_parent_r_parent_body_ref;
std::vector<mat33> m_body_T_parent_ref;
std::vector<vec3> m_body_axis_of_motion;
std::vector<idScalar> m_mass;
std::vector<vec3> m_body_r_body_com;
std::vector<mat33> m_body_I_body;
int m_current_body;
};
}
#endif

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#include <cmath>
#include <cstdlib>
#include <ctime>
#include "BulletInverseDynamics/IDConfig.hpp"
#include "BulletInverseDynamics/IDMath.hpp"
#include "IDRandomUtil.hpp"
namespace btInverseDynamics {
// constants for random mass and inertia generation
// these are arbitrary positive values.
static const float mass_min = 0.001;
static const float mass_max = 1.0;
void randomInit() { srand(time(NULL)); }
int randomInt(int low, int high) { return rand() % (high + 1 - low) + low; }
float randomFloat(float low, float high) {
return low + static_cast<float>(rand()) / RAND_MAX * (high - low);
}
float randomMass() { return randomFloat(mass_min, mass_max); }
vec3 randomInertiaPrincipal() {
vec3 inertia;
do {
inertia(0) = randomFloat(mass_min, mass_max);
inertia(1) = randomFloat(mass_min, mass_max);
inertia(2) = randomFloat(mass_min, mass_max);
} while (inertia(0) + inertia(1) < inertia(2) || inertia(0) + inertia(2) < inertia(1) ||
inertia(1) + inertia(2) < inertia(0));
return inertia;
}
mat33 randomInertiaMatrix() {
// generate random valid inertia matrix by first getting valid components
// along major axes and then rotating by random amount
vec3 principal = randomInertiaPrincipal();
mat33 rot(transformX(randomFloat(-M_PI, M_PI)) * transformY(randomFloat(-M_PI, M_PI)) *
transformZ(randomFloat(-M_PI, M_PI)));
mat33 inertia;
inertia(0, 0) = principal(0);
inertia(0, 1) = 0;
inertia(0, 2) = 0;
inertia(1, 0) = 0;
inertia(1, 1) = principal(1);
inertia(1, 2) = 0;
inertia(2, 0) = 0;
inertia(2, 1) = 0;
inertia(2, 2) = principal(2);
return rot * inertia * rot.transpose();
}
vec3 randomAxis() {
vec3 axis;
idScalar length;
do {
axis(0) = randomFloat(-1.0, 1.0);
axis(1) = randomFloat(-1.0, 1.0);
axis(2) = randomFloat(-1.0, 1.0);
length = std::sqrt(std::pow(axis(0), 2) + std::pow(axis(1), 2) + std::pow(axis(2), 2));
} while (length < 0.01);
return axis / length;
}
}

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#ifndef ID_RANDOM_UTIL_HPP_
#define ID_RANDOM_UTIL_HPP_
#include "BulletInverseDynamics/IDConfig.hpp"
namespace btInverseDynamics {
/// seed random number generator
void randomInit();
/// Generate (not quite) uniformly distributed random integers in [low, high]
/// Note: this is a low-quality implementation using only rand(), as
/// C++11 <random> is not supported in bullet.
/// The results will *not* be perfectly uniform.
/// \param low is the lower bound (inclusive)
/// \param high is the lower bound (inclusive)
/// \return a random number within [\param low, \param high]
int randomInt(int low, int high);
/// Generate a (not quite) uniformly distributed random floats in [low, high]
/// Note: this is a low-quality implementation using only rand(), as
/// C++11 <random> is not supported in bullet.
/// The results will *not* be perfectly uniform.
/// \param low is the lower bound (inclusive)
/// \param high is the lower bound (inclusive)
/// \return a random number within [\param low, \param high]
float randomFloat(float low, float high);
/// generate a random valid mass value
/// \returns random mass
float randomMass();
/// generate a random valid vector of principal moments of inertia
vec3 randomInertiaPrincipal();
/// generate a random valid moment of inertia matrix
mat33 randomInertiaMatrix();
/// generate a random unit vector
vec3 randomAxis();
}
#endif

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#include "MultiBodyNameMap.hpp"
namespace btInverseDynamics {
MultiBodyNameMap::MultiBodyNameMap() {}
int MultiBodyNameMap::addBody(const int index, const std::string& name) {
if (m_index_to_body_name.count(index) > 0) {
error_message("trying to add index %d again\n", index);
return -1;
}
if (m_body_name_to_index.count(name) > 0) {
error_message("trying to add name %s again\n", name.c_str());
return -1;
}
m_index_to_body_name[index] = name;
m_body_name_to_index[name] = index;
return 0;
}
int MultiBodyNameMap::addJoint(const int index, const std::string& name) {
if (m_index_to_joint_name.count(index) > 0) {
error_message("trying to add index %d again\n", index);
return -1;
}
if (m_joint_name_to_index.count(name) > 0) {
error_message("trying to add name %s again\n", name.c_str());
return -1;
}
m_index_to_joint_name[index] = name;
m_joint_name_to_index[name] = index;
return 0;
}
int MultiBodyNameMap::getBodyName(const int index, std::string* name) const {
std::map<int, std::string>::const_iterator it = m_index_to_body_name.find(index);
if (it == m_index_to_body_name.end()) {
error_message("index %d not known\n", index);
return -1;
}
*name = it->second;
return 0;
}
int MultiBodyNameMap::getJointName(const int index, std::string* name) const {
std::map<int, std::string>::const_iterator it = m_index_to_joint_name.find(index);
if (it == m_index_to_joint_name.end()) {
error_message("index %d not known\n", index);
return -1;
}
*name = it->second;
return 0;
}
int MultiBodyNameMap::getBodyIndex(const std::string& name, int* index) const {
std::map<std::string, int>::const_iterator it = m_body_name_to_index.find(name);
if (it == m_body_name_to_index.end()) {
error_message("name %s not known\n", name.c_str());
return -1;
}
*index = it->second;
return 0;
}
int MultiBodyNameMap::getJointIndex(const std::string& name, int* index) const {
std::map<std::string, int>::const_iterator it = m_joint_name_to_index.find(name);
if (it == m_joint_name_to_index.end()) {
error_message("name %s not known\n", name.c_str());
return -1;
}
*index = it->second;
return 0;
}
}

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#ifndef MULTIBODYNAMEMAP_HPP_
#define MULTIBODYNAMEMAP_HPP_
#include "BulletInverseDynamics/IDConfig.hpp"
#include <string>
#include <map>
namespace btInverseDynamics {
/// \brief The MultiBodyNameMap class
/// Utility class that stores a maps from body/joint indices to/from body and joint names
class MultiBodyNameMap {
public:
MultiBodyNameMap();
/// add a body to the map
/// @param index of the body
/// @param name name of the body
/// @return 0 on success, -1 on failure
int addBody(const int index, const std::string& name);
/// add a joint to the map
/// @param index of the joint
/// @param name name of the joint
/// @return 0 on success, -1 on failure
int addJoint(const int index, const std::string& name);
/// get body name from index
/// @param index of the body
/// @param body_name name of the body
/// @return 0 on success, -1 on failure
int getBodyName(const int index, std::string* name) const;
/// get joint name from index
/// @param index of the joint
/// @param joint_name name of the joint
/// @return 0 on success, -1 on failure
int getJointName(const int index, std::string* name) const;
/// get body index from name
/// @param index of the body
/// @param name name of the body
/// @return 0 on success, -1 on failure
int getBodyIndex(const std::string& name, int* index) const;
/// get joint index from name
/// @param index of the joint
/// @param name name of the joint
/// @return 0 on success, -1 on failure
int getJointIndex(const std::string& name, int* index) const;
private:
std::map<int, std::string> m_index_to_joint_name;
std::map<int, std::string> m_index_to_body_name;
std::map<std::string, int> m_joint_name_to_index;
std::map<std::string, int> m_body_name_to_index;
};
}
#endif // MULTIBODYNAMEMAP_HPP_

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#include "MultiBodyTreeCreator.hpp"
namespace btInverseDynamics {
MultiBodyTree* CreateMultiBodyTree(const MultiBodyTreeCreator& creator) {
int num_bodies;
int parent_index;
JointType joint_type;
vec3 body_r_parent_body_ref;
mat33 body_R_parent_ref;
vec3 body_axis_of_motion;
idScalar mass;
vec3 body_r_body_com;
mat33 body_I_body;
int user_int;
void* user_ptr;
MultiBodyTree* tree = new MultiBodyTree();
if (0x0 == tree) {
error_message("cannot allocate tree\n");
return 0x0;
}
// TODO: move to some policy argument
tree->setAcceptInvalidMassParameters(false);
// get number of bodies in the system
if (-1 == creator.getNumBodies(&num_bodies)) {
error_message("getting body indices\n");
delete tree;
return 0x0;
}
// get data for all bodies
for (int index = 0; index < num_bodies; index++) {
// get body parameters from user callbacks
if (-1 ==
creator.getBody(index, &parent_index, &joint_type, &body_r_parent_body_ref,
&body_R_parent_ref, &body_axis_of_motion, &mass, &body_r_body_com,
&body_I_body, &user_int, &user_ptr)) {
error_message("getting data for body %d\n", index);
delete tree;
return 0x0;
}
// add body to system
if (-1 ==
tree->addBody(index, parent_index, joint_type, body_r_parent_body_ref,
body_R_parent_ref, body_axis_of_motion, mass, body_r_body_com,
body_I_body, user_int, user_ptr)) {
error_message("adding body %d\n", index);
delete tree;
return 0x0;
}
}
// finalize initialization
if (-1 == tree->finalize()) {
error_message("building system\n");
delete tree;
return 0x0;
}
return tree;
}
}

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#ifndef MULTI_BODY_TREE_CREATOR_HPP_
#define MULTI_BODY_TREE_CREATOR_HPP_
#include <string>
#include <vector>
#include "BulletInverseDynamics/IDConfig.hpp"
#include "BulletInverseDynamics/IDMath.hpp"
#include "BulletInverseDynamics/MultiBodyTree.hpp"
#include "MultiBodyNameMap.hpp"
namespace btInverseDynamics {
/// Interface class for initializing a MultiBodyTree instance.
/// Data to be provided is modeled on the URDF specification.
/// The user can derive from this class in order to programmatically
/// initialize a system.
class MultiBodyTreeCreator {
public:
/// the dtor
virtual ~MultiBodyTreeCreator() {}
/// Get the number of bodies in the system
/// @param num_bodies write number of bodies here
/// @return 0 on success, -1 on error
virtual int getNumBodies(int* num_bodies) const = 0;
/// Interface for accessing link mass properties.
/// For detailed description of data, @sa MultiBodyTree::addBody
/// \copydoc MultiBodyTree::addBody
virtual int getBody(const int body_index, int* parent_index, JointType* joint_type,
vec3* parent_r_parent_body_ref, mat33* body_T_parent_ref,
vec3* body_axis_of_motion, idScalar* mass, vec3* body_r_body_com,
mat33* body_I_body, int* user_int, void** user_ptr) const = 0;
/// @return a pointer to a name mapping utility class, or 0x0 if not available
virtual const MultiBodyNameMap* getNameMap() const {return 0x0;}
};
/// Create a multibody object.
/// @param creator an object implementing the MultiBodyTreeCreator interface
/// that returns data defining the system
/// @return A pointer to an allocated multibodytree instance, or
/// 0x0 if an error occured.
MultiBodyTree* CreateMultiBodyTree(const MultiBodyTreeCreator& creator);
}
// does urdf have gravity direction ??
#endif // MULTI_BODY_TREE_CREATOR_HPP_

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#include "MultiBodyTreeDebugGraph.hpp"
#include <cstdio>
namespace btInverseDynamics {
int writeGraphvizDotFile(const MultiBodyTree* tree, const MultiBodyNameMap* map,
const char* filename) {
if (0x0 == tree) {
error_message("tree pointer is null\n");
return -1;
}
if (0x0 == filename) {
error_message("filename is null\n");
return -1;
}
FILE* fp = fopen(filename, "w");
if (NULL == fp) {
error_message("cannot open file %s for writing\n", filename);
return -1;
}
fprintf(fp, "// to generate postscript file, run dot -Tps %s -o %s.ps\n"
"// details see graphviz documentation at http://graphviz.org\n"
"digraph tree {\n",
filename, filename);
for (int body = 0; body < tree->numBodies(); body++) {
std::string name;
if (0x0 != map) {
if (-1 == map->getBodyName(body, &name)) {
error_message("can't get name of body %d\n", body);
return -1;
}
fprintf(fp, " %d [label=\"%d/%s\"];\n", body, body, name.c_str());
}
}
for (int body = 0; body < tree->numBodies(); body++) {
int parent;
const char* joint_type;
int qi;
if (-1 == tree->getParentIndex(body, &parent)) {
error_message("indexing error\n");
return -1;
}
if (-1 == tree->getJointTypeStr(body, &joint_type)) {
error_message("indexing error\n");
return -1;
}
if (-1 == tree->getDoFOffset(body, &qi)) {
error_message("indexing error\n");
return -1;
}
if (-1 != parent) {
fprintf(fp, " %d -> %d [label= \"type:%s, q=%d\"];\n", parent, body,
joint_type, qi);
}
}
fprintf(fp, "}\n");
fclose(fp);
return 0;
}
}

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#ifndef MULTIBODYTREEDEBUGGRAPH_HPP_
#define MULTIBODYTREEDEBUGGRAPH_HPP_
#include "BulletInverseDynamics/IDConfig.hpp"
#include "BulletInverseDynamics/MultiBodyTree.hpp"
#include "MultiBodyNameMap.hpp"
namespace btInverseDynamics {
/// generate a dot-file of the multibody tree for generating a graph using graphviz' dot tool
/// @param tree the multibody tree
/// @param map to add names of links (if 0x0, no names will be added)
/// @param filename name for the output file
/// @return 0 on success, -1 on error
int writeGraphvizDotFile(const MultiBodyTree* tree, const MultiBodyNameMap* map,
const char* filename);
}
#endif // MULTIBODYTREEDEBUGGRAPH_HPP

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#include "SimpleTreeCreator.hpp"
#include <cstdio>
namespace btInverseDynamics {
/// minimal "tree" (chain)
SimpleTreeCreator::SimpleTreeCreator(int dim) : m_num_bodies(dim) {
m_mass = 1.0;
m_body_T_parent_ref(0, 0) = 1;
m_body_T_parent_ref(0, 1) = 0;
m_body_T_parent_ref(0, 2) = 0;
m_body_T_parent_ref(1, 0) = 0;
m_body_T_parent_ref(1, 1) = 1;
m_body_T_parent_ref(1, 2) = 0;
m_body_T_parent_ref(2, 0) = 0;
m_body_T_parent_ref(2, 1) = 0;
m_body_T_parent_ref(2, 2) = 1;
m_parent_r_parent_body_ref(0) = 1.0;
m_parent_r_parent_body_ref(1) = 0.0;
m_parent_r_parent_body_ref(2) = 0.0;
m_body_r_body_com(0) = 0.5;
m_body_r_body_com(1) = 0.0;
m_body_r_body_com(2) = 0.0;
m_body_I_body(0, 0) = 1;
m_body_I_body(0, 1) = 0;
m_body_I_body(0, 2) = 0;
m_body_I_body(1, 0) = 0;
m_body_I_body(1, 1) = 1;
m_body_I_body(1, 2) = 0;
m_body_I_body(2, 0) = 0;
m_body_I_body(2, 1) = 0;
m_body_I_body(2, 2) = 1;
m_axis(0) = 0;
m_axis(1) = 0;
m_axis(2) = 1;
}
int SimpleTreeCreator::getNumBodies(int* num_bodies) const {
*num_bodies = m_num_bodies;
return 0;
}
int SimpleTreeCreator::getBody(const int body_index, int* parent_index, JointType* joint_type,
vec3* parent_r_parent_body_ref, mat33* body_T_parent_ref,
vec3* body_axis_of_motion, idScalar* mass, vec3* body_r_body_com,
mat33* body_I_body, int* user_int, void** user_ptr) const {
*parent_index = body_index - 1;
if (body_index % 2) {
*joint_type = PRISMATIC;
} else {
*joint_type = REVOLUTE;
}
*parent_r_parent_body_ref = m_parent_r_parent_body_ref;
if (0 == body_index) {
(*parent_r_parent_body_ref)(2) = 1.0;
}
*body_T_parent_ref = m_body_T_parent_ref;
*body_axis_of_motion = m_axis;
*mass = m_mass;
*body_r_body_com = m_body_r_body_com;
*body_I_body = m_body_I_body;
*user_int = 0;
*user_ptr = 0;
return 0;
}
}

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#ifndef SIMPLETREECREATOR_HPP_
#define SIMPLETREECREATOR_HPP_
#include "MultiBodyTreeCreator.hpp"
namespace btInverseDynamics {
/// minimal "tree" (chain)
class SimpleTreeCreator : public MultiBodyTreeCreator {
public:
/// ctor
/// @param dim number of bodies
SimpleTreeCreator(int dim);
// dtor
~SimpleTreeCreator() {}
///\copydoc MultiBodyTreeCreator::getNumBodies
int getNumBodies(int* num_bodies) const;
///\copydoc MultiBodyTreeCreator::getBody
int getBody(const int body_index, int* parent_index, JointType* joint_type,
vec3* parent_r_parent_body_ref, mat33* body_T_parent_ref, vec3* body_axis_of_motion,
idScalar* mass, vec3* body_r_body_com, mat33* body_I_body, int* user_int,
void** user_ptr) const;
private:
int m_num_bodies;
idScalar m_mass;
mat33 m_body_T_parent_ref;
vec3 m_parent_r_parent_body_ref;
vec3 m_body_r_body_com;
mat33 m_body_I_body;
vec3 m_axis;
};
}
#endif // SIMPLETREECREATOR_HPP_

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#include "User2InternalIndex.hpp"
namespace btInverseDynamics {
User2InternalIndex::User2InternalIndex() : m_map_built(false) {}
void User2InternalIndex::addBody(const int body, const int parent) {
m_user_parent_index_map[body] = parent;
}
int User2InternalIndex::findRoot(int index) {
if (0 == m_user_parent_index_map.count(index)) {
return index;
}
return findRoot(m_user_parent_index_map[index]);
}
// modelled after URDF2Bullet.cpp:void ComputeParentIndices(const
// URDFImporterInterface& u2b, URDF2BulletCachedData& cache, int urdfLinkIndex,
// int urdfParentIndex)
void User2InternalIndex::recurseIndexSets(const int user_body_index) {
m_user_to_internal[user_body_index] = m_current_index;
m_current_index++;
for (size_t i = 0; i < m_user_child_indices[user_body_index].size(); i++) {
recurseIndexSets(m_user_child_indices[user_body_index][i]);
}
}
int User2InternalIndex::buildMapping() {
// find root index
int user_root_index = -1;
for (std::map<int, int>::iterator it = m_user_parent_index_map.begin();
it != m_user_parent_index_map.end(); it++) {
int current_root_index = findRoot(it->second);
if (it == m_user_parent_index_map.begin()) {
user_root_index = current_root_index;
} else {
if (user_root_index != current_root_index) {
error_message("multiple roots (at least) %d and %d\n", user_root_index,
current_root_index);
return -1;
}
}
}
// build child index map
for (std::map<int, int>::iterator it = m_user_parent_index_map.begin();
it != m_user_parent_index_map.end(); it++) {
m_user_child_indices[it->second].push_back(it->first);
}
m_current_index = -1;
// build internal index set
m_user_to_internal[user_root_index] = -1; // add map for root link
recurseIndexSets(user_root_index);
// reverse mapping
for (std::map<int, int>::iterator it = m_user_to_internal.begin();
it != m_user_to_internal.end(); it++) {
m_internal_to_user[it->second] = it->first;
}
m_map_built = true;
return 0;
}
int User2InternalIndex::user2internal(const int user, int *internal) const {
if (!m_map_built) {
return -1;
}
std::map<int, int>::const_iterator it;
it = m_user_to_internal.find(user);
if (it != m_user_to_internal.end()) {
*internal = it->second;
return 0;
} else {
error_message("no user index %d\n", user);
return -1;
}
}
int User2InternalIndex::internal2user(const int internal, int *user) const {
if (!m_map_built) {
return -1;
}
std::map<int, int>::const_iterator it;
it = m_internal_to_user.find(internal);
if (it != m_internal_to_user.end()) {
*user = it->second;
return 0;
} else {
error_message("no internal index %d\n", internal);
return -1;
}
}
}

