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// |
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// Copyright (c) 2016-2021 CNRS INRIA |
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// Copyright (c) 2015 Wandercraft, 86 rue de Paris 91400 Orsay, France. |
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// |
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#include "pinocchio/spatial/explog.hpp" |
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#include <iostream> |
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#include <boost/test/unit_test.hpp> |
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#include <boost/utility/binary.hpp> |
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#include "utils/macros.hpp" |
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using namespace pinocchio; |
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BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE) |
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BOOST_AUTO_TEST_CASE(exp) |
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{ |
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SE3 M(SE3::Random()); |
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Motion v(Motion::Random()); |
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v.linear().setZero(); |
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SE3::Matrix3 R = exp3(v.angular()); |
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BOOST_CHECK( |
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R.isApprox(Eigen::AngleAxis<double>(v.angular().norm(), v.angular().normalized()).matrix())); |
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SE3::Matrix3 R0 = exp3(SE3::Vector3::Zero()); |
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BOOST_CHECK(R0.isIdentity()); |
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// check the NAN case |
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#ifdef NDEBUG |
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Motion::Vector3 vec3_nan(Motion::Vector3::Constant(NAN)); |
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SE3::Matrix3 R_nan = exp3(vec3_nan); |
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BOOST_CHECK(R_nan != R_nan); |
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#endif |
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M = exp6(v); |
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BOOST_CHECK(R.isApprox(M.rotation())); |
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Eigen::Matrix<double, 7, 1> q0; |
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q0 << 0., 0., 0., 0., 0., 0., 1.; |
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Eigen::Matrix<double, 7, 1> q = quaternion::exp6(v); |
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Eigen::Quaterniond quat0(q.tail<4>()); |
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BOOST_CHECK(R.isApprox(quat0.matrix())); |
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// check the NAN case |
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#ifdef NDEBUG |
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Motion::Vector6 vec6_nan(Motion::Vector6::Constant(NAN)); |
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SE3 M_nan = exp6(vec6_nan); |
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BOOST_CHECK(M_nan != M_nan); |
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#endif |
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R = exp3(SE3::Vector3::Zero()); |
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BOOST_CHECK(R.isIdentity()); |
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// Quaternion |
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Eigen::Quaterniond quat; |
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quaternion::exp3(v.angular(), quat); |
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BOOST_CHECK(quat.toRotationMatrix().isApprox(M.rotation())); |
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quaternion::exp3(SE3::Vector3::Zero(), quat); |
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BOOST_CHECK(quat.toRotationMatrix().isIdentity()); |
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BOOST_CHECK(quat.vec().isZero() && quat.coeffs().tail<1>().isOnes()); |
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// Check QuaternionMap |
