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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 "Bullet3Common/b3Random.h"
#include "CloneTreeCreator.hpp"
#include "CoilCreator.hpp"
#include "DillCreator.hpp"
#include "RandomTreeCreator.hpp"
#include "BulletInverseDynamics/MultiBodyTree.hpp"
#include "MultiBodyTreeDebugGraph.hpp"
using namespace btInverseDynamics;
#if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS)
// minimal smart pointer to make this work for c++2003
template <typename T>
class ptr {
ptr();
ptr(const ptr&);
public:
ptr(T* p) : m_p(p) {};
~ptr() { delete m_p; }
T& operator*() { return *m_p; }
T* operator->() { return m_p; }
T*get() {return m_p;}
const T*get() const {return m_p;}
friend bool operator==(const ptr<T>& lhs, const ptr<T>& rhs) { return rhs.m_p == lhs.m_p; }
friend bool operator!=(const ptr<T>& lhs, const ptr<T>& rhs) { return !(rhs.m_p == lhs.m_p);
}
private:
T* m_p;
};
void calculateDotJacUError(const MultiBodyTreeCreator& creator, const int nloops,
double* max_error) {
// tree1 is used as reference to compute dot(Jacobian)*u from acceleration(dot(u)=0)
ptr<MultiBodyTree> tree1(CreateMultiBodyTree(creator));
ASSERT_TRUE(0x0 != tree1);
CloneTreeCreator clone(tree1.get());
// tree2 is used to compute dot(Jacobian)*u using the calculateJacobian function
ptr<MultiBodyTree> tree2(CreateMultiBodyTree(clone));
ASSERT_TRUE(0x0 != tree2);
const int ndofs = tree1->numDoFs();
const int nbodies = tree1->numBodies();
if (ndofs <= 0) {
*max_error = 0;
return;
}
vecx q(ndofs);
vecx u(ndofs);
vecx dot_u(ndofs);
vecx zero(ndofs);
setZero(zero);
double max_lin_error = 0;
double max_ang_error = 0;
for (int loop = 0; loop < nloops; loop++) {
for (int i = 0; i < q.size(); i++) {
q(i) = b3RandRange(-B3_PI, B3_PI);
u(i) = b3RandRange(-B3_PI, B3_PI);
}
EXPECT_EQ(0, tree1->calculateKinematics(q, u, zero));
EXPECT_EQ(0, tree2->calculatePositionAndVelocityKinematics(q, u));
EXPECT_EQ(0, tree2->calculateJacobians(q, u));
for (int idx = 0; idx < nbodies; idx++) {
vec3 tmp1, tmp2;
vec3 diff;
EXPECT_EQ(0, tree1->getBodyLinearAcceleration(idx, &tmp1));
EXPECT_EQ(0, tree2->getBodyDotJacobianTransU(idx, &tmp2));
diff = tmp1 - tmp2;
double lin_error = maxAbs(diff);
if (lin_error > max_lin_error) {
max_lin_error = lin_error;
}
EXPECT_EQ(0, tree1->getBodyAngularAcceleration(idx, &tmp1));
EXPECT_EQ(0, tree2->getBodyDotJacobianRotU(idx, &tmp2));
diff = tmp1 - tmp2;
double ang_error = maxAbs(diff);
if (ang_error > max_ang_error) {
max_ang_error = ang_error;
}
}
}
*max_error = max_ang_error > max_lin_error ? max_ang_error : max_lin_error;
}
void calculateJacobianError(const MultiBodyTreeCreator& creator, const int nloops,
double* max_error) {
// tree1 is used as reference to compute the Jacobian from velocities with unit u vectors.