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#ifndef USER2INTERNALINDEX_HPP
#define USER2INTERNALINDEX_HPP
#include <map>
#include <vector>
#include "BulletInverseDynamics/IDConfig.hpp"
namespace btInverseDynamics {
/// Convert arbitrary indexing scheme to internal indexing
/// used for MultiBodyTree
class User2InternalIndex {
public:
/// Ctor
User2InternalIndex();
/// add body to index maps
/// @param body index of body to add (external)
/// @param parent index of parent body (external)
void addBody(const int body, const int parent);
/// build mapping from external to internal indexing
/// @return 0 on success, -1 on failure
int buildMapping();
/// get internal index from external index
/// @param user external (user) index
/// @param internal pointer for storage of corresponding internal index
/// @return 0 on success, -1 on failure
int user2internal(const int user, int *internal) const;
/// get internal index from external index
/// @param user external (user) index
/// @param internal pointer for storage of corresponding internal index
/// @return 0 on success, -1 on failure
int internal2user(const int internal, int *user) const;
private:
int findRoot(int index);
void recurseIndexSets(const int user_body_index);
bool m_map_built;
std::map<int, int> m_user_parent_index_map;
std::map<int, int> m_user_to_internal;
std::map<int, int> m_internal_to_user;
std::map<int, std::vector<int> > m_user_child_indices;
int m_current_index;
};
}
#endif // USER2INTERNALINDEX_HPP

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#ifndef BTMULTIBODYFROMURDF_HPP
#define BTMULTIBODYFROMURDF_HPP
#include "btBulletDynamicsCommon.h"
#include "BulletDynamics/Featherstone/btMultiBodyConstraintSolver.h"
#include "BulletDynamics/Featherstone/btMultiBodyDynamicsWorld.h"
#include "BulletDynamics/Featherstone/btMultiBodyLinkCollider.h"
#include "BulletDynamics/Featherstone/btMultiBodyPoint2Point.h"
#include "../CommonInterfaces/CommonGUIHelperInterface.h"
#include "../Importers/ImportURDFDemo/BulletUrdfImporter.h"
#include "../Importers/ImportURDFDemo/URDF2Bullet.h"
#include "../Importers/ImportURDFDemo/MyMultiBodyCreator.h"
#include "../Importers/ImportURDFDemo/URDF2Bullet.h"
/// Create a btMultiBody model from URDF.
/// This is adapted from Bullet URDF loader example
class MyBtMultiBodyFromURDF {
public:
/// ctor
/// @param gravity gravitational acceleration (in world frame)
/// @param base_fixed if true, the root body is treated as fixed,
/// if false, it is treated as floating
MyBtMultiBodyFromURDF(const btVector3 &gravity, const bool base_fixed)
: m_gravity(gravity), m_base_fixed(base_fixed) {
m_broadphase = 0x0;
m_dispatcher = 0x0;
m_solver = 0x0;
m_collisionConfiguration = 0x0;
m_dynamicsWorld = 0x0;
m_multibody = 0x0;
}
/// dtor
~MyBtMultiBodyFromURDF() {
delete m_dynamicsWorld;
delete m_solver;
delete m_broadphase;
delete m_dispatcher;
delete m_collisionConfiguration;
delete m_multibody;
}
/// @param name path to urdf file
void setFileName(const std::string name) { m_filename = name; }
/// load urdf file and build btMultiBody model
void init() {
this->createEmptyDynamicsWorld();
m_dynamicsWorld->setGravity(m_gravity);
BulletURDFImporter urdf_importer(&m_nogfx);
URDFImporterInterface &u2b(urdf_importer);
bool loadOk = u2b.loadURDF(m_filename.c_str(), m_base_fixed);
if (loadOk) {
btTransform identityTrans;
identityTrans.setIdentity();
MyMultiBodyCreator creation(&m_nogfx);
const bool use_multibody = true;
ConvertURDF2Bullet(u2b, creation, identityTrans, m_dynamicsWorld, use_multibody,
u2b.getPathPrefix());
m_multibody = creation.getBulletMultiBody();
m_dynamicsWorld->stepSimulation(1. / 240., 0);
}
}
/// @return pointer to the btMultiBody model
btMultiBody *getBtMultiBody() { return m_multibody; }
private:
// internal utility function
void createEmptyDynamicsWorld() {
m_collisionConfiguration = new btDefaultCollisionConfiguration();
/// use the default collision dispatcher. For parallel processing you can use a diffent
/// dispatcher (see Extras/BulletMultiThreaded)
m_dispatcher = new btCollisionDispatcher(m_collisionConfiguration);
m_broadphase = new btDbvtBroadphase();
m_solver = new btMultiBodyConstraintSolver;
m_dynamicsWorld = new btMultiBodyDynamicsWorld(m_dispatcher, m_broadphase, m_solver,
m_collisionConfiguration);
m_dynamicsWorld->setGravity(m_gravity);
}
btBroadphaseInterface *m_broadphase;
btCollisionDispatcher *m_dispatcher;
btMultiBodyConstraintSolver *m_solver;
btDefaultCollisionConfiguration *m_collisionConfiguration;
btMultiBodyDynamicsWorld *m_dynamicsWorld;
std::string m_filename;
DummyGUIHelper m_nogfx;
btMultiBody *m_multibody;
const btVector3 m_gravity;
const bool m_base_fixed;
};
#endif // BTMULTIBODYFROMURDF_HPP

270
Extras/InverseDynamics/btMultiBodyTreeCreator.cpp Normal file
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#include "btMultiBodyTreeCreator.hpp"
namespace btInverseDynamics {
btMultiBodyTreeCreator::btMultiBodyTreeCreator() : m_initialized(false) {}
int btMultiBodyTreeCreator::createFromBtMultiBody(const btMultiBody *btmb, const bool verbose) {
if (0x0 == btmb) {
error_message("cannot create MultiBodyTree from null pointer\n");
return -1;
}
// in case this is a second call, discard old data
m_data.clear();
m_initialized = false;
// btMultiBody treats base link separately
m_data.resize(1 + btmb->getNumLinks());
// add base link data
{
LinkData &link = m_data[0];
link.parent_index = -1;
if (btmb->hasFixedBase()) {
link.joint_type = FIXED;
} else {
link.joint_type = FLOATING;
}
btTransform transform(btmb->getBaseWorldTransform());
link.parent_r_parent_body_ref(0) = transform.getOrigin()[0];
link.parent_r_parent_body_ref(1) = transform.getOrigin()[1];
link.parent_r_parent_body_ref(2) = transform.getOrigin()[2];
link.body_T_parent_ref(0, 0) = transform.getBasis()[0][0];
link.body_T_parent_ref(0, 1) = transform.getBasis()[0][1];
link.body_T_parent_ref(0, 2) = transform.getBasis()[0][2];
link.body_T_parent_ref(1, 0) = transform.getBasis()[1][0];
link.body_T_parent_ref(1, 1) = transform.getBasis()[1][1];
link.body_T_parent_ref(1, 2) = transform.getBasis()[1][2];
link.body_T_parent_ref(2, 0) = transform.getBasis()[2][0];
link.body_T_parent_ref(2, 1) = transform.getBasis()[2][1];
link.body_T_parent_ref(2, 2) = transform.getBasis()[2][2];
// random unit vector. value not used for fixed or floating joints.
link.body_axis_of_motion(0) = 0;
link.body_axis_of_motion(1) = 0;
link.body_axis_of_motion(2) = 1;
link.mass = btmb->getBaseMass();
// link frame in the center of mass
link.body_r_body_com(0) = 0;
link.body_r_body_com(1) = 0;
link.body_r_body_com(2) = 0;
// BulletDynamics uses body-fixed frame in the cog, aligned with principal axes
link.body_I_body(0, 0) = btmb->getBaseInertia()[0];
link.body_I_body(0, 1) = 0.0;
link.body_I_body(0, 2) = 0.0;
link.body_I_body(1, 0) = 0.0;
link.body_I_body(1, 1) = btmb->getBaseInertia()[1];
link.body_I_body(1, 2) = 0.0;
link.body_I_body(2, 0) = 0.0;
link.body_I_body(2, 1) = 0.0;
link.body_I_body(2, 2) = btmb->getBaseInertia()[2];
// shift reference point to link origin (in joint axis)
mat33 tilde_r_com = tildeOperator(link.body_r_body_com);
link.body_I_body = link.body_I_body - link.mass * tilde_r_com * tilde_r_com;
if (verbose) {
id_printf("base: mass= %f, bt_inertia= [%f %f %f]\n"
"Io= [%f %f %f;\n"
" %f %f %f;\n"
" %f %f %f]\n",
link.mass, btmb->getBaseInertia()[0], btmb->getBaseInertia()[1],
btmb->getBaseInertia()[2], link.body_I_body(0, 0), link.body_I_body(0, 1),
link.body_I_body(0, 2), link.body_I_body(1, 0), link.body_I_body(1, 1),
link.body_I_body(1, 2), link.body_I_body(2, 0), link.body_I_body(2, 1),
link.body_I_body(2, 2));
}
}
for (int bt_index = 0; bt_index < btmb->getNumLinks(); bt_index++) {
if (verbose) {
id_printf("bt->id: converting link %d\n", bt_index);
}
const btMultibodyLink &bt_link = btmb->getLink(bt_index);
LinkData &link = m_data[bt_index + 1];
link.parent_index = bt_link.m_parent + 1;
link.mass = bt_link.m_mass;
if (verbose) {
id_printf("mass= %f\n", link.mass);
}
// from this body's pivot to this body's com in this body's frame
link.body_r_body_com[0] = bt_link.m_dVector[0];
link.body_r_body_com[1] = bt_link.m_dVector[1];
link.body_r_body_com[2] = bt_link.m_dVector[2];
if (verbose) {
id_printf("com= %f %f %f\n", link.body_r_body_com[0], link.body_r_body_com[1],
link.body_r_body_com[2]);
}
// BulletDynamics uses a body-fixed frame in the CoM, aligned with principal axes
link.body_I_body(0, 0) = bt_link.m_inertiaLocal[0];
link.body_I_body(0, 1) = 0.0;
link.body_I_body(0, 2) = 0.0;
link.body_I_body(1, 0) = 0.0;
link.body_I_body(1, 1) = bt_link.m_inertiaLocal[1];
link.body_I_body(1, 2) = 0.0;
link.body_I_body(2, 0) = 0.0;
link.body_I_body(2, 1) = 0.0;
link.body_I_body(2, 2) = bt_link.m_inertiaLocal[2];
// shift reference point to link origin (in joint axis)
mat33 tilde_r_com = tildeOperator(link.body_r_body_com);
link.body_I_body = link.body_I_body - link.mass * tilde_r_com * tilde_r_com;
if (verbose) {
id_printf("link %d: mass= %f, bt_inertia= [%f %f %f]\n"
"Io= [%f %f %f;\n"
" %f %f %f;\n"
" %f %f %f]\n",
bt_index, link.mass, bt_link.m_inertiaLocal[0], bt_link.m_inertiaLocal[1],
bt_link.m_inertiaLocal[2], link.body_I_body(0, 0), link.body_I_body(0, 1),
link.body_I_body(0, 2), link.body_I_body(1, 0), link.body_I_body(1, 1),
link.body_I_body(1, 2), link.body_I_body(2, 0), link.body_I_body(2, 1),
link.body_I_body(2, 2));
}
// transform for vectors written in parent frame to this link's body-fixed frame
btMatrix3x3 basis = btTransform(bt_link.m_zeroRotParentToThis).getBasis();
link.body_T_parent_ref(0, 0) = basis[0][0];
link.body_T_parent_ref(0, 1) = basis[0][1];
link.body_T_parent_ref(0, 2) = basis[0][2];
link.body_T_parent_ref(1, 0) = basis[1][0];
link.body_T_parent_ref(1, 1) = basis[1][1];
link.body_T_parent_ref(1, 2) = basis[1][2];
link.body_T_parent_ref(2, 0) = basis[2][0];
link.body_T_parent_ref(2, 1) = basis[2][1];
link.body_T_parent_ref(2, 2) = basis[2][2];
if (verbose) {
id_printf("body_T_parent_ref= %f %f %f\n"
" %f %f %f\n"
" %f %f %f\n",
basis[0][0], basis[0][1], basis[0][2], basis[1][0], basis[1][1], basis[1][2],
basis[2][0], basis[2][1], basis[2][2]);
}
switch (bt_link.m_jointType) {
case btMultibodyLink::eRevolute:
link.joint_type = REVOLUTE;
if (verbose) {
id_printf("type= revolute\n");
}
link.body_axis_of_motion(0) = bt_link.m_axes[0].m_topVec[0];
link.body_axis_of_motion(1) = bt_link.m_axes[0].m_topVec[1];
link.body_axis_of_motion(2) = bt_link.m_axes[0].m_topVec[2];
// for revolute joints, m_eVector = parentComToThisPivotOffset
// m_dVector = thisPivotToThisComOffset
// from parent com to pivot, in parent frame
link.parent_r_parent_body_ref(0) = bt_link.m_eVector[0];
link.parent_r_parent_body_ref(1) = bt_link.m_eVector[1];
link.parent_r_parent_body_ref(2) = bt_link.m_eVector[2];
break;
case btMultibodyLink::ePrismatic:
link.joint_type = PRISMATIC;
if (verbose) {
id_printf("type= prismatic\n");
}
link.body_axis_of_motion(0) = bt_link.m_axes[0].m_bottomVec[0];
link.body_axis_of_motion(1) = bt_link.m_axes[0].m_bottomVec[1];
link.body_axis_of_motion(2) = bt_link.m_axes[0].m_bottomVec[2];
// for prismatic joints, eVector
// according to documentation :
// parentComToThisComOffset
// but seems to be: from parent's com to parent's
// pivot ??
// m_dVector = thisPivotToThisComOffset
link.parent_r_parent_body_ref(0) = bt_link.m_eVector[0];
link.parent_r_parent_body_ref(1) = bt_link.m_eVector[1];
link.parent_r_parent_body_ref(2) = bt_link.m_eVector[2];
break;
case btMultibodyLink::eSpherical:
error_message("spherical joints not implemented\n");
return -1;
case btMultibodyLink::ePlanar:
error_message("planar joints not implemented\n");
return -1;
case btMultibodyLink::eFixed:
link.joint_type = FIXED;
// random unit vector
link.body_axis_of_motion(0) = 0;
link.body_axis_of_motion(1) = 0;
link.body_axis_of_motion(2) = 1;
// for fixed joints, m_dVector = thisPivotToThisComOffset;
// m_eVector = parentComToThisPivotOffset;
link.parent_r_parent_body_ref(0) = bt_link.m_eVector[0];
link.parent_r_parent_body_ref(1) = bt_link.m_eVector[1];
link.parent_r_parent_body_ref(2) = bt_link.m_eVector[2];
break;
default:
error_message("unknown btMultiBody::eFeatherstoneJointType %d\n",
bt_link.m_jointType);
return -1;
}
if (link.parent_index > 0) { // parent body isn't the root
const btMultibodyLink &bt_parent_link = btmb->getLink(link.parent_index - 1);
// from parent pivot to parent com, in parent frame
link.parent_r_parent_body_ref(0) += bt_parent_link.m_dVector[0];
link.parent_r_parent_body_ref(1) += bt_parent_link.m_dVector[1];
link.parent_r_parent_body_ref(2) += bt_parent_link.m_dVector[2];
} else {
// parent is root body. btMultiBody only knows 6-DoF or 0-DoF root bodies,
// whose link frame is in the CoM (ie, no notion of a pivot point)
}
if (verbose) {
id_printf("parent_r_parent_body_ref= %f %f %f\n", link.parent_r_parent_body_ref[0],
link.parent_r_parent_body_ref[1], link.parent_r_parent_body_ref[2]);
}
}
m_initialized = true;
return 0;
}
int btMultiBodyTreeCreator::getNumBodies(int *num_bodies) const {
if (false == m_initialized) {
error_message("btMultiBody not converted yet\n");
return -1;
}
*num_bodies = static_cast<int>(m_data.size());
return 0;
}
int btMultiBodyTreeCreator::getBody(int body_index, int *parent_index, JointType *joint_type,
vec3 *parent_r_parent_body_ref, mat33 *body_T_parent_ref,
vec3 *body_axis_of_motion, idScalar *mass,
vec3 *body_r_body_com, mat33 *body_I_body, int *user_int,
void **user_ptr) const {
if (false == m_initialized) {
error_message("MultiBodyTree not created yet\n");
return -1;
}
if (body_index < 0 || body_index >= static_cast<int>(m_data.size())) {
error_message("index out of range (got %d but only %zu bodies)\n", body_index,
m_data.size());
return -1;
}
*parent_index = m_data[body_index].parent_index;
*joint_type = m_data[body_index].joint_type;
*parent_r_parent_body_ref = m_data[body_index].parent_r_parent_body_ref;
*body_T_parent_ref = m_data[body_index].body_T_parent_ref;
*body_axis_of_motion = m_data[body_index].body_axis_of_motion;
*mass = m_data[body_index].mass;
*body_r_body_com = m_data[body_index].body_r_body_com;
*body_I_body = m_data[body_index].body_I_body;
*user_int = -1;
*user_ptr = 0x0;
return 0;
}
}

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#ifndef BTMULTIBODYTREECREATOR_HPP_
#define BTMULTIBODYTREECREATOR_HPP_
#include <vector>
#include "BulletInverseDynamics/IDConfig.hpp"
#include "MultiBodyTreeCreator.hpp"
#include "BulletDynamics/Featherstone/btMultiBody.h"
namespace btInverseDynamics {
/// MultiBodyTreeCreator implementation for converting
/// a btMultiBody forward dynamics model into a MultiBodyTree inverse dynamics model
class btMultiBodyTreeCreator : public MultiBodyTreeCreator {
public:
/// ctor
btMultiBodyTreeCreator();
/// dtor
~btMultiBodyTreeCreator() {}
/// extract model data from a btMultiBody
/// @param btmb pointer to btMultiBody to convert
/// @param verbose if true, some information is printed
/// @return -1 on error, 0 on success
int createFromBtMultiBody(const btMultiBody *btmb, const bool verbose = false);
/// \copydoc MultiBodyTreeCreator::getNumBodies
int getNumBodies(int *num_bodies) const;
///\copydoc MultiBodyTreeCreator::getBody
int getBody(int body_index, int *parent_index, JointType *joint_type,
vec3 *parent_r_parent_body_ref, mat33 *body_T_parent_ref, vec3 *body_axis_of_motion,
idScalar *mass, vec3 *body_r_body_com, mat33 *body_I_body, int *user_int,
void **user_ptr) const;
private:
// internal struct holding data extracted from btMultiBody
struct LinkData {
int parent_index;
JointType joint_type;
vec3 parent_r_parent_body_ref;
mat33 body_T_parent_ref;
vec3 body_axis_of_motion;
idScalar mass;
vec3 body_r_body_com;
mat33 body_I_body;
};
std::vector<LinkData> m_data;
bool m_initialized;
};
}
#endif // BTMULTIBODYTREECREATOR_HPP_