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Eigen::Vector4d vec4; |
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Eigen::QuaternionMapd quat_map(vec4.data()); |
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quaternion::exp3(v.angular(), quat_map); |
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BOOST_CHECK(quat_map.toRotationMatrix().isApprox(M.rotation())); |
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} |
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BOOST_AUTO_TEST_CASE(renorm_rotation) |
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{ |
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SE3 M0, M1; |
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SE3::Matrix3 R0, R1; |
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SE3::Matrix3 R_normed; |
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SE3::Matrix3 Id(SE3::Matrix3::Identity()); |
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SE3::Vector3 vals; |
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double tr0, tr; |
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const size_t num_tries = 20; |
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for (size_t i = 0; i < num_tries; i++) |
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{ |
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M0.setRandom(); |
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M1 = M0.actInv(M0); |
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R1 = M1.rotation(); |
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R_normed = pinocchio::renormalize_rotation_matrix(R1); |
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BOOST_CHECK((R_normed.transpose() * R_normed).isApprox(Id)); |
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tr0 = R1.trace(); |
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tr = R_normed.trace(); |
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vals = 2. * R_normed.diagonal().array() - tr + 1.; |
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} |
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} |
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BOOST_AUTO_TEST_CASE(log) |
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{ |
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SE3 M(SE3::Identity()); |
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Motion v(Motion::Random()); |
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v.linear().setZero(); |
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SE3::Vector3 omega = log3(M.rotation()); |
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BOOST_CHECK(omega.isZero()); |
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// check the NAN case |
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#ifdef NDEBUG |
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SE3::Matrix3 mat3_nan(SE3::Matrix3::Constant(NAN)); |
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SE3::Vector3 omega_nan = log3(mat3_nan); |
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BOOST_CHECK(omega_nan != omega_nan); |
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#endif |
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M.setRandom(); |
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M.translation().setZero(); |
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v = log6(M); |
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omega = log3(M.rotation()); |
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BOOST_CHECK(omega.isApprox(v.angular())); |
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// check the NAN case |
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#ifdef NDEBUG |
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SE3::Matrix4 mat4_nan(SE3::Matrix4::Constant(NAN)); |
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Motion::Vector6 v_nan = log6(mat4_nan); |
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BOOST_CHECK(v_nan != v_nan); |
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#endif |
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// Quaternion |
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Eigen::Quaterniond quat(SE3::Matrix3::Identity()); |
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omega = quaternion::log3(quat); |
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BOOST_CHECK(omega.isZero()); |
