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cppad-spatial.cpp
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cppad-spatial.cpp
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//
// Copyright (c) 2018-2019 CNRS INRIA
//
#include "pinocchio/autodiff/cppad.hpp"
#include "pinocchio/spatial/se3.hpp"
#include "pinocchio/spatial/motion.hpp"
#include "pinocchio/spatial/explog.hpp"
#include <iostream>
#include <boost/test/unit_test.hpp>
#include <boost/utility/binary.hpp>
BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE)
template<typename Vector3Like>
Eigen::Matrix<typename Vector3Like::Scalar,3,3,0>
computeV(const Eigen::MatrixBase<Vector3Like> & v3)
{
typedef typename Vector3Like::Scalar Scalar;
typedef Eigen::Matrix<Scalar,3,3,0> ReturnType;
typedef ReturnType Matrix3;
Scalar t2 = v3.squaredNorm();
const Scalar t = pinocchio::math::sqrt(t2);
Scalar alpha, beta, zeta;
if (t < 1e-4)
{
alpha = Scalar(1) + t2/Scalar(6) - t2*t2/Scalar(120);
beta = Scalar(1)/Scalar(2) - t2/Scalar(24);
zeta = Scalar(1)/Scalar(6) - t2/Scalar(120);
}
else
{
Scalar st,ct; pinocchio::SINCOS(t,&st,&ct);
alpha = st/t;
beta = (1-ct)/t2;
zeta = (1 - alpha)/(t2);
}
Matrix3 V
= alpha * Matrix3::Identity()
+ beta * pinocchio::skew(v3)
+ zeta * v3 * v3.transpose();
return V;
}
template<typename Vector3Like>
Eigen::Matrix<typename Vector3Like::Scalar,3,3,0>
computeVinv(const Eigen::MatrixBase<Vector3Like> & v3)
{
typedef typename Vector3Like::Scalar Scalar;
typedef Eigen::Matrix<Scalar,3,3,0> ReturnType;
typedef ReturnType Matrix3;
Scalar t2 = v3.squaredNorm();
const Scalar t = pinocchio::math::sqrt(t2);
Scalar alpha, beta;
if (t < 1e-4)
{
alpha = Scalar(1) - t2/Scalar(12) - t2*t2/Scalar(720);
beta = Scalar(1)/Scalar(12) + t2/Scalar(720);
}
else
{
Scalar st,ct; pinocchio::SINCOS(t,&st,&ct);
alpha = t*st/(Scalar(2)*(Scalar(1)-ct));
beta = Scalar(1)/t2 - st/(Scalar(2)*t*(Scalar(1)-ct));
}
Matrix3 Vinv
= alpha * Matrix3::Identity()
- 0.5 * pinocchio::skew(v3)
+ beta * v3 * v3.transpose();
return Vinv;
}
BOOST_AUTO_TEST_CASE(test_log3)
{
using CppAD::AD;
using CppAD::NearEqual;
typedef double Scalar;
typedef AD<Scalar> ADScalar;
typedef pinocchio::SE3Tpl<Scalar> SE3;
typedef pinocchio::MotionTpl<Scalar> Motion;
typedef pinocchio::SE3Tpl<ADScalar> ADSE3;
typedef pinocchio::MotionTpl<ADScalar> ADMotion;
Motion v(Motion::Zero());
SE3 M(SE3::Random()); M.translation().setZero();
SE3::Matrix3 rot_next = M.rotation() * pinocchio::exp3(v.angular());
SE3::Matrix3 Jlog3;
pinocchio::Jlog3(M.rotation(), Jlog3);
typedef Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<ADScalar,Eigen::Dynamic,1> ADVector;
ADMotion ad_v(v.cast<ADScalar>());
ADSE3 ad_M(M.cast<ADScalar>());
ADSE3::Matrix3 rot = ad_M.rotation();
ADVector X(3);
X = ad_v.angular();
CppAD::Independent(X);
ADMotion::Vector3 X_ = X;
ADSE3::Matrix3 ad_rot_next = rot * pinocchio::exp3(X_);
ADMotion::Vector3 log_R_next = pinocchio::log3(ad_rot_next);
ADVector Y(3);
Y = log_R_next;
CppAD::ADFun<Scalar> map(X,Y);
CPPAD_TESTVECTOR(Scalar) x(3);
Eigen::Map<Motion::Vector3>(x.data()).setZero();
CPPAD_TESTVECTOR(Scalar) nu_next_vec = map.Forward(0,x);
Motion::Vector3 nu_next(Eigen::Map<Motion::Vector3>(nu_next_vec.data()));
SE3::Matrix3 rot_next_from_map = pinocchio::exp3(nu_next);
CPPAD_TESTVECTOR(Scalar) jac = map.Jacobian(x);
Matrix jacobian = Eigen::Map<PINOCCHIO_EIGEN_PLAIN_ROW_MAJOR_TYPE(Matrix)>(jac.data(),3,3);
BOOST_CHECK(rot_next_from_map.isApprox(rot_next));
BOOST_CHECK(jacobian.isApprox(Jlog3));
}
BOOST_AUTO_TEST_CASE(test_explog_translation)
{
using CppAD::AD;
using CppAD::NearEqual;
typedef double Scalar;
typedef AD<Scalar> ADScalar;
typedef pinocchio::SE3Tpl<Scalar> SE3;