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#include "invdyn_bullet_comparison.hpp"
#include <cmath>
#include "BulletInverseDynamics/IDConfig.hpp"
#include "BulletInverseDynamics/MultiBodyTree.hpp"
#include "btBulletDynamicsCommon.h"
#include "BulletDynamics/Featherstone/btMultiBodyConstraintSolver.h"
#include "BulletDynamics/Featherstone/btMultiBodyDynamicsWorld.h"
#include "BulletDynamics/Featherstone/btMultiBodyLinkCollider.h"
#include "BulletDynamics/Featherstone/btMultiBodyPoint2Point.h"
namespace btInverseDynamics {
int compareInverseAndForwardDynamics(vecx &q, vecx &u, vecx &dot_u, btVector3 &gravity, bool verbose,
btMultiBody *btmb, MultiBodyTree *id_tree, double *pos_error,
double *acc_error) {
// call function and return -1 if it does, printing an error_message
#define RETURN_ON_FAILURE(x) \
do { \
if (-1 == x) { \
error_message("calling " #x "\n"); \
return -1; \
} \
} while (0)
if (verbose) {
printf("\n ===================================== \n");
}
vecx joint_forces(q.size());
// set positions and velocities for btMultiBody
// base link
mat33 world_T_base;
vec3 world_pos_base;
btTransform base_transform;
vec3 base_velocity;
vec3 base_angular_velocity;
RETURN_ON_FAILURE(id_tree->setGravityInWorldFrame(gravity));
RETURN_ON_FAILURE(id_tree->getBodyOrigin(0, &world_pos_base));
RETURN_ON_FAILURE(id_tree->getBodyTransform(0, &world_T_base));
RETURN_ON_FAILURE(id_tree->getBodyAngularVelocity(0, &base_angular_velocity));
RETURN_ON_FAILURE(id_tree->getBodyLinearVelocityCoM(0, &base_velocity));
base_transform.setBasis(world_T_base);
base_transform.setOrigin(world_pos_base);
btmb->setBaseWorldTransform(base_transform);
btmb->setBaseOmega(base_angular_velocity);
btmb->setBaseVel(base_velocity);
btmb->setLinearDamping(0);
btmb->setAngularDamping(0);
// remaining links
int q_index;
if (btmb->hasFixedBase()) {
q_index = 0;
} else {
q_index = 6;
}
if (verbose) {
printf("bt:num_links= %d, num_dofs= %d\n", btmb->getNumLinks(), btmb->getNumDofs());
}
for (int l = 0; l < btmb->getNumLinks(); l++) {
const btMultibodyLink &link = btmb->getLink(l);
if (verbose) {
printf("link %d, pos_var_count= %d, dof_count= %d\n", l, link.m_posVarCount,
link.m_dofCount);
}
if (link.m_posVarCount == 1) {
btmb->setJointPosMultiDof(l, &q(q_index));
btmb->setJointVelMultiDof(l, &u(q_index));
if (verbose) {
printf("set q[%d]= %f, u[%d]= %f\n", q_index, q(q_index), q_index, u(q_index));
}
q_index++;
}
}
// sanity check
if (q_index != q.size()) {
error_message("error in number of dofs for btMultibody and MultiBodyTree\n");
return -1;
}
// run inverse dynamics to determine joint_forces for given q, u, dot_u
if (-1 == id_tree->calculateInverseDynamics(q, u, dot_u, &joint_forces)) {
error_message("calculating inverse dynamics\n");
return -1;
}
// set up bullet forward dynamics model
btScalar dt = 0;
btAlignedObjectArray<btScalar> scratch_r;
btAlignedObjectArray<btVector3> scratch_v;
btAlignedObjectArray<btMatrix3x3> scratch_m;
// this triggers switch between using either appliedConstraintForce or appliedForce
bool isConstraintPass = false;
// apply gravity forces for btMultiBody model. Must be done manually.
btmb->addBaseForce(btmb->getBaseMass() * gravity);
for (int link = 0; link < btmb->getNumLinks(); link++) {
btmb->addLinkForce(link, gravity * btmb->getLinkMass(link));
if (verbose) {
printf("link %d, applying gravity %f %f %f\n", link,
gravity[0] * btmb->getLinkMass(link), gravity[1] * btmb->getLinkMass(link),
gravity[2] * btmb->getLinkMass(link));
}
}
// apply generalized forces
if (btmb->hasFixedBase()) {
q_index = 0;
} else {
vec3 base_force;
base_force(0) = joint_forces(3);
base_force(1) = joint_forces(4);
base_force(2) = joint_forces(5);
vec3 base_moment;
base_moment(0) = joint_forces(0);
base_moment(1) = joint_forces(1);
base_moment(2) = joint_forces(2);
btmb->addBaseForce(world_T_base * base_force);
btmb->addBaseTorque(world_T_base * base_moment);
if (verbose) {
printf("base force from id: %f %f %f\n", joint_forces(3), joint_forces(4),
joint_forces(5));
printf("base moment from id: %f %f %f\n", joint_forces(0), joint_forces(1),
joint_forces(2));
}
q_index = 6;
}
for (int l = 0; l < btmb->getNumLinks(); l++) {
const btMultibodyLink &link = btmb->getLink(l);
if (link.m_posVarCount == 1) {
if (verbose) {
printf("id:joint_force[%d]= %f, applied to link %d\n", q_index,
joint_forces(q_index), l);
}
btmb->addJointTorque(l, joint_forces(q_index));
q_index++;
}
}
// sanity check
if (q_index != q.size()) {
error_message("error in number of dofs for btMultibody and MultiBodyTree\n");
return -1;
}
// run forward kinematics & forward dynamics
btAlignedObjectArray<btQuaternion> world_to_local;
btAlignedObjectArray<btVector3> local_origin;
btmb->forwardKinematics(world_to_local, local_origin);
btmb->computeAccelerationsArticulatedBodyAlgorithmMultiDof(dt, scratch_r, scratch_v, scratch_m, isConstraintPass);
// read generalized accelerations back from btMultiBody
// the mapping from scratch variables to accelerations is taken from the implementation
// of stepVelocitiesMultiDof
btScalar *base_accel = &scratch_r[btmb->getNumDofs()];
btScalar *joint_accel = base_accel + 6;
*acc_error = 0;
int dot_u_offset = 0;
if (btmb->hasFixedBase()) {
dot_u_offset = 0;
} else {
dot_u_offset = 6;
}
if (true == btmb->hasFixedBase()) {
for (int i = 0; i < btmb->getNumDofs(); i++) {
if (verbose) {
printf("bt:ddot_q[%d]= %f, id:ddot_q= %e, diff= %e\n", i, joint_accel[i],
dot_u(i + dot_u_offset), joint_accel[i] - dot_u(i));
}
*acc_error += std::pow(joint_accel[i] - dot_u(i + dot_u_offset), 2);
}
} else {
vec3 base_dot_omega;
vec3 world_dot_omega;
world_dot_omega(0) = base_accel[0];
world_dot_omega(1) = base_accel[1];
world_dot_omega(2) = base_accel[2];
base_dot_omega = world_T_base.transpose() * world_dot_omega;
// com happens to coincide with link origin here. If that changes, we need to calculate
// ddot_com
vec3 base_ddot_com;
vec3 world_ddot_com;
world_ddot_com(0) = base_accel[3];
world_ddot_com(1) = base_accel[4];
world_ddot_com(2) = base_accel[5];
base_ddot_com = world_T_base.transpose()*world_ddot_com;
for (int i = 0; i < 3; i++) {
if (verbose) {
printf("bt::base_dot_omega(%d)= %e dot_u[%d]= %e, diff= %e\n", i, base_dot_omega(i),
i, dot_u[i], base_dot_omega(i) - dot_u[i]);
}
*acc_error += std::pow(base_dot_omega(i) - dot_u(i), 2);
}
for (int i = 0; i < 3; i++) {
if (verbose) {
printf("bt::base_ddot_com(%d)= %e dot_u[%d]= %e, diff= %e\n", i, base_ddot_com(i),
i, dot_u[i + 3], base_ddot_com(i) - dot_u[i + 3]);
}
*acc_error += std::pow(base_ddot_com(i) - dot_u(i + 3), 2);
}
for (int i = 0; i < btmb->getNumDofs(); i++) {
if (verbose) {
printf("bt:ddot_q[%d]= %f, id:ddot_q= %e, diff= %e\n", i, joint_accel[i],
dot_u(i + 6), joint_accel[i] - dot_u(i + 6));
}
*acc_error += std::pow(joint_accel[i] - dot_u(i + 6), 2);
}
}
*acc_error = std::sqrt(*acc_error);
if (verbose) {
printf("======dynamics-err: %e\n", *acc_error);
}
*pos_error = 0.0;
{
mat33 world_T_body;
if (-1 == id_tree->getBodyTransform(0, &world_T_body)) {
error_message("getting transform for body %d\n", 0);
return -1;
}
vec3 world_com;
if (-1 == id_tree->getBodyCoM(0, &world_com)) {
error_message("getting com for body %d\n", 0);
return -1;
}
if (verbose) {
printf("id:com: %f %f %f\n", world_com(0), world_com(1), world_com(2));
printf("id:transform: %f %f %f\n"
" %f %f %f\n"
" %f %f %f\n",
world_T_body(0, 0), world_T_body(0, 1), world_T_body(0, 2), world_T_body(1, 0),
world_T_body(1, 1), world_T_body(1, 2), world_T_body(2, 0), world_T_body(2, 1),
world_T_body(2, 2));
}
}
for (int l = 0; l < btmb->getNumLinks(); l++) {
const btMultibodyLink &bt_link = btmb->getLink(l);
vec3 bt_origin = bt_link.m_cachedWorldTransform.getOrigin();
mat33 bt_basis = bt_link.m_cachedWorldTransform.getBasis();
if (verbose) {
printf("------------- link %d\n", l + 1);
printf("bt:com: %f %f %f\n", bt_origin(0), bt_origin(1), bt_origin(2));
printf("bt:transform: %f %f %f\n"
" %f %f %f\n"
" %f %f %f\n",
bt_basis(0, 0), bt_basis(0, 1), bt_basis(0, 2), bt_basis(1, 0), bt_basis(1, 1),
bt_basis(1, 2), bt_basis(2, 0), bt_basis(2, 1), bt_basis(2, 2));
}
mat33 id_world_T_body;
vec3 id_world_com;
if (-1 == id_tree->getBodyTransform(l + 1, &id_world_T_body)) {
error_message("getting transform for body %d\n", l);
return -1;
}
if (-1 == id_tree->getBodyCoM(l + 1, &id_world_com)) {
error_message("getting com for body %d\n", l);
return -1;
}
if (verbose) {
printf("id:com: %f %f %f\n", id_world_com(0), id_world_com(1), id_world_com(2));
printf("id:transform: %f %f %f\n"
" %f %f %f\n"
" %f %f %f\n",
id_world_T_body(0, 0), id_world_T_body(0, 1), id_world_T_body(0, 2),
id_world_T_body(1, 0), id_world_T_body(1, 1), id_world_T_body(1, 2),
id_world_T_body(2, 0), id_world_T_body(2, 1), id_world_T_body(2, 2));
}
vec3 diff_com = bt_origin - id_world_com;
mat33 diff_basis = bt_basis - id_world_T_body;
if (verbose) {
printf("diff-com: %e %e %e\n", diff_com(0), diff_com(1), diff_com(2));
printf("diff-transform: %e %e %e %e %e %e %e %e %e\n", diff_basis(0, 0),
diff_basis(0, 1), diff_basis(0, 2), diff_basis(1, 0), diff_basis(1, 1),
diff_basis(1, 2), diff_basis(2, 0), diff_basis(2, 1), diff_basis(2, 2));
}
double total_pos_err =
std::sqrt(std::pow(diff_com(0), 2) + std::pow(diff_com(1), 2) +
std::pow(diff_com(2), 2) + std::pow(diff_basis(0, 0), 2) +
std::pow(diff_basis(0, 1), 2) + std::pow(diff_basis(0, 2), 2) +
std::pow(diff_basis(1, 0), 2) + std::pow(diff_basis(1, 1), 2) +
std::pow(diff_basis(1, 2), 2) + std::pow(diff_basis(2, 0), 2) +
std::pow(diff_basis(2, 1), 2) + std::pow(diff_basis(2, 2), 2));
if (verbose) {
printf("======kin-pos-err: %e\n", total_pos_err);
}
if (total_pos_err > *pos_error) {
*pos_error = total_pos_err;
}
}
return 0;
}
}

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#ifndef INVDYN_BULLET_COMPARISON_HPP
#define INVDYN_BULLET_COMPARISON_HPP
class btMultiBody;
class btVector3;
namespace btInverseDynamics {
class MultiBodyTree;
class vecx;
/// this function compares the forward dynamics computations implemented in btMultiBody to
/// the inverse dynamics implementation in MultiBodyTree. This is done in three steps
/// 1. run inverse dynamics for (q, u, dot_u) to obtain joint forces f
/// 2. run forward dynamics (btMultiBody) for (q,u,f) to obtain dot_u_bullet
/// 3. compare dot_u with dot_u_bullet for cross check of forward and inverse dynamics computations
/// @param btmb the bullet forward dynamics model
/// @param id_tree the inverse dynamics model
/// @param q vector of generalized coordinates (matches id_tree)
/// @param u vector of generalized speeds (matches id_tree)
/// @param gravity gravitational acceleration in world frame
/// @param dot_u vector of generalized accelerations (matches id_tree)
/// @param gravity gravitational acceleration in world frame
/// @param base_fixed set base joint to fixed or
/// @param pos_error is set to the maximum of the euclidean norm of position+rotation errors of all
/// center of gravity positions and link frames
/// @param acc_error is set to the square root of the sum of squared differences of generalized
/// accelerations
/// computed in step 3 relative to dot_u
/// @return -1 on error, 0 on success
int compareInverseAndForwardDynamics(vecx &q, vecx &u, vecx &dot_u, btVector3 &gravity, bool verbose,
btMultiBody *btmb, MultiBodyTree *id_tree, double *pos_error,
double *acc_error);
}
#endif // INVDYN_BULLET_COMPARISON_HPP

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project "BulletInverseDynamicsUtils"
kind "StaticLib"
includedirs {
"../../src"
}
files {
"*.cpp",
"*.hpp"
}

40
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///@file Configuration for Inverse Dynamics Library,
/// such as choice of linear algebra library and underlying scalar type
#ifndef IDCONFIG_HPP_
#define IDCONFIG_HPP_
// If we have a custom configuration, compile without using other parts of bullet.
#ifdef BT_CUSTOM_INVERSE_DYNAMICS_CONFIG_H
#define BT_ID_WO_BULLET
#endif
// error messages
#include "IDErrorMessages.hpp"
#ifdef BT_CUSTOM_INVERSE_DYNAMICS_CONFIG_H
#define INVDYN_INCLUDE_HELPER_2(x) #x
#define INVDYN_INCLUDE_HELPER(x) INVDYN_INCLUDE_HELPER_2(x)
#include INVDYN_INCLUDE_HELPER(BT_CUSTOM_INVERSE_DYNAMICS_CONFIG_H)
#else
// Use default configuration with bullet's types
// Use the same scalar type as rest of bullet library
#include "LinearMath/btScalar.h"
typedef btScalar idScalar;
// use bullet types for arrays and array indices
#include "Bullet3Common/b3AlignedObjectArray.h"
// this is to make it work with C++2003, otherwise we could do this:
// template <typename T>
// using idArray = b3AlignedObjectArray<T>;
template <typename T>
struct idArray {
typedef b3AlignedObjectArray<T> type;
};
typedef int idArrayIdx;
#define ID_DECLARE_ALIGNED_ALLOCATOR B3_DECLARE_ALIGNED_ALLOCATOR
// use bullet's allocator functions
#define idMalloc btAllocFunc
#define idFree btFreeFunc
#define ID_LINEAR_MATH_USE_BULLET
#include "details/IDLinearMathInterface.hpp"
#endif
#endif

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///@file Configuration for Inverse Dynamics Library without external dependencies
#ifndef INVDYNCONFIG_BUILTIN_HPP_
#define INVDYNCONFIG_BUILTIN_HPP_
#ifdef BT_USE_DOUBLE_PRECISION
// choose double/single precision version
typedef double idScalar;
#else
typedef float idScalar;
#endif
// use std::vector for arrays
#include <vector>
// this is to make it work with C++2003, otherwise we could do this
// template <typename T>
// using idArray = std::vector<T>;
template <typename T>
struct idArray {
typedef std::vector<T> type;
};
typedef std::vector<int>::size_type idArrayIdx;
// default to standard malloc/free
#include <cstdlib>
#define idMalloc ::malloc
#define idFree ::free
// currently not aligned at all...
#define ID_DECLARE_ALIGNED_ALLOCATOR() \
inline void* operator new(std::size_t sizeInBytes) { return idMalloc(sizeInBytes); } \
inline void operator delete(void* ptr) { idFree(ptr); } \
inline void* operator new(std::size_t, void* ptr) { return ptr; } \
inline void operator delete(void*, void*) {} \
inline void* operator new[](std::size_t sizeInBytes) { return idMalloc(sizeInBytes); } \
inline void operator delete[](void* ptr) { idFree(ptr); } \
inline void* operator new[](std::size_t, void* ptr) { return ptr; } \
inline void operator delete[](void*, void*) {}
#include "details/IDMatVec.hpp"
#endif

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///@file Configuration for Inverse Dynamics Library with Eigen
#ifndef INVDYNCONFIG_EIGEN_HPP_
#define INVDYNCONFIG_EIGEN_HPP_
#ifdef BT_USE_DOUBLE_PRECISION
// choose double/single precision version
typedef double idScalar;
#else
typedef float idScalar;
#endif
// use std::vector for arrays
#include <vector>
// this is to make it work with C++2003, otherwise we could do this
// template <typename T>
// using idArray = std::vector<T>;
template <typename T>
struct idArray {
typedef std::vector<T> type;
};
typedef std::vector<int>::size_type idArrayIdx;
// default to standard malloc/free
#include <cstdlib>
#define idMalloc ::malloc
#define idFree ::free
// currently not aligned at all...
#define ID_DECLARE_ALIGNED_ALLOCATOR() \
inline void* operator new(std::size_t sizeInBytes) { return idMalloc(sizeInBytes); } \
inline void operator delete(void* ptr) { idFree(ptr); } \
inline void* operator new(std::size_t, void* ptr) { return ptr; } \
inline void operator delete(void*, void*) {} \
inline void* operator new[](std::size_t sizeInBytes) { return idMalloc(sizeInBytes); } \
inline void operator delete[](void* ptr) { idFree(ptr); } \
inline void* operator new[](std::size_t, void* ptr) { return ptr; } \
inline void operator delete[](void*, void*) {}
// Note on interfaces:
// Eigen::Matrix has data(), to get c-array storage
// HOWEVER: default storage is column-major!
#define ID_LINEAR_MATH_USE_EIGEN
#include "Eigen/Eigen"
#include "details/IDEigenInterface.hpp"
#endif