ptr<MultiBodyTree> tree1(CreateMultiBodyTree(creator));
ASSERT_TRUE(0x0 != tree1);
// tree2 is used to compute the Jacobians using the calculateJacobian function
CloneTreeCreator clone(tree1.get());
ptr<MultiBodyTree> tree2(CreateMultiBodyTree(clone));
ASSERT_TRUE(0x0 != tree2);
const int ndofs = tree1->numDoFs();
const int nbodies = tree1->numBodies();
if (ndofs <= 0) {
*max_error = 0;
return;
}
vecx q(ndofs);
vecx zero(ndofs);
setZero(zero);
vecx one(ndofs);
double max_lin_error = 0;
double max_ang_error = 0;
for (int loop = 0; loop < nloops; loop++) {
for (int i = 0; i < q.size(); i++) {
q(i) = b3RandRange(-B3_PI, B3_PI);
}
EXPECT_EQ(0, tree2->calculatePositionKinematics(q));
EXPECT_EQ(0, tree2->calculateJacobians(q));
for (int idx = 0; idx < nbodies; idx++) {
mat3x ref_jac_r(3, ndofs);
mat3x ref_jac_t(3, ndofs);
ref_jac_r.setZero();
ref_jac_t.setZero();
// this re-computes all jacobians for every body ...
// but avoids std::vector<eigen matrix> issues
for (int col = 0; col < ndofs; col++) {
setZero(one);
one(col) = 1.0;
EXPECT_EQ(0, tree1->calculatePositionAndVelocityKinematics(q, one));
vec3 vel, omg;
EXPECT_EQ(0, tree1->getBodyLinearVelocity(idx, &vel));
EXPECT_EQ(0, tree1->getBodyAngularVelocity(idx, &omg));
setMat3xElem(0, col, omg(0), &ref_jac_r);
setMat3xElem(1, col, omg(1), &ref_jac_r);
setMat3xElem(2, col, omg(2), &ref_jac_r);
setMat3xElem(0, col, vel(0), &ref_jac_t);
setMat3xElem(1, col, vel(1), &ref_jac_t);
setMat3xElem(2, col, vel(2), &ref_jac_t);
}
mat3x jac_r(3, ndofs);
mat3x jac_t(3, ndofs);
mat3x diff(3, ndofs);
EXPECT_EQ(0, tree2->getBodyJacobianTrans(idx, &jac_t));
EXPECT_EQ(0, tree2->getBodyJacobianRot(idx, &jac_r));
sub(ref_jac_t,jac_t,&diff);
double lin_error = maxAbsMat3x(diff);
if (lin_error > max_lin_error) {
max_lin_error = lin_error;
}
sub(ref_jac_r, jac_r,&diff);
double ang_error = maxAbsMat3x(diff);
if (ang_error > max_ang_error) {
max_ang_error = ang_error;
}
}
}
*max_error = max_ang_error > max_lin_error ? max_ang_error : max_lin_error;
}
void calculateVelocityJacobianError(const MultiBodyTreeCreator& creator, const int nloops,
double* max_error) {
// tree1 is used as reference to compute the velocities directly
ptr<MultiBodyTree> tree1(CreateMultiBodyTree(creator));
ASSERT_TRUE(0x0 != tree1);
// tree2 is used to compute the velocities via jacobians
CloneTreeCreator clone(tree1.get());
ptr<MultiBodyTree> tree2(CreateMultiBodyTree(clone));
ASSERT_TRUE(0x0 != tree2);
const int ndofs = tree1->numDoFs();
const int nbodies = tree1->numBodies();
if (ndofs <= 0) {
*max_error = 0;
return;
}
vecx q(ndofs);
vecx u(ndofs);
double max_lin_error = 0;
double max_ang_error = 0;
for (int loop = 0; loop < nloops; loop++) {
for (int i = 0; i < q.size(); i++) {
q(i) = b3RandRange(-B3_PI, B3_PI);
u(i) = b3RandRange(-B3_PI, B3_PI);
}
EXPECT_EQ(0, tree1->calculatePositionAndVelocityKinematics(q, u));
EXPECT_EQ(0, tree2->calculatePositionKinematics(q));
EXPECT_EQ(0, tree2->calculateJacobians(q));
for (int idx = 0; idx < nbodies; idx++) {
vec3 vel1;
vec3 omg1;
vec3 vel2;
vec3 omg2;
mat3x jac_r2(3, ndofs);
mat3x jac_t2(3, ndofs);
EXPECT_EQ(0, tree1->getBodyLinearVelocity(idx, &vel1));
EXPECT_EQ(0, tree1->getBodyAngularVelocity(idx, &omg1));
EXPECT_EQ(0, tree2->getBodyJacobianTrans(idx, &jac_t2));
EXPECT_EQ(0, tree2->getBodyJacobianRot(idx, &jac_r2));
omg2 = jac_r2 * u;
vel2 = jac_t2 * u;
double lin_error = maxAbs(vel1 - vel2);
if (lin_error > max_lin_error) {
max_lin_error = lin_error;
}
double ang_error = maxAbs(omg1 - omg2);
if (ang_error > max_ang_error) {
max_ang_error = ang_error;
}
}
}
*max_error = max_ang_error > max_lin_error ? max_ang_error : max_lin_error;
}
// test nonlinear terms: dot(Jacobian)*u (linear and angular acceleration for dot_u ==0)
// from Jacobian calculation method and pseudo-numerically using via the kinematics method.