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for (int k = 0; k < 1e3; ++k) |
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{ |
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SE3::Vector3 w; |
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w.setRandom(); |
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quaternion::exp3(w, quat); |
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SE3::Matrix3 rot = exp3(w); |
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BOOST_CHECK(quat.toRotationMatrix().isApprox(rot)); |
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double theta; |
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omega = quaternion::log3(quat, theta); |
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const double PI_value = PI<double>(); |
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BOOST_CHECK(omega.norm() <= PI_value); |
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double theta_ref; |
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SE3::Vector3 omega_ref = log3(quat.toRotationMatrix(), theta_ref); |
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BOOST_CHECK(omega.isApprox(omega_ref)); |
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} |
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// Check QuaternionMap |
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Eigen::Vector4d vec4; |
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Eigen::QuaternionMapd quat_map(vec4.data()); |
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quat_map = SE3::Random().rotation(); |
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BOOST_CHECK(quaternion::log3(quat_map).isApprox(log3(quat_map.toRotationMatrix()))); |
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} |
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BOOST_AUTO_TEST_CASE(explog3) |
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{ |
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SE3 M(SE3::Random()); |
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SE3::Matrix3 M_res = exp3(log3(M.rotation())); |
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BOOST_CHECK(M_res.isApprox(M.rotation())); |
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Motion::Vector3 v; |
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v.setRandom(); |
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Motion::Vector3 v_res = log3(exp3(v)); |
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BOOST_CHECK(v_res.isApprox(v)); |
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} |
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BOOST_AUTO_TEST_CASE(explog3_quaternion) |
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{ |
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SE3 M(SE3::Random()); |
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Eigen::Quaterniond quat; |
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quat = M.rotation(); |
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Eigen::Quaterniond quat_res; |
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quaternion::exp3(quaternion::log3(quat), quat_res); |
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BOOST_CHECK(quat_res.isApprox(quat) || quat_res.coeffs().isApprox(-quat.coeffs())); |
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Motion::Vector3 v; |
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v.setRandom(); |
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quaternion::exp3(v, quat); |
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BOOST_CHECK(quaternion::log3(quat).isApprox(v)); |
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SE3::Matrix3 R_next = M.rotation() * exp3(v); |
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Motion::Vector3 v_est = log3(M.rotation().transpose() * R_next); |
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BOOST_CHECK(v_est.isApprox(v)); |
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SE3::Quaternion quat_v; |
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quaternion::exp3(v, quat_v); |
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SE3::Quaternion quat_next = quat * quat_v; |
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v_est = quaternion::log3(quat.conjugate() * quat_next); |