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///@file error message utility functions
#ifndef IDUTILS_HPP_
#define IDUTILS_HPP_
#include <cstring>
/// name of file being compiled, without leading path components
#define __INVDYN_FILE_WO_DIR__ (strrchr(__FILE__, '/') ? strrchr(__FILE__, '/') + 1 : __FILE__)
#ifndef BT_ID_WO_BULLET
#include "Bullet3Common/b3Logging.h"
#define error_message(...) b3Error(__VA_ARGS__)
#define warning_message(...) b3Warning(__VA_ARGS__)
#define id_printf(...) b3Printf(__VA_ARGS__)
#else // BT_ID_WO_BULLET
#include <cstdio>
/// print error message with file/line information
#define error_message(...) \
do { \
fprintf(stderr, "[Error:%s:%d] ", __INVDYN_FILE_WO_DIR__, __LINE__); \
fprintf(stderr, __VA_ARGS__); \
} while (0)
/// print warning message with file/line information
#define warning_message(...) \
do { \
fprintf(stderr, "[Warning:%s:%d] ", __INVDYN_FILE_WO_DIR__, __LINE__); \
fprintf(stderr, __VA_ARGS__); \
} while (0)
#define warning_message(...) \
do { \
fprintf(stderr, "[Warning:%s:%d] ", __INVDYN_FILE_WO_DIR__, __LINE__); \
fprintf(stderr, __VA_ARGS__); \
} while (0)
#define id_printf(...) printf(__VA_ARGS__)
#endif // BT_ID_WO_BULLET
#endif

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#include "IDMath.hpp"
#include <cmath>
#include <limits>
namespace btInverseDynamics {
static const idScalar kIsZero = 5 * std::numeric_limits<idScalar>::epsilon();
// requirements for axis length deviation from 1.0
// experimentally set from random euler angle rotation matrices
static const idScalar kAxisLengthEpsilon = 10 * kIsZero;
void setZero(vec3 &v) {
v(0) = 0;
v(1) = 0;
v(2) = 0;
}
void setZero(vecx &v) {
for (int i = 0; i < v.size(); i++) {
v(i) = 0;
}
}
void setZero(mat33 &m) {
m(0, 0) = 0;
m(0, 1) = 0;
m(0, 2) = 0;
m(1, 0) = 0;
m(1, 1) = 0;
m(1, 2) = 0;
m(2, 0) = 0;
m(2, 1) = 0;
m(2, 2) = 0;
}
idScalar maxAbs(const vecx &v) {
idScalar result = 0.0;
for (int i = 0; i < v.size(); i++) {
const idScalar tmp = std::fabs(v(i));
if (tmp > result) {
result = tmp;
}
}
return result;
}
idScalar maxAbs(const vec3 &v) {
idScalar result = 0.0;
for (int i = 0; i < 3; i++) {
const idScalar tmp = std::fabs(v(i));
if (tmp > result) {
result = tmp;
}
}
return result;
}
mat33 transformX(const idScalar &alpha) {
mat33 T;
const idScalar cos_alpha = std::cos(alpha);
const idScalar sin_alpha = std::sin(alpha);
// [1 0 0]
// [0 c s]
// [0 -s c]
T(0, 0) = 1.0;
T(0, 1) = 0.0;
T(0, 2) = 0.0;
T(1, 0) = 0.0;
T(1, 1) = cos_alpha;
T(1, 2) = sin_alpha;
T(2, 0) = 0.0;
T(2, 1) = -sin_alpha;
T(2, 2) = cos_alpha;
return T;
}
mat33 transformY(const idScalar &beta) {
mat33 T;
const idScalar cos_beta = std::cos(beta);
const idScalar sin_beta = std::sin(beta);
// [c 0 -s]
// [0 1 0]
// [s 0 c]
T(0, 0) = cos_beta;
T(0, 1) = 0.0;
T(0, 2) = -sin_beta;
T(1, 0) = 0.0;
T(1, 1) = 1.0;
T(1, 2) = 0.0;
T(2, 0) = sin_beta;
T(2, 1) = 0.0;
T(2, 2) = cos_beta;
return T;
}
mat33 transformZ(const idScalar &gamma) {
mat33 T;
const idScalar cos_gamma = std::cos(gamma);
const idScalar sin_gamma = std::sin(gamma);
// [ c s 0]
// [-s c 0]
// [ 0 0 1]
T(0, 0) = cos_gamma;
T(0, 1) = sin_gamma;
T(0, 2) = 0.0;
T(1, 0) = -sin_gamma;
T(1, 1) = cos_gamma;
T(1, 2) = 0.0;
T(2, 0) = 0.0;
T(2, 1) = 0.0;
T(2, 2) = 1.0;
return T;
}
mat33 tildeOperator(const vec3 &v) {
mat33 m;
m(0, 0) = 0.0;
m(0, 1) = -v(2);
m(0, 2) = v(1);
m(1, 0) = v(2);
m(1, 1) = 0.0;
m(1, 2) = -v(0);
m(2, 0) = -v(1);
m(2, 1) = v(0);
m(2, 2) = 0.0;
return m;
}
void getVecMatFromDH(idScalar theta, idScalar d, idScalar a, idScalar alpha, vec3 *r, mat33 *T) {
const idScalar sa = std::sin(alpha);
const idScalar ca = std::cos(alpha);
const idScalar st = std::sin(theta);
const idScalar ct = std::cos(theta);
(*r)(0) = a;
(*r)(1) = -sa * d;
(*r)(2) = ca * d;
(*T)(0, 0) = ct;
(*T)(0, 1) = -st;
(*T)(0, 2) = 0.0;
(*T)(1, 0) = st * ca;
(*T)(1, 1) = ct * ca;
(*T)(1, 2) = -sa;
(*T)(2, 0) = st * sa;
(*T)(2, 1) = ct * sa;
(*T)(2, 2) = ca;
}
void bodyTParentFromAxisAngle(const vec3 &axis, const idScalar &angle, mat33 *T) {
const idScalar c = cos(angle);
const idScalar s = -sin(angle);
const idScalar one_m_c = 1.0 - c;
const idScalar &x = axis(0);
const idScalar &y = axis(1);
const idScalar &z = axis(2);
(*T)(0, 0) = x * x * one_m_c + c;
(*T)(0, 1) = x * y * one_m_c - z * s;
(*T)(0, 2) = x * z * one_m_c + y * s;
(*T)(1, 0) = x * y * one_m_c + z * s;
(*T)(1, 1) = y * y * one_m_c + c;
(*T)(1, 2) = y * z * one_m_c - x * s;
(*T)(2, 0) = x * z * one_m_c - y * s;
(*T)(2, 1) = y * z * one_m_c + x * s;
(*T)(2, 2) = z * z * one_m_c + c;
}
bool isPositiveDefinite(const mat33 &m) {
// test if all upper left determinants are positive
if (m(0, 0) <= 0) { // upper 1x1
return false;
}
if (m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0) <= 0) { // upper 2x2
return false;
}
if ((m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1)) -
m(0, 1) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0)) +
m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0))) < 0) {
return false;
}
return true;
}
bool isPositiveSemiDefinite(const mat33 &m) {
// test if all upper left determinants are positive
if (m(0, 0) < 0) { // upper 1x1
return false;
}
if (m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0) < 0) { // upper 2x2
return false;
}
if ((m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1)) -
m(0, 1) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0)) +
m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0))) < 0) {
return false;
}
return true;
}
bool isPositiveSemiDefiniteFuzzy(const mat33 &m) {
// test if all upper left determinants are positive
if (m(0, 0) < -kIsZero) { // upper 1x1
return false;
}
if (m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0) < -kIsZero) { // upper 2x2
return false;
}
if ((m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1)) -
m(0, 1) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0)) +
m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0))) < -kIsZero) {
return false;
}
return true;
}
idScalar determinant(const mat33 &m) {
return m(0, 0) * m(1, 1) * m(2, 2) + m(0, 1) * m(1, 2) * m(2, 0) + m(0, 2) * m(1, 0) * m(2, 1) -
m(0, 2) * m(1, 1) * m(2, 0) - m(0, 0) * m(1, 2) * m(2, 1) - m(0, 1) * m(1, 0) * m(2, 2);
}
bool isValidInertiaMatrix(const mat33 &I, const int index, bool has_fixed_joint) {
// TODO(Thomas) do we really want this?
// in cases where the inertia tensor about the center of mass is zero,
// the determinant of the inertia tensor about the joint axis is almost
// zero and can have a very small negative value.
if (!isPositiveSemiDefiniteFuzzy(I)) {
error_message("invalid inertia matrix for body %d, not positive definite "
"(fixed joint)\n",
index);
error_message("matrix is:\n"
"[%.20e %.20e %.20e;\n"
"%.20e %.20e %.20e;\n"
"%.20e %.20e %.20e]\n",
I(0, 0), I(0, 1), I(0, 2), I(1, 0), I(1, 1), I(1, 2), I(2, 0), I(2, 1),
I(2, 2));
return false;
}
// check triangle inequality, must have I(i,i)+I(j,j)>=I(k,k)
if (!has_fixed_joint) {
if (I(0, 0) + I(1, 1) < I(2, 2)) {
error_message("invalid inertia tensor for body %d, I(0,0) + I(1,1) < I(2,2)\n", index);
error_message("matrix is:\n"
"[%.20e %.20e %.20e;\n"
"%.20e %.20e %.20e;\n"
"%.20e %.20e %.20e]\n",
I(0, 0), I(0, 1), I(0, 2), I(1, 0), I(1, 1), I(1, 2), I(2, 0), I(2, 1),
I(2, 2));
return false;
}
if (I(0, 0) + I(1, 1) < I(2, 2)) {
error_message("invalid inertia tensor for body %d, I(0,0) + I(1,1) < I(2,2)\n", index);
error_message("matrix is:\n"
"[%.20e %.20e %.20e;\n"
"%.20e %.20e %.20e;\n"
"%.20e %.20e %.20e]\n",
I(0, 0), I(0, 1), I(0, 2), I(1, 0), I(1, 1), I(1, 2), I(2, 0), I(2, 1),
I(2, 2));
return false;
}
if (I(1, 1) + I(2, 2) < I(0, 0)) {
error_message("invalid inertia tensor for body %d, I(1,1) + I(2,2) < I(0,0)\n", index);
error_message("matrix is:\n"
"[%.20e %.20e %.20e;\n"
"%.20e %.20e %.20e;\n"
"%.20e %.20e %.20e]\n",
I(0, 0), I(0, 1), I(0, 2), I(1, 0), I(1, 1), I(1, 2), I(2, 0), I(2, 1),
I(2, 2));
return false;
}
}
// check positive/zero diagonal elements
for (int i = 0; i < 3; i++) {
if (I(i, i) < 0) { // accept zero
error_message("invalid inertia tensor, I(%d,%d)= %e <0\n", i, i, I(i, i));
return false;
}
}
// check symmetry
if (std::fabs(I(1, 0) - I(0, 1)) > kIsZero) {
error_message("invalid inertia tensor for body %d I(1,0)!=I(0,1). I(1,0)-I(0,1)= "
"%e\n",
index, I(1, 0) - I(0, 1));
return false;
}
if (std::fabs(I(2, 0) - I(0, 2)) > kIsZero) {
error_message("invalid inertia tensor for body %d I(2,0)!=I(0,2). I(2,0)-I(0,2)= "
"%e\n",
index, I(2, 0) - I(0, 2));
return false;
}
if (std::fabs(I(1, 2) - I(2, 1)) > kIsZero) {
error_message("invalid inertia tensor body %d I(1,2)!=I(2,1). I(1,2)-I(2,1)= %e\n", index,
I(1, 2) - I(2, 1));
return false;
}
return true;
}
bool isValidTransformMatrix(const mat33 &m) {
#define print_mat(x) \
error_message("matrix is [%e, %e, %e; %e, %e, %e; %e, %e, %e]\n", x(0, 0), x(0, 1), x(0, 2), \
x(1, 0), x(1, 1), x(1, 2), x(2, 0), x(2, 1), x(2, 2))
// check for unit length column vectors
for (int i = 0; i < 3; i++) {
const idScalar length_minus_1 =
std::fabs(m(0, i) * m(0, i) + m(1, i) * m(1, i) + m(2, i) * m(2, i) - 1.0);
if (length_minus_1 > kAxisLengthEpsilon) {
error_message("Not a valid rotation matrix (column %d not unit length)\n"
"column = [%.18e %.18e %.18e]\n"
"length-1.0= %.18e\n",
i, m(0, i), m(1, i), m(2, i), length_minus_1);
print_mat(m);
return false;
}
}
// check for orthogonal column vectors
if (std::fabs(m(0, 0) * m(0, 1) + m(1, 0) * m(1, 1) + m(2, 0) * m(2, 1)) > kAxisLengthEpsilon) {
error_message("Not a valid rotation matrix (columns 0 and 1 not orthogonal)\n");
print_mat(m);
return false;
}
if (std::fabs(m(0, 0) * m(0, 2) + m(1, 0) * m(1, 2) + m(2, 0) * m(2, 2)) > kAxisLengthEpsilon) {
error_message("Not a valid rotation matrix (columns 0 and 2 not orthogonal)\n");
print_mat(m);
return false;
}
if (std::fabs(m(0, 1) * m(0, 2) + m(1, 1) * m(1, 2) + m(2, 1) * m(2, 2)) > kAxisLengthEpsilon) {
error_message("Not a valid rotation matrix (columns 0 and 2 not orthogonal)\n");
print_mat(m);
return false;
}
// check determinant (rotation not reflection)
if (determinant(m) <= 0) {
error_message("Not a valid rotation matrix (determinant <=0)\n");
print_mat(m);
return false;
}
return true;
}
bool isUnitVector(const vec3 &vector) {
return std::fabs(vector(0) * vector(0) + vector(1) * vector(1) + vector(2) * vector(2) - 1.0) <
kIsZero;
}
vec3 rpyFromMatrix(const mat33 &rot) {
vec3 rpy;
rpy(2) = std::atan2(-rot(1, 0), rot(0, 0));
rpy(1) = std::atan2(rot(2, 0), std::cos(rpy(2)) * rot(0, 0) - std::sin(rpy(0)) * rot(1, 0));
rpy(0) = std::atan2(-rot(2, 0), rot(2, 2));
return rpy;
}
}

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/// @file Math utility functions used in inverse dynamics library.
/// Defined here as they may not be provided by the math library.
#ifndef IDMATH_HPP_
#define IDMATH_HPP_
#include "IDConfig.hpp"
namespace btInverseDynamics {
/// set all elements to zero
void setZero(vec3& v);
/// set all elements to zero
void setZero(vecx& v);
/// set all elements to zero
void setZero(mat33& m);
/// return maximum absolute value
idScalar maxAbs(const vecx& v);
#ifndef ID_LINEAR_MATH_USE_EIGEN
/// return maximum absolute value
idScalar maxAbs(const vec3& v);
#endif //ID_LINEAR_MATH_USE_EIGEN
/// get offset vector & transform matrix from DH parameters
/// TODO: add documentation
void getVecMatFromDH(idScalar theta, idScalar d, idScalar a, idScalar alpha, vec3* r, mat33* T);
/// Check if a 3x3 matrix is positive definite
/// @param m a 3x3 matrix
/// @return true if m>0, false otherwise
bool isPositiveDefinite(const mat33& m);
/// Check if a 3x3 matrix is positive semi definite
/// @param m a 3x3 matrix
/// @return true if m>=0, false otherwise
bool isPositiveSemiDefinite(const mat33& m);
/// Check if a 3x3 matrix is positive semi definite within numeric limits
/// @param m a 3x3 matrix
/// @return true if m>=-eps, false otherwise
bool isPositiveSemiDefiniteFuzzy(const mat33& m);
/// Determinant of 3x3 matrix
/// NOTE: implemented here for portability, as determinant operation
/// will be implemented differently for various matrix/vector libraries
/// @param m a 3x3 matrix
/// @return det(m)
idScalar determinant(const mat33& m);
/// Test if a 3x3 matrix satisfies some properties of inertia matrices
/// @param I a 3x3 matrix
/// @param index body index (for error messages)
/// @param has_fixed_joint: if true, positive semi-definite matrices are accepted
/// @return true if I satisfies inertia matrix properties, false otherwise.
bool isValidInertiaMatrix(const mat33& I, int index, bool has_fixed_joint);
/// Check if a 3x3 matrix is a valid transform (rotation) matrix
/// @param m a 3x3 matrix
/// @return true if m is a rotation matrix, false otherwise
bool isValidTransformMatrix(const mat33& m);
/// Transform matrix from parent to child frame,
/// when the child frame is rotated about @param axis by @angle
/// (mathematically positive)
/// @param axis the axis of rotation
/// @param angle rotation angle
/// @param T pointer to transform matrix
void bodyTParentFromAxisAngle(const vec3& axis, const idScalar& angle, mat33* T);
/// Check if this is a unit vector
/// @param vector
/// @return true if |vector|=1 within numeric limits
bool isUnitVector(const vec3& vector);
/// @input a vector in R^3
/// @returns corresponding spin tensor
mat33 tildeOperator(const vec3& v);
/// @param alpha angle in radians
/// @returns transform matrix for ratation with @param alpha about x-axis
mat33 transformX(const idScalar& alpha);
/// @param beta angle in radians
/// @returns transform matrix for ratation with @param beta about y-axis
mat33 transformY(const idScalar& beta);
/// @param gamma angle in radians
/// @returns transform matrix for ratation with @param gamma about z-axis
mat33 transformZ(const idScalar& gamma);
///calculate rpy angles (x-y-z Euler angles) from a given rotation matrix
/// @param rot rotation matrix
/// @returns x-y-z Euler angles
vec3 rpyFromMatrix(const mat33&rot);
}
#endif // IDMATH_HPP_