TEST(InvDynJacobians, JacDotJacU) {
const int kNumLevels = 5;
#ifdef B3_USE_DOUBLE_PRECISION
const double kMaxError = 1e-12;
#else
const double kMaxError = 5e-5;
#endif
const int kNumLoops = 20;
for (int level = 0; level < kNumLevels; level++) {
const int nbodies = BT_ID_POW(2, level);
CoilCreator coil(nbodies);
double error;
calculateDotJacUError(coil, kNumLoops, &error);
EXPECT_GT(kMaxError, error);
DillCreator dill(level);
calculateDotJacUError(dill, kNumLoops, &error);
EXPECT_GT(kMaxError, error);
}
const int kRandomLoops = 100;
const int kMaxRandomBodies = 128;
for (int loop = 0; loop < kRandomLoops; loop++) {
RandomTreeCreator random(kMaxRandomBodies);
double error;
calculateDotJacUError(random, kNumLoops, &error);
EXPECT_GT(kMaxError, error);
}
}
// Jacobians: linear and angular acceleration for dot_u ==0
// from Jacobian calculation method and pseudo-numerically using via the kinematics method.
TEST(InvDynJacobians, Jacobians) {
const int kNumLevels = 5;
#ifdef B3_USE_DOUBLE_PRECISION
const double kMaxError = 1e-12;
#else
const double kMaxError = 5e-5;
#endif
const int kNumLoops = 20;
for (int level = 0; level < kNumLevels; level++) {
const int nbodies = BT_ID_POW(2, level);
CoilCreator coil(nbodies);
double error;
calculateJacobianError(coil, kNumLoops, &error);
EXPECT_GT(kMaxError, error);
DillCreator dill(level);
calculateDotJacUError(dill, kNumLoops, &error);
EXPECT_GT(kMaxError, error);
}
const int kRandomLoops = 20;
const int kMaxRandomBodies = 16;
for (int loop = 0; loop < kRandomLoops; loop++) {
RandomTreeCreator random(kMaxRandomBodies);
double error;
calculateJacobianError(random, kNumLoops, &error);
EXPECT_GT(kMaxError, error);
}
}
// test for jacobian*u == velocity
TEST(InvDynJacobians, VelocitiesFromJacobians) {
const int kRandomLoops = 20;
const int kMaxRandomBodies = 16;
const int kNumLoops = 20;
#ifdef B3_USE_DOUBLE_PRECISION
const double kMaxError = 1e-12;
#else
const double kMaxError = 5e-5;
#endif
for (int loop = 0; loop < kRandomLoops; loop++) {
RandomTreeCreator random(kMaxRandomBodies);
double error;
calculateVelocityJacobianError(random, kNumLoops, &error);
EXPECT_GT(kMaxError, error);
}
}
#endif
int main(int argc, char** argv) {
b3Srand(1234);
::testing::InitGoogleTest(&argc, argv);
return RUN_ALL_TESTS();
}
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