typedef pinocchio::MotionTpl<Scalar> Motion;
typedef pinocchio::SE3Tpl<ADScalar> ADSE3;
typedef pinocchio::MotionTpl<ADScalar> ADMotion;
Motion v(Motion::Zero());
SE3 M(SE3::Random()); //M.rotation().setIdentity();
{
Motion::Vector3 v3_test; v3_test.setRandom();
SE3::Matrix3 V = computeV(v3_test);
SE3::Matrix3 Vinv = computeVinv(v3_test);
BOOST_CHECK((V*Vinv).isIdentity());
}
SE3 M_next = M * pinocchio::exp6(v);
// BOOST_CHECK(M_next.rotation().isIdentity());
typedef Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<ADScalar,Eigen::Dynamic,1> ADVector;
ADMotion ad_v(v.cast<ADScalar>());
ADSE3 ad_M(M.cast<ADScalar>());
ADVector X(6);
X = ad_v.toVector();
CppAD::Independent(X);
ADMotion::Vector6 X_ = X;
pinocchio::MotionRef<ADMotion::Vector6> ad_v_ref(X_);
ADSE3 ad_M_next = ad_M * pinocchio::exp6(ad_v_ref);
ADVector Y(6);
Y.head<3>() = ad_M_next.translation();
Y.tail<3>() = ad_M.translation() + ad_M.rotation() * computeV(ad_v_ref.angular()) * ad_v_ref.linear();
CppAD::ADFun<Scalar> map(X,Y);
CPPAD_TESTVECTOR(Scalar) x((size_t)X.size());
Eigen::Map<Motion::Vector6>(x.data()).setZero();
CPPAD_TESTVECTOR(Scalar) translation_vec = map.Forward(0,x);
Motion::Vector3 translation1(Eigen::Map<Motion::Vector3>(translation_vec.data()));
Motion::Vector3 translation2(Eigen::Map<Motion::Vector3>(translation_vec.data()+3));
BOOST_CHECK(translation1.isApprox(M_next.translation()));
BOOST_CHECK(translation2.isApprox(M_next.translation()));
CPPAD_TESTVECTOR(Scalar) jac = map.Jacobian(x);
Matrix jacobian = Eigen::Map<PINOCCHIO_EIGEN_PLAIN_ROW_MAJOR_TYPE(Matrix)>(jac.data(),Y.size(),X.size());
BOOST_CHECK(jacobian.topLeftCorner(3,3).isApprox(M.rotation()));
}
BOOST_AUTO_TEST_CASE(test_explog)
{
using CppAD::AD;
using CppAD::NearEqual;
typedef double Scalar;
typedef AD<Scalar> ADScalar;
typedef pinocchio::SE3Tpl<Scalar> SE3;
typedef pinocchio::MotionTpl<Scalar> Motion;
typedef pinocchio::SE3Tpl<ADScalar> ADSE3;
typedef pinocchio::MotionTpl<ADScalar> ADMotion;
Motion v(Motion::Zero());
SE3 M(SE3::Random()); //M.translation().setZero();
SE3::Matrix6 Jlog6;
pinocchio::Jlog6(M, Jlog6);
typedef Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<ADScalar,Eigen::Dynamic,1> ADVector;
ADMotion ad_v(v.cast<ADScalar>());
ADSE3 ad_M(M.cast<ADScalar>());
ADVector X(6);
X.segment<3>(Motion::LINEAR) = ad_v.linear();
X.segment<3>(Motion::ANGULAR) = ad_v.angular();
CppAD::Independent(X);
ADMotion::Vector6 X_ = X;
pinocchio::MotionRef< ADMotion::Vector6> v_X(X_);
ADSE3 ad_M_next = ad_M * pinocchio::exp6(v_X);
ADMotion ad_log_M_next = pinocchio::log6(ad_M_next);
ADVector Y(6);
Y.segment<3>(Motion::LINEAR) = ad_log_M_next.linear();
Y.segment<3>(Motion::ANGULAR) = ad_log_M_next.angular();
CppAD::ADFun<Scalar> map(X,Y);
CPPAD_TESTVECTOR(Scalar) x(6);
Eigen::Map<Motion::Vector6>(x.data()).setZero();
CPPAD_TESTVECTOR(Scalar) nu_next_vec = map.Forward(0,x);
Motion nu_next(Eigen::Map<Motion::Vector6>(nu_next_vec.data()));
CPPAD_TESTVECTOR(Scalar) jac = map.Jacobian(x);
Matrix jacobian = Eigen::Map<PINOCCHIO_EIGEN_PLAIN_ROW_MAJOR_TYPE(Matrix)>(jac.data(),6,6);
// Check using finite differencies
Motion dv(Motion::Zero());
typedef Eigen::Matrix<Scalar,6,6> Matrix6;
Matrix6 Jlog6_fd(Matrix6::Zero());
Motion v_plus, v0(log6(M));
const Scalar eps = 1e-8;
for(int k = 0; k < 6; ++k)
{
dv.toVector()[k] = eps;
SE3 M_plus = M * exp6(dv);
v_plus = log6(M_plus);
Jlog6_fd.col(k) = (v_plus-v0).toVector()/eps;
dv.toVector()[k] = 0;
}
SE3::Matrix6 Jlog6_analytic;
pinocchio::Jlog6(M, Jlog6_analytic);
BOOST_CHECK(Jlog6.isApprox(Jlog6_analytic));
BOOST_CHECK(Jlog6_fd.isApprox(Jlog6,pinocchio::math::sqrt(eps)));
}
BOOST_AUTO_TEST_SUITE_END()