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#include "MultiBodyTree.hpp"
#include <cmath>
#include <limits>
#include <vector>
#include "IDMath.hpp"
#include "details/MultiBodyTreeImpl.hpp"
#include "details/MultiBodyTreeInitCache.hpp"
namespace btInverseDynamics {
MultiBodyTree::MultiBodyTree()
: m_is_finalized(false),
m_mass_parameters_are_valid(true),
m_accept_invalid_mass_parameters(false),
m_impl(0x0),
m_init_cache(0x0) {
m_init_cache = new InitCache();
}
MultiBodyTree::~MultiBodyTree() {
delete m_impl;
delete m_init_cache;
}
void MultiBodyTree::setAcceptInvalidMassParameters(bool flag) {
m_accept_invalid_mass_parameters = flag;
}
bool MultiBodyTree::getAcceptInvalidMassProperties() const {
return m_accept_invalid_mass_parameters;
}
int MultiBodyTree::getBodyOrigin(const int body_index, vec3 *world_origin) const {
return m_impl->getBodyOrigin(body_index, world_origin);
}
int MultiBodyTree::getBodyCoM(const int body_index, vec3 *world_com) const {
return m_impl->getBodyCoM(body_index, world_com);
}
int MultiBodyTree::getBodyTransform(const int body_index, mat33 *world_T_body) const {
return m_impl->getBodyTransform(body_index, world_T_body);
}
int MultiBodyTree::getBodyAngularVelocity(const int body_index, vec3 *world_omega) const {
return m_impl->getBodyAngularVelocity(body_index, world_omega);
}
int MultiBodyTree::getBodyLinearVelocity(const int body_index, vec3 *world_velocity) const {
return m_impl->getBodyLinearVelocity(body_index, world_velocity);
}
int MultiBodyTree::getBodyLinearVelocityCoM(const int body_index, vec3 *world_velocity) const {
return m_impl->getBodyLinearVelocityCoM(body_index, world_velocity);
}
int MultiBodyTree::getBodyAngularAcceleration(const int body_index, vec3 *world_dot_omega) const {
return m_impl->getBodyAngularAcceleration(body_index, world_dot_omega);
}
int MultiBodyTree::getBodyLinearAcceleration(const int body_index, vec3 *world_acceleration) const {
return m_impl->getBodyLinearAcceleration(body_index, world_acceleration);
}
void MultiBodyTree::printTree() { m_impl->printTree(); }
void MultiBodyTree::printTreeData() { m_impl->printTreeData(); }
int MultiBodyTree::numBodies() const { return m_impl->m_num_bodies; }
int MultiBodyTree::numDoFs() const { return m_impl->m_num_dofs; }
int MultiBodyTree::calculateInverseDynamics(const vecx &q, const vecx &u, const vecx &dot_u,
vecx *joint_forces) {
if (false == m_is_finalized) {
error_message("system has not been initialized\n");
return -1;
}
if (-1 == m_impl->calculateInverseDynamics(q, u, dot_u, joint_forces)) {
error_message("error in inverse dynamics calculation\n");
return -1;
}
return 0;
}
int MultiBodyTree::calculateMassMatrix(const vecx &q, const bool update_kinematics,
const bool initialize_matrix,
const bool set_lower_triangular_matrix, matxx *mass_matrix) {
if (false == m_is_finalized) {
error_message("system has not been initialized\n");
return -1;
}
if (-1 ==
m_impl->calculateMassMatrix(q, update_kinematics, initialize_matrix,
set_lower_triangular_matrix, mass_matrix)) {
error_message("error in mass matrix calculation\n");
return -1;
}
return 0;
}
int MultiBodyTree::calculateMassMatrix(const vecx &q, matxx *mass_matrix) {
return calculateMassMatrix(q, true, true, true, mass_matrix);
}
int MultiBodyTree::addBody(int body_index, int parent_index, JointType joint_type,
const vec3 &parent_r_parent_body_ref, const mat33 &body_T_parent_ref,
const vec3 &body_axis_of_motion_, idScalar mass,
const vec3 &body_r_body_com, const mat33 &body_I_body,
const int user_int, void *user_ptr) {
if (body_index < 0) {
error_message("body index must be positive (got %d)\n", body_index);
return -1;
}
vec3 body_axis_of_motion(body_axis_of_motion_);
switch (joint_type) {
case REVOLUTE:
case PRISMATIC:
// check if axis is unit vector
if (!isUnitVector(body_axis_of_motion)) {
warning_message(
"axis of motion not a unit axis ([%f %f %f]), will use normalized vector\n",
body_axis_of_motion(0), body_axis_of_motion(1), body_axis_of_motion(2));
idScalar length = std::sqrt(std::pow(body_axis_of_motion(0), 2) +
std::pow(body_axis_of_motion(1), 2) +
std::pow(body_axis_of_motion(2), 2));
if (length < std::sqrt(std::numeric_limits<idScalar>::min())) {
error_message("axis of motion vector too short (%e)\n", length);
return -1;
}
body_axis_of_motion = (1.0 / length) * body_axis_of_motion;
}
break;
case FIXED:
break;
case FLOATING:
break;
default:
error_message("unknown joint type %d\n", joint_type);
return -1;
}
// sanity check for mass properties. Zero mass is OK.
if (mass < 0) {
m_mass_parameters_are_valid = false;
error_message("Body %d has invalid mass %e\n", body_index, mass);
if (!m_accept_invalid_mass_parameters) {
return -1;
}
}
if (!isValidInertiaMatrix(body_I_body, body_index, FIXED == joint_type)) {
m_mass_parameters_are_valid = false;
// error message printed in function call
if (!m_accept_invalid_mass_parameters) {
return -1;
}
}
if (!isValidTransformMatrix(body_T_parent_ref)) {
return -1;
}
return m_init_cache->addBody(body_index, parent_index, joint_type, parent_r_parent_body_ref,
body_T_parent_ref, body_axis_of_motion, mass, body_r_body_com,
body_I_body, user_int, user_ptr);
}
int MultiBodyTree::getParentIndex(const int body_index, int *parent_index) const {
return m_impl->getParentIndex(body_index, parent_index);
}
int MultiBodyTree::getUserInt(const int body_index, int *user_int) const {
return m_impl->getUserInt(body_index, user_int);
}
int MultiBodyTree::getUserPtr(const int body_index, void **user_ptr) const {
return m_impl->getUserPtr(body_index, user_ptr);
}
int MultiBodyTree::setUserInt(const int body_index, const int user_int) {
return m_impl->setUserInt(body_index, user_int);
}
int MultiBodyTree::setUserPtr(const int body_index, void *const user_ptr) {
return m_impl->setUserPtr(body_index, user_ptr);
}
int MultiBodyTree::finalize() {
const int &num_bodies = m_init_cache->numBodies();
const int &num_dofs = m_init_cache->numDoFs();
// 1 allocate internal MultiBody structure
m_impl = new MultiBodyImpl(num_bodies, num_dofs);
// 2 build new index set assuring index(parent) < index(child)
if (-1 == m_init_cache->buildIndexSets()) {
return -1;
}
m_init_cache->getParentIndexArray(&m_impl->m_parent_index);
// 3 setup internal kinematic and dynamic data
for (int index = 0; index < num_bodies; index++) {
InertiaData inertia;
JointData joint;
if (-1 == m_init_cache->getInertiaData(index, &inertia)) {
return -1;
}
if (-1 == m_init_cache->getJointData(index, &joint)) {
return -1;
}
RigidBody &rigid_body = m_impl->m_body_list[index];
rigid_body.m_mass = inertia.m_mass;
rigid_body.m_body_mass_com = inertia.m_mass * inertia.m_body_pos_body_com;
rigid_body.m_body_I_body = inertia.m_body_I_body;
rigid_body.m_joint_type = joint.m_type;
rigid_body.m_parent_pos_parent_body_ref = joint.m_parent_pos_parent_child_ref;
rigid_body.m_body_T_parent_ref = joint.m_child_T_parent_ref;
rigid_body.m_parent_pos_parent_body_ref = joint.m_parent_pos_parent_child_ref;
rigid_body.m_joint_type = joint.m_type;
// Set joint Jacobians. Note that the dimension is always 3x1 here to avoid variable sized
// matrices.
switch (rigid_body.m_joint_type) {
case REVOLUTE:
rigid_body.m_Jac_JR(0) = joint.m_child_axis_of_motion(0);
rigid_body.m_Jac_JR(1) = joint.m_child_axis_of_motion(1);
rigid_body.m_Jac_JR(2) = joint.m_child_axis_of_motion(2);
rigid_body.m_Jac_JT(0) = 0.0;
rigid_body.m_Jac_JT(1) = 0.0;
rigid_body.m_Jac_JT(2) = 0.0;
break;
case PRISMATIC:
rigid_body.m_Jac_JR(0) = 0.0;
rigid_body.m_Jac_JR(1) = 0.0;
rigid_body.m_Jac_JR(2) = 0.0;
rigid_body.m_Jac_JT(0) = joint.m_child_axis_of_motion(0);
rigid_body.m_Jac_JT(1) = joint.m_child_axis_of_motion(1);
rigid_body.m_Jac_JT(2) = joint.m_child_axis_of_motion(2);
break;
case FIXED:
// NOTE/TODO: dimension really should be zero ..
rigid_body.m_Jac_JR(0) = 0.0;
rigid_body.m_Jac_JR(1) = 0.0;
rigid_body.m_Jac_JR(2) = 0.0;
rigid_body.m_Jac_JT(0) = 0.0;
rigid_body.m_Jac_JT(1) = 0.0;
rigid_body.m_Jac_JT(2) = 0.0;
break;
case FLOATING:
// NOTE/TODO: this is not really correct.
// the Jacobians should be 3x3 matrices here !
rigid_body.m_Jac_JR(0) = 0.0;
rigid_body.m_Jac_JR(1) = 0.0;
rigid_body.m_Jac_JR(2) = 0.0;
rigid_body.m_Jac_JT(0) = 0.0;
rigid_body.m_Jac_JT(1) = 0.0;
rigid_body.m_Jac_JT(2) = 0.0;
break;
default:
error_message("unsupported joint type %d\n", rigid_body.m_joint_type);
return -1;
}
}
// 4 assign degree of freedom indices & build per-joint-type index arrays
if (-1 == m_impl->generateIndexSets()) {
error_message("generating index sets\n");
return -1;
}
// 5 do some pre-computations ..
m_impl->calculateStaticData();
// 6. make sure all user forces are set to zero, as this might not happen
// in the vector ctors.
m_impl->clearAllUserForcesAndMoments();
m_is_finalized = true;
return 0;
}
int MultiBodyTree::setGravityInWorldFrame(const vec3 &gravity) {
return m_impl->setGravityInWorldFrame(gravity);
}
int MultiBodyTree::getJointType(const int body_index, JointType *joint_type) const {
return m_impl->getJointType(body_index, joint_type);
}
int MultiBodyTree::getJointTypeStr(const int body_index, const char **joint_type) const {
return m_impl->getJointTypeStr(body_index, joint_type);
}
int MultiBodyTree::getDoFOffset(const int body_index, int *q_offset) const {
return m_impl->getDoFOffset(body_index, q_offset);
}
int MultiBodyTree::setBodyMass(const int body_index, idScalar mass) {
return m_impl->setBodyMass(body_index, mass);
}
int MultiBodyTree::setBodyFirstMassMoment(const int body_index, vec3 first_mass_moment) {
return m_impl->setBodyFirstMassMoment(body_index, first_mass_moment);
}
int MultiBodyTree::setBodySecondMassMoment(const int body_index, mat33 second_mass_moment) {
return m_impl->setBodySecondMassMoment(body_index, second_mass_moment);
}
int MultiBodyTree::getBodyMass(const int body_index, idScalar *mass) const {
return m_impl->getBodyMass(body_index, mass);
}
int MultiBodyTree::getBodyFirstMassMoment(const int body_index, vec3 *first_mass_moment) const {
return m_impl->getBodyFirstMassMoment(body_index, first_mass_moment);
}
int MultiBodyTree::getBodySecondMassMoment(const int body_index, mat33 *second_mass_moment) const {
return m_impl->getBodySecondMassMoment(body_index, second_mass_moment);
}
void MultiBodyTree::clearAllUserForcesAndMoments() { m_impl->clearAllUserForcesAndMoments(); }
int MultiBodyTree::addUserForce(const int body_index, const vec3 &body_force) {
return m_impl->addUserForce(body_index, body_force);
}
int MultiBodyTree::addUserMoment(const int body_index, const vec3 &body_moment) {
return m_impl->addUserMoment(body_index, body_moment);
}
}

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#ifndef MULTIBODYTREE_HPP_
#define MULTIBODYTREE_HPP_
#include "IDMath.hpp"
namespace btInverseDynamics {
/// Enumeration of supported joint types
enum JointType {
/// no degree of freedom, moves with parent
FIXED = 0,
/// one rotational degree of freedom relative to parent
REVOLUTE,
/// one translational degree of freedom relative to parent
PRISMATIC,
/// six degrees of freedom relative to parent
FLOATING
};
/// Interface class for calculating inverse dynamics for tree structured
/// multibody systems
///
/// Note on degrees of freedom
/// The q vector contains the generalized coordinate set defining the tree's configuration.
/// Every joint adds elements that define the corresponding link's frame pose relative to
/// its parent. For the joint types that is:
/// - FIXED: none
/// - REVOLUTE: angle of rotation [rad]
/// - PRISMATIC: displacement [m]
/// - FLOATING: Euler x-y-z angles [rad] and displacement in body-fixed frame of parent [m]
/// (in that order)
/// The u vector contains the generalized speeds, which are
/// - FIXED: none
/// - REVOLUTE: time derivative of angle of rotation [rad/s]
/// - PRISMATIC: time derivative of displacement [m/s]
/// - FLOATING: angular velocity [rad/s] (*not* time derivative of rpy angles)
/// and time derivative of displacement in parent frame [m/s]
///
/// The q and u vectors are obtained by stacking contributions of all bodies in one
/// vector in the order of body indices.
///
/// Note on generalized forces: analogous to u, i.e.,
/// - FIXED: none
/// - REVOLUTE: moment [Nm], about joint axis
/// - PRISMATIC: force [N], along joint axis
/// - FLOATING: moment vector [Nm] and force vector [N], both in body-fixed frame
/// (in that order)
///
/// TODO - force element interface (friction, springs, dampers, etc)
/// - gears and motor inertia
class MultiBodyTree {
public:
/// The contructor.
/// Initialization & allocation is via addBody and buildSystem calls.
MultiBodyTree();
/// the destructor. This also deallocates all memory
~MultiBodyTree();
/// Add body to the system. this allocates memory and not real-time safe.
/// This only adds the data to an initial cache. After all bodies have been
/// added,
/// the system is setup using the buildSystem call
/// @param body_index index of the body to be added. Must >=0, <number of bodies,
/// and index of parent must be < index of body
/// @param parent_index index of the parent body
/// The root of the tree has index 0 and its parent (the world frame)
/// is assigned index -1
/// the rotation and translation relative to the parent are taken as
/// pose of the root body relative to the world frame. Other parameters
/// are ignored
/// @param JointType type of joint connecting the body to the parent
/// @param mass the mass of the body
/// @param body_r_body_com the center of mass of the body relative to and
/// described in
/// the body fixed frame, which is located in the joint axis connecting
/// the body to its parent
/// @param body_I_body the moment of inertia of the body w.r.t the body-fixed
/// frame
/// (ie, the reference point is the origin of the body-fixed frame and
/// the matrix is written
/// w.r.t. those unit vectors)
/// @param parent_r_parent_body_ref position of joint relative to the parent
/// body's reference frame
/// for q=0, written in the parent bodies reference frame
/// @param body_axis_of_motion translation/rotation axis in body-fixed frame.
/// Ignored for joints that are not revolute or prismatic.
/// must be a unit vector.
/// @param body_T_parent_ref transform matrix from parent to body reference
/// frame for q=0.
/// This is the matrix transforming a vector represented in the
/// parent's reference frame into one represented
/// in this body's reference frame.
/// ie, if parent_vec is a vector in R^3 whose components are w.r.t to
/// the parent's reference frame,
/// then the same vector written w.r.t. this body's frame (for q=0) is
/// given by
/// body_vec = parent_R_body_ref * parent_vec
/// @param user_ptr pointer to user data
/// @param user_int pointer to user integer
/// @return 0 on success, -1 on error
int addBody(int body_index, int parent_index, JointType joint_type,
const vec3& parent_r_parent_body_ref, const mat33& body_T_parent_ref,
const vec3& body_axis_of_motion, idScalar mass, const vec3& body_r_body_com,
const mat33& body_I_body, const int user_int, void* user_ptr);
/// set policy for invalid mass properties
/// @param flag if true, invalid mass properties are accepted,
/// the default is false
void setAcceptInvalidMassParameters(bool flag);
/// @return the mass properties policy flag
bool getAcceptInvalidMassProperties() const;
/// build internal data structures
/// call this after all bodies have been added via addBody
/// @return 0 on success, -1 on error
int finalize();
/// pretty print ascii description of tree to stdout
void printTree();
/// print tree data to stdout
void printTreeData();
/// calculate joint forces for given generalized state & derivatives
/// @param q generalized coordinates
/// @param u generalized velocities. In the general case, u=T(q)*dot(q) and dim(q)>=dim(u)
/// @param dot_u time derivative of u
/// @param joint_forces this is where the resulting joint forces will be
/// stored. dim(joint_forces) = dim(u)
/// @return 0 on success, -1 on error
int calculateInverseDynamics(const vecx& q, const vecx& u, const vecx& dot_u,
vecx* joint_forces);
/// Calculate joint space mass matrix
/// @param q generalized coordinates
/// @param initialize_matrix if true, initialize mass matrix with zero.
/// If mass_matrix is initialized to zero externally and only used
/// for mass matrix computations for the same system, it is safe to
/// set this to false.
/// @param set_lower_triangular_matrix if true, the lower triangular section of mass_matrix
/// is also populated, otherwise not.
/// @param mass_matrix matrix for storing the output (should be dim(q)xdim(q))
/// @return -1 on error, 0 on success
int calculateMassMatrix(const vecx& q, const bool update_kinematics,
const bool initialize_matrix, const bool set_lower_triangular_matrix,
matxx* mass_matrix);
/// Calculate joint space mass matrix.
/// This version will update kinematics, initialize all mass_matrix elements to zero and
/// populate all mass matrix entries.
/// @param q generalized coordinates
/// @param mass_matrix matrix for storing the output (should be dim(q)xdim(q))
/// @return -1 on error, 0 on success
int calculateMassMatrix(const vecx& q, matxx* mass_matrix);
/// set gravitational acceleration
/// the default is [0;0;-9.8] in the world frame
/// @param gravity the gravitational acceleration in world frame
/// @return 0 on success, -1 on error
int setGravityInWorldFrame(const vec3& gravity);
/// returns number of bodies in tree
int numBodies() const;
/// returns number of mechanical degrees of freedom (dimension of q-vector)
int numDoFs() const;
/// get origin of a body-fixed frame, represented in world frame
/// @param body_index index for frame/body
/// @param world_origin pointer for return data
/// @return 0 on success, -1 on error
int getBodyOrigin(const int body_index, vec3* world_origin) const;
/// get center of mass of a body, represented in world frame
/// @param body_index index for frame/body
/// @param world_com pointer for return data
/// @return 0 on success, -1 on error
int getBodyCoM(const int body_index, vec3* world_com) const;
/// get transform from of a body-fixed frame to the world frame
/// @param body_index index for frame/body
/// @param world_T_body pointer for return data
/// @return 0 on success, -1 on error
int getBodyTransform(const int body_index, mat33* world_T_body) const;
/// get absolute angular velocity for a body, represented in the world frame
/// @param body_index index for frame/body
/// @param world_omega pointer for return data
/// @return 0 on success, -1 on error
int getBodyAngularVelocity(const int body_index, vec3* world_omega) const;
/// get linear velocity of a body, represented in world frame
/// @param body_index index for frame/body
/// @param world_velocity pointer for return data
/// @return 0 on success, -1 on error
int getBodyLinearVelocity(const int body_index, vec3* world_velocity) const;
/// get linear velocity of a body's CoM, represented in world frame
/// (not required for inverse dynamics, provided for convenience)
/// @param body_index index for frame/body
/// @param world_vel_com pointer for return data
/// @return 0 on success, -1 on error
int getBodyLinearVelocityCoM(const int body_index, vec3* world_velocity) const;
/// get origin of a body-fixed frame, represented in world frame
/// @param body_index index for frame/body
/// @param world_origin pointer for return data
/// @return 0 on success, -1 on error
int getBodyAngularAcceleration(const int body_index, vec3* world_dot_omega) const;
/// get origin of a body-fixed frame, represented in world frame
/// NOTE: this will include the gravitational acceleration, so the actual acceleration is
/// obtainened by setting gravitational acceleration to zero, or subtracting it.
/// @param body_index index for frame/body
/// @param world_origin pointer for return data
/// @return 0 on success, -1 on error
int getBodyLinearAcceleration(const int body_index, vec3* world_acceleration) const;
/// returns the (internal) index of body
/// @param body_index is the index of a body (internal: TODO: fix/clarify
/// indexing!)
/// @param parent_index pointer to where parent index will be stored
/// @return 0 on success, -1 on error
int getParentIndex(const int body_index, int* parent_index) const;
/// get joint type
/// @param body_index index of the body
/// @param joint_type the corresponding joint type
/// @return 0 on success, -1 on failure
int getJointType(const int body_index, JointType* joint_type) const;
/// get joint type as string
/// @param body_index index of the body
/// @param joint_type string naming the corresponding joint type
/// @return 0 on success, -1 on failure
int getJointTypeStr(const int body_index, const char** joint_type) const;
/// get offset for degrees of freedom of this body into the q-vector
/// @param body_index index of the body
/// @param q_offset offset the q vector
/// @return -1 on error, 0 on success
int getDoFOffset(const int body_index, int* q_offset) const;
/// get user integer. not used by the library.
/// @param body_index index of the body
/// @param user_int the user integer
/// @return 0 on success, -1 on error
int getUserInt(const int body_index, int* user_int) const;
/// get user pointer. not used by the library.
/// @param body_index index of the body
/// @param user_ptr the user pointer
/// @return 0 on success, -1 on error
int getUserPtr(const int body_index, void** user_ptr) const;
/// set user integer. not used by the library.
/// @param body_index index of the body
/// @param user_int the user integer
/// @return 0 on success, -1 on error
int setUserInt(const int body_index, const int user_int);
/// set user pointer. not used by the library.
/// @param body_index index of the body
/// @param user_ptr the user pointer
/// @return 0 on success, -1 on error
int setUserPtr(const int body_index, void* const user_ptr);
/// set mass for a body
/// @param body_index index of the body
/// @param mass the mass to set
/// @return 0 on success, -1 on failure
int setBodyMass(const int body_index, const idScalar mass);
/// set first moment of mass for a body
/// (mass * center of mass, in body fixed frame, relative to joint)
/// @param body_index index of the body
/// @param first_mass_moment the vector to set
/// @return 0 on success, -1 on failure
int setBodyFirstMassMoment(const int body_index, const vec3 first_mass_moment);
/// set second moment of mass for a body
/// (moment of inertia, in body fixed frame, relative to joint)
/// @param body_index index of the body
/// @param second_mass_moment the inertia matrix
/// @return 0 on success, -1 on failure
int setBodySecondMassMoment(const int body_index, const mat33 second_mass_moment);
/// get mass for a body
/// @param body_index index of the body
/// @param mass the mass
/// @return 0 on success, -1 on failure
int getBodyMass(const int body_index, idScalar* mass) const;
/// get first moment of mass for a body
/// (mass * center of mass, in body fixed frame, relative to joint)
/// @param body_index index of the body
/// @param first_moment the vector
/// @return 0 on success, -1 on failure
int getBodyFirstMassMoment(const int body_index, vec3* first_mass_moment) const;
/// get second moment of mass for a body
/// (moment of inertia, in body fixed frame, relative to joint)
/// @param body_index index of the body
/// @param second_mass_moment the inertia matrix
/// @return 0 on success, -1 on failure
int getBodySecondMassMoment(const int body_index, mat33* second_mass_moment) const;
/// set all user forces and moments to zero
void clearAllUserForcesAndMoments();
/// Add an external force to a body, acting at the origin of the body-fixed frame.
/// Calls to addUserForce are cumulative. Set the user force and moment to zero
/// via clearAllUserForcesAndMoments()
/// @param body_force the force represented in the body-fixed frame of reference
/// @return 0 on success, -1 on error
int addUserForce(const int body_index, const vec3& body_force);
/// Add an external moment to a body.
/// Calls to addUserMoment are cumulative. Set the user force and moment to zero
/// via clearAllUserForcesAndMoments()
/// @param body_moment the moment represented in the body-fixed frame of reference
/// @return 0 on success, -1 on error
int addUserMoment(const int body_index, const vec3& body_moment);
private:
// flag indicating if system has been initialized
bool m_is_finalized;
// flag indicating if mass properties are physically valid
bool m_mass_parameters_are_valid;
// flag defining if unphysical mass parameters are accepted
bool m_accept_invalid_mass_parameters;
// This struct implements the inverse dynamics calculations
class MultiBodyImpl;
MultiBodyImpl* m_impl;
// cache data structure for initialization
class InitCache;
InitCache* m_init_cache;
};
} // namespace btInverseDynamics
#endif // MULTIBODYTREE_HPP_

