bullet3/test/InverseDynamics/test_invdyn_kinematics.cpp

// 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 = BT_ID_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 BT_ID_SQRT(BT_ID_POW(v(0), 2) + BT_ID_POW(v(1), 2) + BT_ID_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];
			BT_ID_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;
	}
	idScalar getMaxValue() const
	{
		idScalar max_value = 0;
		for (int i = 0; i < m_fd.size(); i++)
		{
			const idScalar value = m_fd[i].getMaxValue();
			if (value > max_value)
			{
				max_value = value;
			}
		}
		return max_value;
	}
	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 * BT_ID_PI * kFrequency);
			dot_q(body) = kAmplitude * 2.0 * BT_ID_PI * kFrequency * cos(t * 2.0 * BT_ID_PI * kFrequency);
			ddot_q(body) =
				-kAmplitude * pow(2.0 * BT_ID_PI * kFrequency, 2) * sin(t * 2.0 * BT_ID_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);

			//        fd_vel.printCurrent();
			//fd_acc.printCurrent();
			//fd_omg.printCurrent();
			//fd_omgd.printCurrent();
		}
	}

	*max_linear_velocity_error = fd_vel.getMaxError() / fd_vel.getMaxValue();
	*max_angular_velocity_error = fd_omg.getMaxError() / fd_omg.getMaxValue();
	*max_linear_acceleration_error = fd_acc.getMaxError() / fd_acc.getMaxValue();
	*max_angular_acceleration_error = fd_omgd.getMaxError() / fd_omgd.getMaxValue();

	delete tree;
	return 0;
}

// first test: absolute difference between numerical and numerial
// differentiation should be small
TEST(InvDynKinematicsDifferentiation, errorAbsolute)
{
	//CAVEAT:these values are hand-tuned to work for the specific trajectory defined above.
#ifdef BT_ID_USE_DOUBLE_PRECISION
	const idScalar kDeltaT = 1e-7;
	const idScalar kAcceptableError = 1e-4;
#else
	const idScalar kDeltaT = 1e-4;
	const idScalar kAcceptableError = 5e-3;
#endif
	const idScalar kDuration = 0.01;

	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(dill_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;
}