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BOOST_CHECK(v_est.isApprox(v)); |
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} |
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BOOST_AUTO_TEST_CASE(Jlog3_fd) |
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{ |
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SE3 M(SE3::Random()); |
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SE3::Matrix3 R(M.rotation()); |
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PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
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PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
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SE3::Matrix3 Jfd, Jlog; |
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Jlog3(R, Jlog); |
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PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
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Jfd.setZero(); |
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Motion::Vector3 dR; |
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dR.setZero(); |
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const double eps = 1e-8; |
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for (int i = 0; i < 3; ++i) |
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{ |
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dR[i] = eps; |
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SE3::Matrix3 R_dR_plus = R * exp3(dR); |
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SE3::Matrix3 R_dR_minus = R * exp3(-dR); |
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Jfd.col(i) = (log3(R_dR_plus) - log3(R_dR_minus)) / (2 * eps); |
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dR[i] = 0; |
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} |
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BOOST_CHECK(Jfd.isApprox(Jlog, std::sqrt(eps))); |
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} |
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BOOST_AUTO_TEST_CASE(Jexp3_fd) |
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{ |
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SE3 M(SE3::Random()); |
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SE3::Matrix3 R(M.rotation()); |
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Motion::Vector3 v = log3(R); |
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PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
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PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
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SE3::Matrix3 Jexp_fd, Jexp; |
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Jexp3(Motion::Vector3::Zero(), Jexp); |
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BOOST_CHECK(Jexp.isIdentity()); |
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Jexp3(v, Jexp); |
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PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
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Motion::Vector3 dv; |
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dv.setZero(); |
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const double eps = 1e-3; |
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for (int i = 0; i < 3; ++i) |
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{ |
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dv[i] = eps; |
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SE3::Matrix3 R_next = exp3(v + dv); |
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SE3::Matrix3 R_prev = exp3(v - dv); |
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SE3::Matrix3 Rpn = R_prev.transpose() * R_next; |
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Jexp_fd.col(i) = log3(Rpn) / (2. * eps); |
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dv[i] = 0; |
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} |
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BOOST_CHECK(Jexp_fd.isApprox(Jexp, std::sqrt(eps))); |
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} |
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template<typename QuaternionLike, typename Matrix43Like> |
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void Jexp3QuatLocal( |