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#ifndef INVDYNEIGENINTERFACE_HPP_
#define INVDYNEIGENINTERFACE_HPP_
#include "../IDConfig.hpp"
namespace btInverseDynamics {
#ifdef BT_USE_DOUBLE_PRECISION
typedef Eigen::VectorXd vecx;
typedef Eigen::Vector3d vec3;
typedef Eigen::Matrix3d mat33;
typedef Eigen::MatrixXd matxx;
#else
typedef Eigen::VectorXf vecx;
typedef Eigen::Vector3f vec3;
typedef Eigen::Matrix3f mat33;
typedef Eigen::MatrixXf matxx;
#endif //
}
#endif // INVDYNEIGENINTERFACE_HPP_

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#ifndef IDLINEARMATHINTERFACE_HPP_
#define IDLINEARMATHINTERFACE_HPP_
#include <cstdlib>
#include "../IDConfig.hpp"
#include "../../LinearMath/btMatrix3x3.h"
#include "../../LinearMath/btVector3.h"
#include "../../LinearMath/btMatrixX.h"
namespace btInverseDynamics {
class vec3;
class vecx;
class mat33;
typedef btMatrixX<idScalar> matxx;
class vec3 : public btVector3 {
public:
vec3() : btVector3() {}
vec3(const btVector3& btv) { *this = btv; }
idScalar& operator()(int i) { return (*this)[i]; }
const idScalar& operator()(int i) const { return (*this)[i]; }
const int size() const { return 3; }
const vec3& operator=(const btVector3& rhs) {
*static_cast<btVector3*>(this) = rhs;
return *this;
}
};
class mat33 : public btMatrix3x3 {
public:
mat33() : btMatrix3x3() {}
mat33(const btMatrix3x3& btm) { *this = btm; }
idScalar& operator()(int i, int j) { return (*this)[i][j]; }
const idScalar& operator()(int i, int j) const { return (*this)[i][j]; }
const mat33& operator=(const btMatrix3x3& rhs) {
*static_cast<btMatrix3x3*>(this) = rhs;
return *this;
}
friend mat33 operator*(const idScalar& s, const mat33& a);
friend mat33 operator/(const mat33& a, const idScalar& s);
};
inline mat33 operator/(const mat33& a, const idScalar& s) { return a * (1.0 / s); }
inline mat33 operator*(const idScalar& s, const mat33& a) { return a * s; }
class vecx : public btVectorX<idScalar> {
public:
vecx(int size) : btVectorX(size) {}
const vecx& operator=(const btVectorX<idScalar>& rhs) {
*static_cast<btVectorX*>(this) = rhs;
return *this;
}
idScalar& operator()(int i) { return (*this)[i]; }
const idScalar& operator()(int i) const { return (*this)[i]; }
friend vecx operator*(const vecx& a, const idScalar& s);
friend vecx operator*(const idScalar& s, const vecx& a);
friend vecx operator+(const vecx& a, const vecx& b);
friend vecx operator-(const vecx& a, const vecx& b);
friend vecx operator/(const vecx& a, const idScalar& s);
};
inline vecx operator*(const vecx& a, const idScalar& s) {
vecx result(a.size());
for (int i = 0; i < result.size(); i++) {
result(i) = a(i) * s;
}
return result;
}
inline vecx operator*(const idScalar& s, const vecx& a) { return a * s; }
inline vecx operator+(const vecx& a, const vecx& b) {
vecx result(a.size());
// TODO: error handling for a.size() != b.size()??
if (a.size() != b.size()) {
error_message("size missmatch. a.size()= %d, b.size()= %d\n", a.size(), b.size());
abort();
}
for (int i = 0; i < a.size(); i++) {
result(i) = a(i) + b(i);
}
return result;
}
inline vecx operator-(const vecx& a, const vecx& b) {
vecx result(a.size());
// TODO: error handling for a.size() != b.size()??
if (a.size() != b.size()) {
error_message("size missmatch. a.size()= %d, b.size()= %d\n", a.size(), b.size());
abort();
}
for (int i = 0; i < a.size(); i++) {
result(i) = a(i) - b(i);
}
return result;
}
inline vecx operator/(const vecx& a, const idScalar& s) {
vecx result(a.size());
for (int i = 0; i < result.size(); i++) {
result(i) = a(i) / s;
}
return result;
}
}
#endif // IDLINEARMATHINTERFACE_HPP_

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/// @file Built-In Matrix-Vector functions
#ifndef IDMATVEC_HPP_
#define IDMATVEC_HPP_
#include <cstdlib>
namespace btInverseDynamics {
class vec3;
class vecx;
class mat33;
class matxx;
/// This is a very basic implementation to enable stand-alone use of the library.
/// The implementation is not really optimized and misses many features that you would
/// want from a "fully featured" linear math library.
class vec3 {
public:
idScalar& operator()(int i) { return m_data[i]; }
const idScalar& operator()(int i) const { return m_data[i]; }
const int size() const { return 3; }
const vec3& operator=(const vec3& rhs);
const vec3& operator+=(const vec3& b);
const vec3& operator-=(const vec3& b);
vec3 cross(const vec3& b) const;
idScalar dot(const vec3& b) const;
friend vec3 operator*(const mat33& a, const vec3& b);
friend vec3 operator*(const vec3& a, const idScalar& s);
friend vec3 operator*(const idScalar& s, const vec3& a);
friend vec3 operator+(const vec3& a, const vec3& b);
friend vec3 operator-(const vec3& a, const vec3& b);
friend vec3 operator/(const vec3& a, const idScalar& s);
private:
idScalar m_data[3];
};
class mat33 {
public:
idScalar& operator()(int i, int j) { return m_data[3 * i + j]; }
const idScalar& operator()(int i, int j) const { return m_data[3 * i + j]; }
const mat33& operator=(const mat33& rhs);
mat33 transpose() const;
const mat33& operator+=(const mat33& b);
const mat33& operator-=(const mat33& b);
friend mat33 operator*(const mat33& a, const mat33& b);
friend vec3 operator*(const mat33& a, const vec3& b);
friend mat33 operator*(const mat33& a, const idScalar& s);
friend mat33 operator*(const idScalar& s, const mat33& a);
friend mat33 operator+(const mat33& a, const mat33& b);
friend mat33 operator-(const mat33& a, const mat33& b);
friend mat33 operator/(const mat33& a, const idScalar& s);
private:
// layout is [0,1,2;3,4,5;6,7,8]
idScalar m_data[9];
};
class vecx {
public:
vecx(int size) : m_size(size) {
m_data = static_cast<idScalar*>(idMalloc(sizeof(idScalar) * size));
}
~vecx() { idFree(m_data); }
const vecx& operator=(const vecx& rhs);
idScalar& operator()(int i) { return m_data[i]; }
const idScalar& operator()(int i) const { return m_data[i]; }
const int& size() const { return m_size; }
friend vecx operator*(const vecx& a, const idScalar& s);
friend vecx operator*(const idScalar& s, const vecx& a);
friend vecx operator+(const vecx& a, const vecx& b);
friend vecx operator-(const vecx& a, const vecx& b);
friend vecx operator/(const vecx& a, const idScalar& s);
private:
int m_size;
idScalar* m_data;
};
class matxx {
public:
matxx(int rows, int cols) : m_rows(rows), m_cols(cols) {
m_data = static_cast<idScalar*>(idMalloc(sizeof(idScalar) * rows * cols));
}
~matxx() { idFree(m_data); }
const matxx& operator=(const matxx& rhs);
idScalar& operator()(int row, int col) { return m_data[row * m_rows + col]; }
const idScalar& operator()(int row, int col) const { return m_data[row * m_rows + col]; }
const int& rows() const { return m_rows; }
const int& cols() const { return m_cols; }
private:
int m_rows;
int m_cols;
idScalar* m_data;
};
inline const vec3& vec3::operator=(const vec3& rhs) {
if (&rhs != this) {
memcpy(m_data, rhs.m_data, 3 * sizeof(idScalar));
}
return *this;
}
inline vec3 vec3::cross(const vec3& b) const {
vec3 result;
result.m_data[0] = m_data[1] * b.m_data[2] - m_data[2] * b.m_data[1];
result.m_data[1] = m_data[2] * b.m_data[0] - m_data[0] * b.m_data[2];
result.m_data[2] = m_data[0] * b.m_data[1] - m_data[1] * b.m_data[0];
return result;
}
inline idScalar vec3::dot(const vec3& b) const {
return m_data[0] * b.m_data[0] + m_data[1] * b.m_data[1] + m_data[2] * b.m_data[2];
}
inline const mat33& mat33::operator=(const mat33& rhs) {
if (&rhs != this) {
memcpy(m_data, rhs.m_data, 9 * sizeof(idScalar));
}
return *this;
}
inline mat33 mat33::transpose() const {
mat33 result;
result.m_data[0] = m_data[0];
result.m_data[1] = m_data[3];
result.m_data[2] = m_data[6];
result.m_data[3] = m_data[1];
result.m_data[4] = m_data[4];
result.m_data[5] = m_data[7];
result.m_data[6] = m_data[2];
result.m_data[7] = m_data[5];
result.m_data[8] = m_data[8];
return result;
}
inline mat33 operator*(const mat33& a, const mat33& b) {
mat33 result;
result.m_data[0] =
a.m_data[0] * b.m_data[0] + a.m_data[1] * b.m_data[3] + a.m_data[2] * b.m_data[6];
result.m_data[1] =
a.m_data[0] * b.m_data[1] + a.m_data[1] * b.m_data[4] + a.m_data[2] * b.m_data[7];
result.m_data[2] =
a.m_data[0] * b.m_data[2] + a.m_data[1] * b.m_data[5] + a.m_data[2] * b.m_data[8];
result.m_data[3] =
a.m_data[3] * b.m_data[0] + a.m_data[4] * b.m_data[3] + a.m_data[5] * b.m_data[6];
result.m_data[4] =
a.m_data[3] * b.m_data[1] + a.m_data[4] * b.m_data[4] + a.m_data[5] * b.m_data[7];
result.m_data[5] =
a.m_data[3] * b.m_data[2] + a.m_data[4] * b.m_data[5] + a.m_data[5] * b.m_data[8];
result.m_data[6] =
a.m_data[6] * b.m_data[0] + a.m_data[7] * b.m_data[3] + a.m_data[8] * b.m_data[6];
result.m_data[7] =
a.m_data[6] * b.m_data[1] + a.m_data[7] * b.m_data[4] + a.m_data[8] * b.m_data[7];
result.m_data[8] =
a.m_data[6] * b.m_data[2] + a.m_data[7] * b.m_data[5] + a.m_data[8] * b.m_data[8];
return result;
}
inline const mat33& mat33::operator+=(const mat33& b) {
for (int i = 0; i < 9; i++) {
m_data[i] += b.m_data[i];
}
return *this;
}
inline const mat33& mat33::operator-=(const mat33& b) {
for (int i = 0; i < 9; i++) {
m_data[i] -= b.m_data[i];
}
return *this;
}
inline vec3 operator*(const mat33& a, const vec3& b) {
vec3 result;
result.m_data[0] =
a.m_data[0] * b.m_data[0] + a.m_data[1] * b.m_data[1] + a.m_data[2] * b.m_data[2];
result.m_data[1] =
a.m_data[3] * b.m_data[0] + a.m_data[4] * b.m_data[1] + a.m_data[5] * b.m_data[2];
result.m_data[2] =
a.m_data[6] * b.m_data[0] + a.m_data[7] * b.m_data[1] + a.m_data[8] * b.m_data[2];
return result;
}
inline const vec3& vec3::operator+=(const vec3& b) {
for (int i = 0; i < 3; i++) {
m_data[i] += b.m_data[i];
}
return *this;
}
inline const vec3& vec3::operator-=(const vec3& b) {
for (int i = 0; i < 3; i++) {
m_data[i] -= b.m_data[i];
}
return *this;
}
inline mat33 operator*(const mat33& a, const idScalar& s) {
mat33 result;
for (int i = 0; i < 9; i++) {
result.m_data[i] = a.m_data[i] * s;
}
return result;
}
inline mat33 operator*(const idScalar& s, const mat33& a) { return a * s; }
inline vec3 operator*(const vec3& a, const idScalar& s) {
vec3 result;
for (int i = 0; i < 3; i++) {
result.m_data[i] = a.m_data[i] * s;
}
return result;
}
inline vec3 operator*(const idScalar& s, const vec3& a) { return a * s; }
inline mat33 operator+(const mat33& a, const mat33& b) {
mat33 result;
for (int i = 0; i < 9; i++) {
result.m_data[i] = a.m_data[i] + b.m_data[i];
}
return result;
}
inline vec3 operator+(const vec3& a, const vec3& b) {
vec3 result;
for (int i = 0; i < 3; i++) {
result.m_data[i] = a.m_data[i] + b.m_data[i];
}
return result;
}
inline mat33 operator-(const mat33& a, const mat33& b) {
mat33 result;
for (int i = 0; i < 9; i++) {
result.m_data[i] = a.m_data[i] - b.m_data[i];
}
return result;
}
inline vec3 operator-(const vec3& a, const vec3& b) {
vec3 result;
for (int i = 0; i < 3; i++) {
result.m_data[i] = a.m_data[i] - b.m_data[i];
}
return result;
}
inline mat33 operator/(const mat33& a, const idScalar& s) {
mat33 result;
for (int i = 0; i < 9; i++) {
result.m_data[i] = a.m_data[i] / s;
}
return result;
}
inline vec3 operator/(const vec3& a, const idScalar& s) {
vec3 result;
for (int i = 0; i < 3; i++) {
result.m_data[i] = a.m_data[i] / s;
}
return result;
}
inline const vecx& vecx::operator=(const vecx& rhs) {
if (size() != rhs.size()) {
error_message("size missmatch, size()= %d but rhs.size()= %d\n", size(), rhs.size());
abort();
}
if (&rhs != this) {
memcpy(m_data, rhs.m_data, rhs.size() * sizeof(idScalar));
}
return *this;
}
inline vecx operator*(const vecx& a, const idScalar& s) {
vecx result(a.size());
for (int i = 0; i < result.size(); i++) {
result.m_data[i] = a.m_data[i] * s;
}
return result;
}
inline vecx operator*(const idScalar& s, const vecx& a) { return a * s; }
inline vecx operator+(const vecx& a, const vecx& b) {
vecx result(a.size());
// TODO: error handling for a.size() != b.size()??
if (a.size() != b.size()) {
error_message("size missmatch. a.size()= %d, b.size()= %d\n", a.size(), b.size());
abort();
}
for (int i = 0; i < a.size(); i++) {
result.m_data[i] = a.m_data[i] + b.m_data[i];
}
return result;
}
inline vecx operator-(const vecx& a, const vecx& b) {
vecx result(a.size());
// TODO: error handling for a.size() != b.size()??
if (a.size() != b.size()) {
error_message("size missmatch. a.size()= %d, b.size()= %d\n", a.size(), b.size());
abort();
}
for (int i = 0; i < a.size(); i++) {
result.m_data[i] = a.m_data[i] - b.m_data[i];
}
return result;
}
inline vecx operator/(const vecx& a, const idScalar& s) {
vecx result(a.size());
for (int i = 0; i < result.size(); i++) {
result.m_data[i] = a.m_data[i] / s;
}
return result;
}
}
#endif

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src/BulletInverseDynamics/details/MultiBodyTreeImpl.cpp Normal file
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@@ -0,0 +1,844 @@
#include "MultiBodyTreeImpl.hpp"
namespace btInverseDynamics {
MultiBodyTree::MultiBodyImpl::MultiBodyImpl(int num_bodies_, int num_dofs_)
: m_num_bodies(num_bodies_), m_num_dofs(num_dofs_) {
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;
}
}
}
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. 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;
// body.m_parent_r_parent_body= fixed
body.m_body_ang_vel_rel = body.m_Jac_JR * u(body.m_q_index);
// body.m_parent_dot_r_rel = fixed;
// NOTE: this assumes that Jac_JR is constant, which is true for revolute
// joints, but not in the general case (eg, slider-crank type mechanisms)
body.m_body_ang_acc_rel = body.m_Jac_JR * dot_u(body.m_q_index);
// body.m_parent_ddot_r_rel = fixed;
}
// 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_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);
// body.m_parent_omega_rel = 0;
body.m_parent_vel_rel =
body.m_body_T_parent_ref.transpose() * body.m_Jac_JT * u(body.m_q_index);
// body.parent_dot_omega_rel = 0;
// NOTE: this assumes that Jac_JT is constant, which is true for
// prismatic joints, but not in the general case
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_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_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_pos_parent_body = body.m_body_T_parent * body.m_parent_pos_parent_body;
body.m_parent_vel_rel = body.m_body_T_parent.transpose() * body.m_parent_vel_rel;
body.m_parent_acc_rel = body.m_body_T_parent.transpose() * body.m_parent_acc_rel;
}
// 3. absolute kinematic quantities & dynamic quantities
// 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;
// 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;
// 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]];
// 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 * (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;
// 3.2 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);
// 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_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);
}
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;
}
// 4. 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;
}
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();
}
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.
// Macro for setting matrix elements depending on underlying math library.
#ifdef ID_LINEAR_MATH_USE_BULLET
#define setMassMatrixElem(row, col, val) mass_matrix->setElem(row, col, val)
#else
#define setMassMatrixElem(row, col, val) (*mass_matrix)(row, col) = val
#endif
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++) {
setMassMatrixElem(i, j, 0.0);
}
}
}
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);
setMassMatrixElem(col, col, Jac_JR.dot(body_eom_rot) + Jac_JT.dot(body_eom_trans));
// 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);
setMassMatrixElem(col, row, Mrc);
}
// 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);
setMassMatrixElem(col, row, Mrc);
}
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++) {
setMassMatrixElem(row, col, (*mass_matrix)(col, row));
}
}
}
#undef setMassMatrixElem
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::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;
}
}

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src/BulletInverseDynamics/details/MultiBodyTreeImpl.hpp Normal file
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// The structs and classes defined here provide a basic inverse fynamics implementation used
// by MultiBodyTree
// User interaction should be through MultiBodyTree
#ifndef MULTI_BODY_REFERENCE_IMPL_HPP_
#define MULTI_BODY_REFERENCE_IMPL_HPP_
#include "../IDConfig.hpp"
#include "../MultiBodyTree.hpp"
namespace btInverseDynamics {
/// Structure for for rigid body mass properties, connectivity and kinematic state
/// all vectors and matrices are in body-fixed frame, if not indicated otherwise.
/// The body-fixed frame is located in the joint connecting the body to its parent.
struct RigidBody {
ID_DECLARE_ALIGNED_ALLOCATOR();
// 1 Inertial properties
/// Mass
idScalar m_mass;
/// Mass times center of gravity in body-fixed frame
vec3 m_body_mass_com;
/// Moment of inertia w.r.t. body-fixed frame
mat33 m_body_I_body;
// 2 dynamic properties
/// Left-hand side of the body equation of motion, translational part
vec3 m_eom_lhs_translational;
/// Left-hand side of the body equation of motion, rotational part
vec3 m_eom_lhs_rotational;
/// Force acting at the joint when the body is cut from its parent;
/// includes impressed joint force in J_JT direction,
/// as well as constraint force,
/// in body-fixed frame
vec3 m_force_at_joint;
/// Moment acting at the joint when the body is cut from its parent;
/// includes impressed joint moment in J_JR direction, and constraint moment
/// in body-fixed frame
vec3 m_moment_at_joint;
/// external (user provided) force acting at the body-fixed frame's origin, written in that
/// frame
vec3 m_body_force_user;
/// external (user provided) moment acting at the body-fixed frame's origin, written in that
/// frame
vec3 m_body_moment_user;
// 3 absolute kinematic properties
/// Position of body-fixed frame relative to world frame
/// this is currently only for debugging purposes
vec3 m_body_pos;
/// Absolute velocity of body-fixed frame
vec3 m_body_vel;
/// Absolute acceleration of body-fixed frame
/// NOTE: if gravitational acceleration is not zero, this is the accelation PLUS gravitational
/// acceleration!
vec3 m_body_acc;
/// Absolute angular velocity
vec3 m_body_ang_vel;
/// Absolute angular acceleration
/// NOTE: if gravitational acceleration is not zero, this is the accelation PLUS gravitational
/// acceleration!
vec3 m_body_ang_acc;
// 4 relative kinematic properties.
// these are in the parent body frame
/// Transform from world to body-fixed frame;
/// this is currently only for debugging purposes
mat33 m_body_T_world;
/// Transform from parent to body-fixed frame
mat33 m_body_T_parent;
/// Vector from parent to child frame in parent frame
vec3 m_parent_pos_parent_body;
/// Relative angular velocity
vec3 m_body_ang_vel_rel;
/// Relative linear velocity
vec3 m_parent_vel_rel;
/// Relative angular acceleration
vec3 m_body_ang_acc_rel;
/// Relative linear acceleration
vec3 m_parent_acc_rel;
// 5 Data describing the joint type and geometry
/// Type of joint
JointType m_joint_type;
/// Position of joint frame (body-fixed frame at q=0) relative to the parent frame
/// Components are in body-fixed frame of the parent
vec3 m_parent_pos_parent_body_ref;
/// Orientation of joint frame (body-fixed frame at q=0) relative to the parent frame
mat33 m_body_T_parent_ref;
/// Joint rotational Jacobian, ie, the partial derivative of the body-fixed frames absolute
/// angular velocity w.r.t. the generalized velocity of this body's relative degree of freedom.
/// For revolute joints this is the joint axis, for prismatic joints it is a null matrix.
/// (NOTE: dimensions will have to be dynamic for additional joint types!)
vec3 m_Jac_JR;
/// Joint translational Jacobian, ie, the partial derivative of the body-fixed frames absolute
/// linear velocity w.r.t. the generalized velocity of this body's relative degree of freedom.
/// For prismatic joints this is the joint axis, for revolute joints it is a null matrix.
/// (NOTE: dimensions might have to be dynamic for additional joint types!)
vec3 m_Jac_JT;
/// m_Jac_JT in the parent frame, it, m_body_T_parent_ref.transpose()*m_Jac_JT
vec3 m_parent_Jac_JT;
/// Start of index range for the position degree(s) of freedom describing this body's motion
/// relative to
/// its parent. The indices are wrt the multibody system's q-vector of generalized coordinates.
int m_q_index;
// 6 Scratch data for mass matrix computation using "composite rigid body algorithm"
/// mass of the subtree rooted in this body
idScalar m_subtree_mass;
/// center of mass * mass for subtree rooted in this body, in body-fixed frame
vec3 m_body_subtree_mass_com;
/// moment of inertia of subtree rooted in this body, w.r.t. body origin, in body-fixed frame
mat33 m_body_subtree_I_body;
};
/// The MBS implements a tree structured multibody system
class MultiBodyTree::MultiBodyImpl {
friend class MultiBodyTree;
public:
ID_DECLARE_ALIGNED_ALLOCATOR();
/// constructor
/// @param num_bodies the number of bodies in the system
/// @param num_dofs number of degrees of freedom in the system
MultiBodyImpl(int num_bodies_, int num_dofs_);
/// \copydoc MultiBodyTree::calculateInverseDynamics
int calculateInverseDynamics(const vecx& q, const vecx& u, const vecx& dot_u,
vecx* joint_forces);
///\copydoc MultiBodyTree::calculateMassMatrix
int calculateMassMatrix(const vecx& q, const bool update_kinematics,
const bool initialize_matrix, const bool set_lower_triangular_matrix,
matxx* mass_matrix);
/// generate additional index sets from the parent_index array
/// @return -1 on error, 0 on success
int generateIndexSets();
/// set gravity acceleration in world frame
/// @param gravity gravity vector in the world frame
/// @return 0 on success, -1 on error
int setGravityInWorldFrame(const vec3& gravity);
/// pretty print tree
void printTree();
/// print tree data
void printTreeData();
/// initialize fixed data
void calculateStaticData();
/// \copydoc MultiBodyTree::getBodyFrame
int getBodyFrame(const int index, vec3* world_origin, mat33* body_T_world) const;
/// \copydoc MultiBodyTree::getParentIndex
int getParentIndex(const int body_index, int* m_parent_index);
/// \copydoc MultiBodyTree::getJointType
int getJointType(const int body_index, JointType* joint_type) const;
/// \copydoc MultiBodyTree::getJointTypeStr
int getJointTypeStr(const int body_index, const char** joint_type) const;
/// \copydoc MultiBodyTree:getDoFOffset
int getDoFOffset(const int body_index, int* q_index) const;
/// \copydoc MultiBodyTree::getBodyOrigin
int getBodyOrigin(const int body_index, vec3* world_origin) const;
/// \copydoc MultiBodyTree::getBodyCoM
int getBodyCoM(const int body_index, vec3* world_com) const;
/// \copydoc MultiBodyTree::getBodyTransform
int getBodyTransform(const int body_index, mat33* world_T_body) const;
/// \copydoc MultiBodyTree::getBodyAngularVelocity
int getBodyAngularVelocity(const int body_index, vec3* world_omega) const;
/// \copydoc MultiBodyTree::getBodyLinearVelocity
int getBodyLinearVelocity(const int body_index, vec3* world_velocity) const;
/// \copydoc MultiBodyTree::getBodyLinearVelocityCoM
int getBodyLinearVelocityCoM(const int body_index, vec3* world_velocity) const;
/// \copydoc MultiBodyTree::getBodyAngularAcceleration
int getBodyAngularAcceleration(const int body_index, vec3* world_dot_omega) const;
/// \copydoc MultiBodyTree::getBodyLinearAcceleration
int getBodyLinearAcceleration(const int body_index, vec3* world_acceleration) const;
/// \copydoc MultiBodyTree::getUserInt
int getUserInt(const int body_index, int* user_int) const;
/// \copydoc MultiBodyTree::getUserPtr
int getUserPtr(const int body_index, void** user_ptr) const;
/// \copydoc MultiBodyTree::setUserInt
int setUserInt(const int body_index, const int user_int);
/// \copydoc MultiBodyTree::setUserPtr
int setUserPtr(const int body_index, void* const user_ptr);
///\copydoc MultiBodytTree::setBodyMass
int setBodyMass(const int body_index, const idScalar mass);
///\copydoc MultiBodytTree::setBodyFirstMassMoment
int setBodyFirstMassMoment(const int body_index, const vec3 first_mass_moment);
///\copydoc MultiBodytTree::setBodySecondMassMoment
int setBodySecondMassMoment(const int body_index, const mat33 second_mass_moment);
///\copydoc MultiBodytTree::getBodyMass
int getBodyMass(const int body_index, idScalar* mass) const;
///\copydoc MultiBodytTree::getBodyFirstMassMoment
int getBodyFirstMassMoment(const int body_index, vec3* first_mass_moment) const;
///\copydoc MultiBodytTree::getBodySecondMassMoment
int getBodySecondMassMoment(const int body_index, mat33* second_mass_moment) const;
/// \copydoc MultiBodyTree::clearAllUserForcesAndMoments
void clearAllUserForcesAndMoments();
/// \copydoc MultiBodyTree::addUserForce
int addUserForce(const int body_index, const vec3& body_force);
/// \copydoc MultiBodyTree::addUserMoment
int addUserMoment(const int body_index, const vec3& body_moment);
private:
// debug function. print tree structure to stdout
void printTree(int index, int indentation);
// get string representation of JointType (for debugging)
const char* jointTypeToString(const JointType& type) const;
// get number of degrees of freedom from joint type
int bodyNumDoFs(const JointType& type) const;
// number of bodies in the system
int m_num_bodies;
// number of degrees of freedom
int m_num_dofs;
// Gravitational acceleration (in world frame)
vec3 m_world_gravity;
// vector of bodies in the system
// body 0 is used as an environment body and is allways fixed.
// The bodies are ordered such that a parent body always has an index
// smaller than its child.
idArray<RigidBody>::type m_body_list;
// Parent_index[i] is the index for i's parent body in body_list.
// This fully describes the tree.
idArray<int>::type m_parent_index;
// child_indices[i] contains a vector of indices of
// all children of the i-th body
idArray<idArray<int>::type>::type m_child_indices;
// Indices of rotary joints
idArray<int>::type m_body_revolute_list;
// Indices of prismatic joints
idArray<int>::type m_body_prismatic_list;
// Indices of floating joints
idArray<int>::type m_body_floating_list;
// a user-provided integer
idArray<int>::type m_user_int;
// a user-provided pointer
idArray<void*>::type m_user_ptr;
};
}
#endif

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#include "MultiBodyTreeInitCache.hpp"
namespace btInverseDynamics {
MultiBodyTree::InitCache::InitCache() {
m_inertias.resize(0);
m_joints.resize(0);
m_num_dofs = 0;
m_root_index=-1;
}
int MultiBodyTree::InitCache::addBody(const int body_index, const int parent_index,
const JointType joint_type,
const vec3& parent_r_parent_body_ref,
const mat33& body_T_parent_ref,
const vec3& body_axis_of_motion, const idScalar mass,
const vec3& body_r_body_com, const mat33& body_I_body,
const int user_int, void* user_ptr) {
switch (joint_type) {
case REVOLUTE:
case PRISMATIC:
m_num_dofs += 1;
break;
case FIXED:
// does not add a degree of freedom
// m_num_dofs+=0;
break;
case FLOATING:
m_num_dofs += 6;
break;
default:
error_message("unknown joint type %d\n", joint_type);
return -1;
}
if(-1 == parent_index) {
if(m_root_index>=0) {
error_message("trying to add body %d as root, but already added %d as root body\n",
body_index, m_root_index);
return -1;
}
m_root_index=body_index;
}
JointData joint;
joint.m_child = body_index;
joint.m_parent = parent_index;
joint.m_type = joint_type;
joint.m_parent_pos_parent_child_ref = parent_r_parent_body_ref;
joint.m_child_T_parent_ref = body_T_parent_ref;
joint.m_child_axis_of_motion = body_axis_of_motion;
InertiaData body;
body.m_mass = mass;
body.m_body_pos_body_com = body_r_body_com;
body.m_body_I_body = body_I_body;
m_inertias.push_back(body);
m_joints.push_back(joint);
m_user_int.push_back(user_int);
m_user_ptr.push_back(user_ptr);
return 0;
}
int MultiBodyTree::InitCache::getInertiaData(const int index, InertiaData* inertia) const {
if (index < 0 || index > static_cast<int>(m_inertias.size())) {
error_message("index out of range\n");
return -1;
}
*inertia = m_inertias[index];
return 0;
}
int MultiBodyTree::InitCache::getUserInt(const int index, int* user_int) const {
if (index < 0 || index > static_cast<int>(m_user_int.size())) {
error_message("index out of range\n");
return -1;
}
*user_int = m_user_int[index];
return 0;
}
int MultiBodyTree::InitCache::getUserPtr(const int index, void** user_ptr) const {
if (index < 0 || index > static_cast<int>(m_user_ptr.size())) {
error_message("index out of range\n");
return -1;
}
*user_ptr = m_user_ptr[index];
return 0;
}
int MultiBodyTree::InitCache::getJointData(const int index, JointData* joint) const {
if (index < 0 || index > static_cast<int>(m_joints.size())) {
error_message("index out of range\n");
return -1;
}
*joint = m_joints[index];
return 0;
}
int MultiBodyTree::InitCache::buildIndexSets() {
// NOTE: This function assumes that proper indices were provided
// User2InternalIndex from utils can be used to facilitate this.
m_parent_index.resize(numBodies());
for (idArrayIdx j = 0; j < m_joints.size(); j++) {
const JointData& joint = m_joints[j];
m_parent_index[joint.m_child] = joint.m_parent;
}
return 0;
}
}

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#ifndef MULTIBODYTREEINITCACHE_HPP_
#define MULTIBODYTREEINITCACHE_HPP_
#include "../IDConfig.hpp"
#include "../IDMath.hpp"
#include "../MultiBodyTree.hpp"
namespace btInverseDynamics {
/// Mass properties of a rigid body
struct InertiaData {
ID_DECLARE_ALIGNED_ALLOCATOR();
/// mass
idScalar m_mass;
/// vector from body-fixed frame to center of mass,
/// in body-fixed frame, multiplied by the mass
vec3 m_body_pos_body_com;
/// moment of inertia w.r.t. the origin of the body-fixed
/// frame, represented in that frame
mat33 m_body_I_body;
};
/// Joint properties
struct JointData {
ID_DECLARE_ALIGNED_ALLOCATOR();
/// type of joint
JointType m_type;
/// index of parent body
int m_parent;
/// index of child body
int m_child;
/// vector from parent's body-fixed frame to child's body-fixed
/// frame for q=0, written in the parent's body fixed frame
vec3 m_parent_pos_parent_child_ref;
/// Transform matrix converting vectors written in the parent's frame
/// into vectors written in the child's frame for q=0
/// ie, child_vector = child_T_parent_ref * parent_vector;
mat33 m_child_T_parent_ref;
/// Axis of motion for 1 degree-of-freedom joints,
/// written in the child's frame
/// For revolute joints, the q-value is positive for a positive
/// rotation about this axis.
/// For prismatic joints, the q-value is positive for a positive
/// translation is this direction.
vec3 m_child_axis_of_motion;
};
/// Data structure to store data passed by the user.
/// This is used in MultiBodyTree::finalize to build internal data structures.
class MultiBodyTree::InitCache {
public:
ID_DECLARE_ALIGNED_ALLOCATOR();
/// constructor
InitCache();
///\copydoc MultiBodyTree::addBody
int addBody(const int body_index, const int parent_index, const JointType joint_type,
const vec3 &parent_r_parent_body_ref, const mat33 &body_T_parent_ref,
const vec3 &body_axis_of_motion, idScalar mass, const vec3 &body_r_body_com,
const mat33 &body_I_body, const int user_int, void *user_ptr);
/// build index arrays
/// @return 0 on success, -1 on failure
int buildIndexSets();
/// @return number of degrees of freedom
int numDoFs() const { return m_num_dofs; }
/// @return number of bodies
int numBodies() const { return m_inertias.size(); }
/// get inertia data for index
/// @param index of the body
/// @param inertia pointer for return data
/// @return 0 on success, -1 on failure
int getInertiaData(const int index, InertiaData *inertia) const;
/// get joint data for index
/// @param index of the body
/// @param joint pointer for return data
/// @return 0 on success, -1 on failure
int getJointData(const int index, JointData *joint) const;
/// get parent index array (paren_index[i] is the index of the parent of i)
/// @param parent_index pointer for return data
void getParentIndexArray(idArray<int>::type *parent_index) { *parent_index = m_parent_index; }
/// get user integer
/// @param index body index
/// @param user_int user integer
/// @return 0 on success, -1 on failure
int getUserInt(const int index, int *user_int) const;
/// get user pointer
/// @param index body index
/// @param user_int user pointer
/// @return 0 on success, -1 on failure
int getUserPtr(const int index, void **user_ptr) const;
private:
// vector of bodies
idArray<InertiaData>::type m_inertias;
// vector of joints
idArray<JointData>::type m_joints;
// number of mechanical degrees of freedom
int m_num_dofs;
// parent index array
idArray<int>::type m_parent_index;
// user integers
idArray<int>::type m_user_int;
// user pointers
idArray<void *>::type m_user_ptr;
// index of root body (or -1 if not set)
int m_root_index;
};
}
#endif // MULTIBODYTREEINITCACHE_HPP_