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const Eigen::QuaternionBase<QuaternionLike> & quat, const Eigen::MatrixBase<Matrix43Like> & Jexp) |
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{ |
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Matrix43Like & Jout = PINOCCHIO_EIGEN_CONST_CAST(Matrix43Like, Jexp); |
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skew(0.5 * quat.vec(), Jout.template topRows<3>()); |
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Jout.template topRows<3>().diagonal().array() += 0.5 * quat.w(); |
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Jout.template bottomRows<1>() = -0.5 * quat.vec().transpose(); |
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} |
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BOOST_AUTO_TEST_CASE(Jexp3_quat_fd) |
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{ |
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typedef double Scalar; |
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SE3::Vector3 w; |
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w.setRandom(); |
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SE3::Quaternion quat; |
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quaternion::exp3(w, quat); |
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typedef Eigen::Matrix<Scalar, 4, 3> Matrix43; |
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PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
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PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
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Matrix43 Jexp3, Jexp3_fd; |
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quaternion::Jexp3CoeffWise(w, Jexp3); |
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PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
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SE3::Vector3 dw; |
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dw.setZero(); |
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const double eps = 1e-8; |
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for (int i = 0; i < 3; ++i) |
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{ |
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dw[i] = eps; |
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SE3::Quaternion quat_plus; |
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quaternion::exp3(w + dw, quat_plus); |
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Jexp3_fd.col(i) = (quat_plus.coeffs() - quat.coeffs()) / eps; |
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dw[i] = 0; |
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} |
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BOOST_CHECK(Jexp3.isApprox(Jexp3_fd, sqrt(eps))); |
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PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
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PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
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SE3::Matrix3 Jlog; |
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pinocchio::Jlog3(quat.toRotationMatrix(), Jlog); |
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Matrix43 Jexp_quat_local; |
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Jexp3QuatLocal(quat, Jexp_quat_local); |
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PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
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Matrix43 Jcompositon = Jexp3 * Jlog; |
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BOOST_CHECK(Jcompositon.isApprox(Jexp_quat_local)); |
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// std::cout << "Jcompositon\n" << Jcompositon << std::endl; |
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// std::cout << "Jexp_quat_local\n" << Jexp_quat_local << std::endl; |
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// Arount zero |
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w.setZero(); |
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w.fill(1e-6); |
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quaternion::exp3(w, quat); |
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quaternion::Jexp3CoeffWise(w, Jexp3); |
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for (int i = 0; i < 3; ++i) |
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{ |
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dw[i] = eps; |
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SE3::Quaternion quat_plus; |
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quaternion::exp3(w + dw, quat_plus); |
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Jexp3_fd.col(i) = (quat_plus.coeffs() - quat.coeffs()) / eps; |
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dw[i] = 0; |
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} |
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BOOST_CHECK(Jexp3.isApprox(Jexp3_fd, sqrt(eps))); |
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} |
| 321 |
|
|
|
| 322 |
|
✗ |
BOOST_AUTO_TEST_CASE(Jexp3_quat) |
| 323 |
|
|
{ |
| 324 |
|
✗ |
SE3 M(SE3::Random()); |
| 325 |
|
✗ |
SE3::Quaternion quat(M.rotation()); |
| 326 |
|
|
|
| 327 |
|
✗ |
Motion dv(Motion::Zero()); |
| 328 |
|
✗ |
const double eps = 1e-8; |
| 329 |
|
|
|
| 330 |
|
|
typedef Eigen::Matrix<double, 7, 6> Matrix76; |
| 331 |
|
✗ |
Matrix76 Jexp6_fd, Jexp6_quat; |
| 332 |
|
✗ |
Jexp6_quat.setZero(); |
| 333 |
|
|
typedef Eigen::Matrix<double, 4, 3> Matrix43; |
| 334 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
| 335 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
| 336 |
|
✗ |
Matrix43 Jexp3_quat; |
| 337 |
|
✗ |
Jexp3QuatLocal(quat, Jexp3_quat); |
| 338 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
| 339 |
|
✗ |
SE3 M_next; |
| 340 |
|
|
|
| 341 |
|
✗ |
Jexp6_quat.middleRows<3>(Motion::LINEAR).middleCols<3>(Motion::LINEAR) = M.rotation(); |
| 342 |
|
✗ |
Jexp6_quat.middleRows<4>(Motion::ANGULAR).middleCols<3>(Motion::ANGULAR) = |
| 343 |
|
✗ |
Jexp3_quat; // * Jlog6_SE3.middleRows<3>(Motion::ANGULAR); |
| 344 |
|
✗ |
for (int i = 0; i < 6; ++i) |
| 345 |
|
|
{ |
| 346 |
|
✗ |
dv.toVector()[i] = eps; |
| 347 |
|
✗ |
M_next = M * exp6(dv); |
| 348 |
|
✗ |
const SE3::Quaternion quat_next(M_next.rotation()); |
| 349 |
|
✗ |
Jexp6_fd.middleRows<3>(Motion::LINEAR).col(i) = (M_next.translation() - M.translation()) / eps; |
| 350 |
|
✗ |
Jexp6_fd.middleRows<4>(Motion::ANGULAR).col(i) = (quat_next.coeffs() - quat.coeffs()) / eps; |
| 351 |
|
✗ |
dv.toVector()[i] = 0.; |
| 352 |
|
|
} |
| 353 |
|
|
|
| 354 |
|
✗ |
BOOST_CHECK(Jexp6_quat.isApprox(Jexp6_fd, sqrt(eps))); |
| 355 |
|
|
} |
| 356 |
|
|
|
| 357 |
|
✗ |
BOOST_AUTO_TEST_CASE(Jexplog3) |
| 358 |
|
|
{ |
| 359 |
|
✗ |
Motion v(Motion::Random()); |
| 360 |
|
|
|
| 361 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
| 362 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
| 363 |
|
✗ |
Eigen::Matrix3d R(exp3(v.angular())), Jexp, Jlog; |
| 364 |
|
✗ |
Jexp3(v.angular(), Jexp); |
| 365 |
|
✗ |
Jlog3(R, Jlog); |
| 366 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
| 367 |
|
|
|
| 368 |
|
✗ |
BOOST_CHECK((Jlog * Jexp).isIdentity()); |
| 369 |
|
|
|
| 370 |
|
✗ |
SE3 M(SE3::Random()); |
| 371 |
|
✗ |
R = M.rotation(); |
| 372 |
|
✗ |
v.angular() = log3(R); |
| 373 |
|
✗ |
Jlog3(R, Jlog); |
| 374 |
|
✗ |
Jexp3(v.angular(), Jexp); |
| 375 |
|
|
|
| 376 |
|
✗ |
BOOST_CHECK((Jexp * Jlog).isIdentity()); |
| 377 |
|
|
} |
| 378 |
|
|
|
| 379 |
|
✗ |
BOOST_AUTO_TEST_CASE(Jlog3_quat) |
| 380 |
|
|
{ |
| 381 |
|
✗ |
SE3::Vector3 w; |
| 382 |
|
✗ |
w.setRandom(); |
| 383 |
|
✗ |
SE3::Quaternion quat; |
| 384 |
|
✗ |
quaternion::exp3(w, quat); |
| 385 |
|
|
|
| 386 |
|
✗ |
SE3::Matrix3 R(quat.toRotationMatrix()); |
| 387 |
|
|
|
| 388 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
| 389 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
| 390 |
|
✗ |
SE3::Matrix3 res, res_ref; |
| 391 |
|
✗ |
quaternion::Jlog3(quat, res); |
| 392 |
|
✗ |
Jlog3(R, res_ref); |
| 393 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
| 394 |
|
|
|
| 395 |
|
✗ |
BOOST_CHECK(res.isApprox(res_ref)); |
| 396 |
|
|
} |
| 397 |
|
|
|
| 398 |
|
✗ |
BOOST_AUTO_TEST_CASE(explog6) |
| 399 |
|
|
{ |
| 400 |
|
✗ |
SE3 M(SE3::Random()); |
| 401 |
|
✗ |
SE3 M_res = exp6(log6(M)); |
| 402 |
|
✗ |
BOOST_CHECK(M_res.isApprox(M)); |
| 403 |
|
|
|
| 404 |
|
✗ |
Motion v(Motion::Random()); |
| 405 |
|
✗ |
Motion v_res = log6(exp6(v)); |
| 406 |
|
✗ |
BOOST_CHECK(v_res.toVector().isApprox(v.toVector())); |
| 407 |
|
|
} |
| 408 |
|
|
|
| 409 |
|
✗ |
BOOST_AUTO_TEST_CASE(Jlog6_fd) |
| 410 |
|
|
{ |
| 411 |
|
✗ |
SE3 M(SE3::Random()); |
| 412 |
|
|
|
| 413 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