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project "BulletInverseDynamics"
kind "StaticLib"
includedirs {
"..",
}
files {
"IDMath.cpp",
"MultiBodyTree.cpp",
"details/MultiBodyTreeInitCache.cpp",
"details/MultiBodyTreeImpl.cpp",
}

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project "Test_InverseDynamicsKinematics"
kind "ConsoleApp"
-- defines { }
includedirs
{
".",
"../../src",
"../../examples/InverseDynamics",
"../../Extras/InverseDynamics",
"../gtest-1.7.0/include"
}
if os.is("Windows") then
--see http://stackoverflow.com/questions/12558327/google-test-in-visual-studio-2012
defines {"_VARIADIC_MAX=10"}
end
links {"BulletInverseDynamicsUtils", "BulletInverseDynamics","Bullet3Common","LinearMath", "gtest"}
files {
"test_invdyn_kinematics.cpp",
}
if os.is("Linux") then
links {"pthread"}
end

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/// create a bullet btMultiBody model of a tree structured multibody system,
/// convert that model to a MultiBodyTree model.
/// Then - run inverse dynamics on random input data (q, u, dot_u) to get forces
/// - run forward dynamics on (q,u, forces) to get accelerations
/// - compare input accelerations to inverse dynamics to output from forward dynamics
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <string>
#include <random>
#include <btBulletDynamicsCommon.h>
#include <btMultiBodyTreeCreator.hpp>
#include <BulletDynamics/Featherstone/btMultiBodyConstraintSolver.h>
#include <BulletDynamics/Featherstone/btMultiBodyDynamicsWorld.h>
#include <BulletDynamics/Featherstone/btMultiBodyPoint2Point.h>
#include <BulletDynamics/Featherstone/btMultiBodyLinkCollider.h>
#include <../CommonInterfaces/CommonGUIHelperInterface.h>
#include <gflags/gflags.h>
#include <gtest/gtest.h>
#include <../Importers/ImportURDFDemo/BulletUrdfImporter.h>
#include <../Importers/ImportURDFDemo/URDF2Bullet.h>
#include <../Importers/ImportURDFDemo/MyMultiBodyCreator.h>
#include <../Importers/ImportURDFDemo/URDF2Bullet.h>
#include "../../examples/Utils/b3ResourcePath.h"
#include <invdyn_bullet_comparison.hpp>
#include <btMultiBodyFromURDF.hpp>
#include <MultiBodyTreeCreator.hpp>
#include <MultiBodyTreeDebugGraph.hpp>
using namespace btInverseDynamics;
DEFINE_bool(verbose, false, "print extra info");
static btVector3 gravity(0, 0, -10);
static const bool kBaseFixed = false;
static const char kUrdfFile[] = "r2d2.urdf";
/// this test loads the a urdf model with fixed, floating, prismatic and rotational joints,
/// converts in to an inverse dynamics model and compares forward to inverse dynamics for
/// random input
TEST(InvDynCompare, bulletUrdfR2D2) {
MyBtMultiBodyFromURDF mb_load(gravity, kBaseFixed);
char relativeFileName[1024];
ASSERT_TRUE(b3ResourcePath::findResourcePath(kUrdfFile, relativeFileName, 1024));
mb_load.setFileName(relativeFileName);
mb_load.init();
btMultiBodyTreeCreator id_creator;
btMultiBody *btmb = mb_load.getBtMultiBody();
ASSERT_EQ(id_creator.createFromBtMultiBody(btmb), 0);
MultiBodyTree *id_tree = CreateMultiBodyTree(id_creator);
ASSERT_EQ(0x0 != id_tree, true);
vecx q(id_tree->numDoFs());
vecx u(id_tree->numDoFs());
vecx dot_u(id_tree->numDoFs());
vecx joint_forces(id_tree->numDoFs());
const int kNLoops = 10;
double max_pos_error = 0;
double max_acc_error = 0;
std::default_random_engine generator;
std::uniform_real_distribution<double> distribution(-M_PI, M_PI);
auto rnd = std::bind(distribution, generator);
for (int loop = 0; loop < kNLoops; loop++) {
for (int i = 0; i < q.size(); i++) {
q(i) = rnd();
u(i) = rnd();
dot_u(i) = rnd();
}
double pos_error;
double acc_error;
btmb->clearForcesAndTorques();
id_tree->clearAllUserForcesAndMoments();
// call inverse dynamics once, to get global position & velocity of root body
// (fixed, so q, u, dot_u arbitrary)
EXPECT_EQ(id_tree->calculateInverseDynamics(q, u, dot_u, &joint_forces), 0);
EXPECT_EQ(compareInverseAndForwardDynamics(q, u, dot_u, gravity, FLAGS_verbose, btmb, id_tree,
&pos_error, &acc_error),
0);
if (pos_error > max_pos_error) {
max_pos_error = pos_error;
}
if (acc_error > max_acc_error) {
max_acc_error = acc_error;
}
}
if (FLAGS_verbose) {
printf("max_pos_error= %e\n", max_pos_error);
printf("max_acc_error= %e\n", max_acc_error);
}
EXPECT_LT(max_pos_error, std::numeric_limits<idScalar>::epsilon()*1e4);
EXPECT_LT(max_acc_error, std::numeric_limits<idScalar>::epsilon()*1e5);
}
int main(int argc, char **argv) {
gflags::SetUsageMessage("Usage: invdyn_from_btmultibody -verbose = true/false");
gflags::ParseCommandLineFlags(&argc, &argv, false);
::testing::InitGoogleTest(&argc, argv);
return RUN_ALL_TESTS();
}

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// Test of kinematic consistency: check if finite differences of velocities, accelerations
// match positions
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <gtest/gtest.h>
#include "../Extras/InverseDynamics/CoilCreator.hpp"
#include "../Extras/InverseDynamics/DillCreator.hpp"
#include "../Extras/InverseDynamics/SimpleTreeCreator.hpp"
#include "BulletInverseDynamics/MultiBodyTree.hpp"
using namespace btInverseDynamics;
const int kLevel = 5;
const int kNumBodies = std::pow(2, kLevel);
// template function for calculating the norm
template <typename T>
idScalar calculateNorm(T&);
// only implemented for vec3
template <>
idScalar calculateNorm(vec3& v) {
return std::sqrt(std::pow(v(0), 2) + std::pow(v(1), 2) + std::pow(v(2), 2));
}
// template function to convert a DiffType (finite differences)
// to a ValueType. This is for angular velocity calculations
// via finite differences.
template <typename ValueType, typename DiffType>
DiffType toDiffType(ValueType& fd, ValueType& val);
// vector case: just return finite difference approximation
template <>
vec3 toDiffType(vec3& fd, vec3& val) {
return fd;
}
// orientation case: calculate spin tensor and extract angular velocity
template <>
vec3 toDiffType(mat33& fd, mat33& val) {
// spin tensor
mat33 omega_tilde = fd * val.transpose();
// extract vector from spin tensor
vec3 omega;
omega(0) = 0.5 * (omega_tilde(2, 1) - omega_tilde(1, 2));
omega(1) = 0.5 * (omega_tilde(0, 2) - omega_tilde(2, 0));
omega(2) = 0.5 * (omega_tilde(1, 0) - omega_tilde(0, 1));
return omega;
}
/// Class for calculating finite difference approximation
/// of time derivatives and comparing it to an analytical solution
/// DiffType and ValueType can be different, to allow comparison
/// of angular velocity vectors and orientations given as transform matrices.
template <typename ValueType, typename DiffType>
class DiffFD {
public:
DiffFD() : m_dt(0.0), m_num_updates(0), m_max_error(0.0), m_max_value(0.0), m_valid_fd(false) {}
void init(std::string name, idScalar dt) {
m_name = name;
m_dt = dt;
m_num_updates = 0;
m_max_error = 0.0;
m_max_value = 0.0;
m_valid_fd = false;
}
void update(const ValueType& val, const DiffType& true_diff) {
m_val = val;
if (m_num_updates > 2) {
// 2nd order finite difference approximation for d(value)/dt
ValueType diff_value_fd = (val - m_older_val) / (2.0 * m_dt);
// convert to analytical diff type. This is for angular velocities
m_diff_fd = toDiffType<ValueType, DiffType>(diff_value_fd, m_old_val);
// now, calculate the error
DiffType error_value_type = m_diff_fd - m_old_true_diff;
idScalar error = calculateNorm<DiffType>(error_value_type);
if (error > m_max_error) {
m_max_error = error;
}
idScalar value = calculateNorm<DiffType>(m_old_true_diff);
if (value > m_max_value) {
m_max_value = value;
}
m_valid_fd = true;
}
m_older_val = m_old_val;
m_old_val = m_val;
m_old_true_diff = true_diff;
m_num_updates++;
m_time += m_dt;
}
void printMaxError() {
printf("max_error: %e dt= %e max_value= %e fraction= %e\n", m_max_error, m_dt, m_max_value,
m_max_value > 0.0 ? m_max_error / m_max_value : 0.0);
}
void printCurrent() {
if (m_valid_fd) {
// note: m_old_true_diff already equals m_true_diff here, so values are not aligned.
// (but error calculation takes this into account)
printf("%s time: %e fd: %e %e %e true: %e %e %e\n", m_name.c_str(), m_time,
m_diff_fd(0), m_diff_fd(1), m_diff_fd(2), m_old_true_diff(0), m_old_true_diff(1),
m_old_true_diff(2));
}
}
idScalar getMaxError() const { return m_max_error; }
idScalar getMaxValue() const { return m_max_value; }
private:
idScalar m_dt;
ValueType m_val;
ValueType m_old_val;
ValueType m_older_val;
DiffType m_old_true_diff;
DiffType m_diff_fd;
int m_num_updates;
idScalar m_max_error;
idScalar m_max_value;
idScalar m_time;
std::string m_name;
bool m_valid_fd;
};
template <typename ValueType, typename DiffType>
class VecDiffFD {
public:
VecDiffFD(std::string name, int dim, idScalar dt) : m_name(name), m_fd(dim), m_dt(dt) {
for (int i = 0; i < m_fd.size(); i++) {
char buf[256];
snprintf(buf, 256, "%s-%.2d", name.c_str(), i);
m_fd[i].init(buf, dt);
}
}
void update(int i, ValueType& val, DiffType& true_diff) { m_fd[i].update(val, true_diff); }
idScalar getMaxError() const {
idScalar max_error = 0;
for (int i = 0; i < m_fd.size(); i++) {
const idScalar error = m_fd[i].getMaxError();
if (error > max_error) {
max_error = error;
}
}
return max_error;
}
void printMaxError() {
printf("%s: total dt= %e max_error= %e\n", m_name.c_str(), m_dt, getMaxError());
}
void printCurrent() {
for (int i = 0; i < m_fd.size(); i++) {
m_fd[i].printCurrent();
}
}
private:
std::string m_name;
std::vector<DiffFD<ValueType, DiffType> > m_fd;
const idScalar m_dt;
idScalar m_max_error;
};
// calculate maximum difference between finite difference and analytical differentiation
int calculateDifferentiationError(const MultiBodyTreeCreator& creator, idScalar deltaT,
idScalar endTime, idScalar* max_linear_velocity_error,
idScalar* max_angular_velocity_error,
idScalar* max_linear_acceleration_error,
idScalar* max_angular_acceleration_error) {
// setup system
MultiBodyTree* tree = CreateMultiBodyTree(creator);
if (0x0 == tree) {
return -1;
}
// set gravity to zero, so nothing is added to accelerations in forward kinematics
vec3 gravity_zero;
gravity_zero(0) = 0;
gravity_zero(1) = 0;
gravity_zero(2) = 0;
tree->setGravityInWorldFrame(gravity_zero);
//
const idScalar kAmplitude = 1.0;
const idScalar kFrequency = 1.0;
vecx q(tree->numDoFs());
vecx dot_q(tree->numDoFs());
vecx ddot_q(tree->numDoFs());
vecx joint_forces(tree->numDoFs());
VecDiffFD<vec3, vec3> fd_vel("linear-velocity", tree->numBodies(), deltaT);
VecDiffFD<vec3, vec3> fd_acc("linear-acceleration", tree->numBodies(), deltaT);
VecDiffFD<mat33, vec3> fd_omg("angular-velocity", tree->numBodies(), deltaT);
VecDiffFD<vec3, vec3> fd_omgd("angular-acceleration", tree->numBodies(), deltaT);
for (idScalar t = 0.0; t < endTime; t += deltaT) {
for (int body = 0; body < tree->numBodies(); body++) {
q(body) = kAmplitude * sin(t * 2.0 * M_PI * kFrequency);
dot_q(body) = kAmplitude * 2.0 * M_PI * kFrequency * cos(t * 2.0 * M_PI * kFrequency);
ddot_q(body) =
-kAmplitude * pow(2.0 * M_PI * kFrequency, 2) * sin(t * 2.0 * M_PI * kFrequency);
}
if (-1 == tree->calculateInverseDynamics(q, dot_q, ddot_q, &joint_forces)) {
delete tree;
return -1;
}
// position/velocity
for (int body = 0; body < tree->numBodies(); body++) {
vec3 pos;
vec3 vel;
mat33 world_T_body;
vec3 omega;
vec3 dot_omega;
vec3 acc;
tree->getBodyOrigin(body, &pos);
tree->getBodyTransform(body, &world_T_body);
tree->getBodyLinearVelocity(body, &vel);
tree->getBodyAngularVelocity(body, &omega);
tree->getBodyLinearAcceleration(body, &acc);
tree->getBodyAngularAcceleration(body, &dot_omega);
fd_vel.update(body, pos, vel);
fd_omg.update(body, world_T_body, omega);
fd_acc.update(body, vel, acc);
fd_omgd.update(body, omega, dot_omega);
}
}
*max_linear_velocity_error = fd_vel.getMaxError();
*max_angular_velocity_error = fd_omg.getMaxError();
*max_linear_acceleration_error = fd_acc.getMaxError();
*max_angular_acceleration_error = fd_omgd.getMaxError();
delete tree;
return 0;
}
// first test: absolute difference between numerical and numerial
// differentiation should be small
TEST(InvDynKinematicsDifferentiation, errorAbsolute) {
const idScalar kDeltaT = 1e-7;
const idScalar kDuration = 1e-2;
const idScalar kAcceptableError = 1e-4;
CoilCreator coil_creator(kNumBodies);
DillCreator dill_creator(kLevel);
SimpleTreeCreator simple_creator(kNumBodies);
idScalar max_linear_velocity_error;
idScalar max_angular_velocity_error;
idScalar max_linear_acceleration_error;
idScalar max_angular_acceleration_error;
// test serial chain
calculateDifferentiationError(coil_creator, kDeltaT, kDuration, &max_linear_velocity_error,
&max_angular_velocity_error, &max_linear_acceleration_error,
&max_angular_acceleration_error);
EXPECT_LT(max_linear_velocity_error, kAcceptableError);
EXPECT_LT(max_angular_velocity_error, kAcceptableError);
EXPECT_LT(max_linear_acceleration_error, kAcceptableError);
EXPECT_LT(max_angular_acceleration_error, kAcceptableError);
// test branched tree
calculateDifferentiationError(coil_creator, kDeltaT, kDuration, &max_linear_velocity_error,
&max_angular_velocity_error, &max_linear_acceleration_error,
&max_angular_acceleration_error);
EXPECT_LT(max_linear_velocity_error, kAcceptableError);
EXPECT_LT(max_angular_velocity_error, kAcceptableError);
EXPECT_LT(max_linear_acceleration_error, kAcceptableError);
EXPECT_LT(max_angular_acceleration_error, kAcceptableError);
// test system with different joint types
calculateDifferentiationError(simple_creator, kDeltaT, kDuration, &max_linear_velocity_error,
&max_angular_velocity_error, &max_linear_acceleration_error,
&max_angular_acceleration_error);
EXPECT_LT(max_linear_velocity_error, kAcceptableError);
EXPECT_LT(max_angular_velocity_error, kAcceptableError);
EXPECT_LT(max_linear_acceleration_error, kAcceptableError);
EXPECT_LT(max_angular_acceleration_error, kAcceptableError);
}
// second test: check if the change in the differentiation error
// is consitent with the second order approximation, ie, error ~ O(dt^2)
TEST(InvDynKinematicsDifferentiation, errorOrder) {
const idScalar kDeltaTs[2] = {1e-4, 1e-5};
const idScalar kDuration = 1e-2;
CoilCreator coil_creator(kNumBodies);
// DillCreator dill_creator(kLevel);
// SimpleTreeCreator simple_creator(kNumBodies);
idScalar max_linear_velocity_error[2];
idScalar max_angular_velocity_error[2];
idScalar max_linear_acceleration_error[2];
idScalar max_angular_acceleration_error[2];
// test serial chain
calculateDifferentiationError(coil_creator, kDeltaTs[0], kDuration,
&max_linear_velocity_error[0], &max_angular_velocity_error[0],
&max_linear_acceleration_error[0],
&max_angular_acceleration_error[0]);
calculateDifferentiationError(coil_creator, kDeltaTs[1], kDuration,
&max_linear_velocity_error[1], &max_angular_velocity_error[1],
&max_linear_acceleration_error[1],
&max_angular_acceleration_error[1]);
const idScalar expected_linear_velocity_error_1 =
max_linear_velocity_error[0] * pow(kDeltaTs[1] / kDeltaTs[0], 2);
const idScalar expected_angular_velocity_error_1 =
max_angular_velocity_error[0] * pow(kDeltaTs[1] / kDeltaTs[0], 2);
const idScalar expected_linear_acceleration_error_1 =
max_linear_acceleration_error[0] * pow(kDeltaTs[1] / kDeltaTs[0], 2);
const idScalar expected_angular_acceleration_error_1 =
max_angular_acceleration_error[0] * pow(kDeltaTs[1] / kDeltaTs[0], 2);
printf("linear vel error: %e %e %e\n", max_linear_velocity_error[1],
expected_linear_velocity_error_1,
max_linear_velocity_error[1] - expected_linear_velocity_error_1);
printf("angular vel error: %e %e %e\n", max_angular_velocity_error[1],
expected_angular_velocity_error_1,
max_angular_velocity_error[1] - expected_angular_velocity_error_1);
printf("linear acc error: %e %e %e\n", max_linear_acceleration_error[1],
expected_linear_acceleration_error_1,
max_linear_acceleration_error[1] - expected_linear_acceleration_error_1);
printf("angular acc error: %e %e %e\n", max_angular_acceleration_error[1],
expected_angular_acceleration_error_1,
max_angular_acceleration_error[1] - expected_angular_acceleration_error_1);
}
int main(int argc, char** argv) {
::testing::InitGoogleTest(&argc, argv);
return RUN_ALL_TESTS();
return EXIT_SUCCESS;
}