| 414 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
| 415 |
|
✗ |
SE3::Matrix6 Jfd, Jlog; |
| 416 |
|
✗ |
Jlog6(M, Jlog); |
| 417 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
| 418 |
|
✗ |
Jfd.setZero(); |
| 419 |
|
|
|
| 420 |
|
✗ |
Motion dM; |
| 421 |
|
✗ |
dM.setZero(); |
| 422 |
|
✗ |
double step = 1e-8; |
| 423 |
|
✗ |
for (int i = 0; i < 6; ++i) |
| 424 |
|
|
{ |
| 425 |
|
✗ |
dM.toVector()[i] = step; |
| 426 |
|
✗ |
SE3 M_dM = M * exp6(dM); |
| 427 |
|
✗ |
Jfd.col(i) = (log6(M_dM).toVector() - log6(M).toVector()) / step; |
| 428 |
|
✗ |
dM.toVector()[i] = 0; |
| 429 |
|
|
} |
| 430 |
|
|
|
| 431 |
|
✗ |
BOOST_CHECK(Jfd.isApprox(Jlog, sqrt(step))); |
| 432 |
|
|
|
| 433 |
|
✗ |
SE3::Matrix6 Jlog2 = Jlog6(M); |
| 434 |
|
✗ |
BOOST_CHECK(Jlog2.isApprox(Jlog)); |
| 435 |
|
|
} |
| 436 |
|
|
|
| 437 |
|
✗ |
BOOST_AUTO_TEST_CASE(Jlog6_singular) |
| 438 |
|
|
{ |
| 439 |
|
✗ |
for (size_t i = 0; i < 15; i++) |
| 440 |
|
|
{ |
| 441 |
|
✗ |
SE3 M0; |
| 442 |
|
✗ |
if (i == 0) |
| 443 |
|
|
{ |
| 444 |
|
✗ |
M0 = SE3::Identity(); |
| 445 |
|
|
} |
| 446 |
|
|
else |
| 447 |
|
|
{ |
| 448 |
|
✗ |
M0 = SE3::Random(); |
| 449 |
|
|
} |
| 450 |
|
✗ |
SE3 dM(M0.actInv(M0)); |
| 451 |
|
|
|
| 452 |
|
✗ |
BOOST_CHECK(dM.isApprox(SE3::Identity())); |
| 453 |
|
✗ |
SE3::Matrix6 J0(SE3::Matrix6::Identity()); |
| 454 |
|
|
|
| 455 |
|
✗ |
SE3::Matrix6 J_val = Jlog6(dM); |
| 456 |
|
✗ |
BOOST_CHECK(J0.isApprox(J_val)); |
| 457 |
|
|
} |
| 458 |
|
|
} |
| 459 |
|
|
|
| 460 |
|
✗ |
BOOST_AUTO_TEST_CASE(Jexp6_fd) |
| 461 |
|
|
{ |
| 462 |
|
✗ |
SE3 M(SE3::Random()); |
| 463 |
|
|
|
| 464 |
|
✗ |
const Motion v = log6(M); |
| 465 |
|
|
|
| 466 |
|
✗ |
SE3::Matrix6 Jexp_fd, Jexp; |
| 467 |
|
|
|
| 468 |
|
✗ |
Jexp6(Motion::Zero(), Jexp); |
| 469 |
|
✗ |
BOOST_CHECK(Jexp.isIdentity()); |
| 470 |
|
|
|
| 471 |
|
✗ |
Jexp6(v, Jexp); |
| 472 |
|
|
|
| 473 |
|
✗ |
Motion::Vector6 dv; |
| 474 |
|
✗ |
dv.setZero(); |
| 475 |
|
✗ |
const double eps = 1e-8; |
| 476 |
|
✗ |
for (int i = 0; i < 6; ++i) |
| 477 |
|
|
{ |
| 478 |
|
✗ |
dv[i] = eps; |
| 479 |
|
✗ |
SE3 M_next = exp6(v + Motion(dv)); |
| 480 |
|
✗ |
Jexp_fd.col(i) = log6(M.actInv(M_next)).toVector() / eps; |
| 481 |
|
✗ |
dv[i] = 0; |
| 482 |
|
|
} |
| 483 |
|
✗ |
BOOST_CHECK(Jexp_fd.isApprox(Jexp, std::sqrt(eps))); |
| 484 |
|
|
|
| 485 |
|
✗ |
SE3::Matrix6 Jexp2 = Jexp6(v); |
| 486 |
|
✗ |
BOOST_CHECK(Jexp2.isApprox(Jexp)); |
| 487 |
|
|
} |
| 488 |
|
|
|
| 489 |
|
✗ |
BOOST_AUTO_TEST_CASE(Jlog6_of_product_fd) |
| 490 |
|
|
{ |
| 491 |
|
✗ |
SE3 Ma(SE3::Random()); |
| 492 |
|
✗ |
SE3 Mb(SE3::Random()); |
| 493 |
|
|
|
| 494 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH |
| 495 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED |
| 496 |
|
✗ |
SE3::Matrix6 Jlog, Ja, Jb, Jfda, Jfdb; |
| 497 |
|
✗ |
Jlog6(Ma.inverse() * Mb, Jlog); |
| 498 |
|
|
PINOCCHIO_COMPILER_DIAGNOSTIC_POP |
| 499 |
|
✗ |
Ja = -Jlog * (Ma.inverse() * Mb).toActionMatrixInverse(); |
| 500 |
|
✗ |
Jb = Jlog; |
| 501 |
|
✗ |
Jfda.setZero(); |
| 502 |
|
✗ |
Jfdb.setZero(); |
| 503 |
|
|
|
| 504 |
|
✗ |
Motion dM; |
| 505 |
|
✗ |
dM.setZero(); |
| 506 |
|
✗ |
double step = 1e-8; |
| 507 |
|
✗ |
for (int i = 0; i < 6; ++i) |
| 508 |
|
|
{ |
| 509 |
|
✗ |
dM.toVector()[i] = step; |
| 510 |
|
✗ |
Jfda.col(i) = |
| 511 |
|
✗ |
(log6((Ma * exp6(dM)).inverse() * Mb).toVector() - log6(Ma.inverse() * Mb).toVector()) / step; |
| 512 |
|
✗ |
Jfdb.col(i) = |
| 513 |
|
✗ |
(log6(Ma.inverse() * Mb * exp6(dM)).toVector() - log6(Ma.inverse() * Mb).toVector()) / step; |
| 514 |
|
✗ |
dM.toVector()[i] = 0; |
| 515 |
|
|
} |
| 516 |
|
|
|
| 517 |
|
✗ |
BOOST_CHECK(Jfda.isApprox(Ja, sqrt(step))); |
| 518 |
|
✗ |
BOOST_CHECK(Jfdb.isApprox(Jb, sqrt(step))); |
| 519 |
|
|
} |
| 520 |
|
|
|
| 521 |
|
✗ |
BOOST_AUTO_TEST_CASE(Jexplog6) |
| 522 |
|
|
{ |
| 523 |
|
✗ |
Motion v(Motion::Random()); |
| 524 |
|
|
|
| 525 |
|
✗ |
SE3 M(exp6(v)); |
| 526 |
|
|
{ |
| 527 |
|
✗ |
Eigen::Matrix<double, 6, 6, Eigen::RowMajor> Jexp, Jlog; |
| 528 |
|
✗ |
Jexp6(v, Jexp); |
| 529 |
|
✗ |
Jlog6(M, Jlog); |
| 530 |
|
|
|
| 531 |
|
✗ |
BOOST_CHECK((Jlog * Jexp).isIdentity()); |
| 532 |
|
|
} |
| 533 |
|
|
|
| 534 |
|
✗ |
M.setRandom(); |
| 535 |
|
|
|
| 536 |
|
✗ |
v = log6(M); |
| 537 |
|
|
{ |
| 538 |
|
✗ |
Eigen::Matrix<double, 6, 6> Jexp, Jlog; |
| 539 |
|
✗ |
Jlog6(M, Jlog); |
| 540 |
|
✗ |
Jexp6(v, Jexp); |
| 541 |
|
|
|
| 542 |
|
✗ |
BOOST_CHECK((Jexp * Jlog).isIdentity()); |
| 543 |
|
|
} |
| 544 |
|
|
} |
| 545 |
|
|
|
| 546 |
|
✗ |
BOOST_AUTO_TEST_CASE(Hlog3_fd) |
| 547 |
|
|
{ |
| 548 |
|
|
typedef SE3::Vector3 Vector3; |
| 549 |
|
|
typedef SE3::Matrix3 Matrix3; |
| 550 |
|
✗ |
SE3::Quaternion q; |
| 551 |
|
✗ |
quaternion::uniformRandom(q); |
| 552 |
|
✗ |
Matrix3 R(q.matrix()); |
| 553 |
|
|
|
| 554 |
|
|
// Hlog3(R, v) returns the matrix H * v |
| 555 |
|
|
// We check that H * e_k matches the finite difference of Hlog3(R, e_k) |
| 556 |
|
✗ |
Vector3 dR; |
| 557 |
|
✗ |
dR.setZero(); |
| 558 |
|
✗ |
double step = 1e-8; |
| 559 |
|
✗ |
for (int k = 0; k < 3; ++k) |
| 560 |
|
|
{ |
| 561 |
|
✗ |
Vector3 e_k(Vector3::Zero()); |
| 562 |
|
✗ |
e_k[k] = 1.; |
| 563 |
|
|
|
| 564 |
|
✗ |
Matrix3 Hlog_e_k; |
| 565 |
|
✗ |
Hlog3(R, e_k, Hlog_e_k); |
| 566 |
|
|
|
| 567 |
|
✗ |
Matrix3 R_dR = R * exp3(step * e_k); |
| 568 |
|
✗ |
Matrix3 Jlog_R, Jlog_R_dR; |
| 569 |
|
✗ |
Jlog3(R, Jlog_R); |
| 570 |
|
✗ |
Jlog3(R_dR, Jlog_R_dR); |
| 571 |
|
|
|
| 572 |
|
✗ |
Matrix3 Hlog_e_k_fd = (Jlog_R_dR - Jlog_R) / step; |
| 573 |
|
|
|
| 574 |
|
✗ |
BOOST_CHECK(Hlog_e_k.isApprox(Hlog_e_k_fd, sqrt(step))); |
| 575 |
|
|
} |
| 576 |
|
|
} |
| 577 |
|
|
|
| 578 |
|
✗ |
BOOST_AUTO_TEST_CASE(test_basic) |
| 579 |
|
|
{ |
| 580 |
|
|
typedef pinocchio::SE3::Vector3 Vector3; |
| 581 |
|
|
typedef pinocchio::SE3::Matrix3 Matrix3; |
| 582 |
|
|
typedef Eigen::Matrix4d Matrix4; |
| 583 |
|
|
typedef pinocchio::Motion::Vector6 Vector6; |
| 584 |
|
|
|
| 585 |
|
✗ |
const double EPSILON = 1e-12; |
| 586 |
|
|
|
| 587 |
|
|
// exp3 and log3. |
| 588 |
|
✗ |
Vector3 v3(Vector3::Random()); |
| 589 |
|
✗ |
Matrix3 R(pinocchio::exp3(v3)); |
| 590 |
|
✗ |
BOOST_CHECK(R.transpose().isApprox(R.inverse(), EPSILON)); |
| 591 |
|
✗ |
BOOST_CHECK_SMALL(R.determinant() - 1.0, EPSILON); |
| 592 |
|
✗ |
Vector3 v3FromLog(pinocchio::log3(R)); |
| 593 |
|
✗ |
BOOST_CHECK(v3.isApprox(v3FromLog, EPSILON)); |
| 594 |
|
|
|
| 595 |
|
|
// exp6 and log6. |
| 596 |
|
✗ |
pinocchio::Motion nu = pinocchio::Motion::Random(); |
| 597 |
|
✗ |
pinocchio::SE3 m = pinocchio::exp6(nu); |
| 598 |
|
✗ |
BOOST_CHECK(m.rotation().transpose().isApprox(m.rotation().inverse(), EPSILON)); |
| 599 |
|
✗ |
BOOST_CHECK_SMALL(m.rotation().determinant() - 1.0, EPSILON); |
| 600 |
|
✗ |
pinocchio::Motion nuFromLog(pinocchio::log6(m)); |
| 601 |
|
✗ |
BOOST_CHECK(nu.linear().isApprox(nuFromLog.linear(), EPSILON)); |
| 602 |
|
✗ |
BOOST_CHECK(nu.angular().isApprox(nuFromLog.angular(), EPSILON)); |
| 603 |
|
|
|
| 604 |
|
✗ |
Vector6 v6(Vector6::Random()); |
| 605 |
|
✗ |
pinocchio::SE3 m2(pinocchio::exp6(v6)); |
| 606 |
|
✗ |
BOOST_CHECK(m2.rotation().transpose().isApprox(m2.rotation().inverse(), EPSILON)); |
| 607 |
|
✗ |
BOOST_CHECK_SMALL(m2.rotation().determinant() - 1.0, EPSILON); |
| 608 |
|
✗ |
Matrix4 M = m2.toHomogeneousMatrix(); |
| 609 |
|
✗ |
pinocchio::Motion nu2FromLog(pinocchio::log6(M)); |
| 610 |
|
✗ |
Vector6 v6FromLog(nu2FromLog.toVector()); |
| 611 |
|
✗ |
BOOST_CHECK(v6.isApprox(v6FromLog, EPSILON)); |
| 612 |
|
|
} |
| 613 |
|
|
|
| 614 |
|
✗ |
BOOST_AUTO_TEST_CASE(test_SE3_interpolate) |
| 615 |
|
|
{ |
| 616 |
|
✗ |
SE3 A = SE3::Random(); |
| 617 |
|
✗ |
SE3 B = SE3::Random(); |
| 618 |
|
|
|
| 619 |
|
✗ |
SE3 A_bis = SE3::Interpolate(A, B, 0.); |
| 620 |
|
✗ |
BOOST_CHECK(A_bis.isApprox(A)); |
| 621 |
|
✗ |
SE3 B_bis = SE3::Interpolate(A, B, 1.); |
| 622 |
|
✗ |
BOOST_CHECK(B_bis.isApprox(B)); |
| 623 |
|
|
|
| 624 |
|
✗ |
A_bis = SE3::Interpolate(A, A, 1.); |
| 625 |
|
✗ |
BOOST_CHECK(A_bis.isApprox(A)); |
| 626 |
|
|
|
| 627 |
|
✗ |
B_bis = SE3::Interpolate(B, B, 1.); |
| 628 |
|
✗ |
BOOST_CHECK(B_bis.isApprox(B)); |
| 629 |
|
|
|
| 630 |
|
✗ |
SE3 C = SE3::Interpolate(A, B, 0.5); |
| 631 |
|
✗ |
SE3 D = SE3::Interpolate(B, A, 0.5); |
| 632 |
|
✗ |
BOOST_CHECK(D.isApprox(C)); |
| 633 |
|
|
} |
| 634 |
|
|
|
| 635 |
|
✗ |
BOOST_AUTO_TEST_CASE(test_Jlog6_robustness) |
| 636 |
|
|
{ |
| 637 |
|
✗ |
const int num_tests = 1e1; |
| 638 |
|
✗ |
for (int k = 0; k < num_tests; ++k) |
| 639 |
|
|
{ |
| 640 |
|
✗ |
const SE3 M = SE3::Random(); |
| 641 |
|
✗ |
SE3::Matrix6 res = Jlog6(M.actInv(M)); |
| 642 |
|
|
|
| 643 |
|
✗ |
BOOST_CHECK(res.isIdentity()); |
| 644 |
|
|
} |
| 645 |
|
|
} |
| 646 |
|
|
|
| 647 |
|
|
BOOST_AUTO_TEST_SUITE_END() |
| 648 |
|
|
|