| Directory: | ./ |
|---|---|
| File: | unittest/explog.cpp |
| Date: | 2025-02-12 21:03:38 |
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| Lines: | 385 | 385 | 100.0% |
| Branches: | 1662 | 3296 | 50.4% |
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| 1 | // | ||
| 2 | // Copyright (c) 2016-2021 CNRS INRIA | ||
| 3 | // Copyright (c) 2015 Wandercraft, 86 rue de Paris 91400 Orsay, France. | ||
| 4 | // | ||
| 5 | |||
| 6 | #include "pinocchio/spatial/explog.hpp" | ||
| 7 | |||
| 8 | #include <iostream> | ||
| 9 | #include <boost/test/unit_test.hpp> | ||
| 10 | #include <boost/utility/binary.hpp> | ||
| 11 | |||
| 12 | #include "utils/macros.hpp" | ||
| 13 | |||
| 14 | using namespace pinocchio; | ||
| 15 | |||
| 16 | BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE) | ||
| 17 | |||
| 18 |
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4 | BOOST_AUTO_TEST_CASE(exp) |
| 19 | { | ||
| 20 |
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2 | SE3 M(SE3::Random()); |
| 21 |
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2 | Motion v(Motion::Random()); |
| 22 |
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2 | v.linear().setZero(); |
| 23 | |||
| 24 |
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2 | SE3::Matrix3 R = exp3(v.angular()); |
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2 | BOOST_CHECK( |
| 26 | R.isApprox(Eigen::AngleAxis<double>(v.angular().norm(), v.angular().normalized()).matrix())); | ||
| 27 | |||
| 28 |
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2 | SE3::Matrix3 R0 = exp3(SE3::Vector3::Zero()); |
| 29 |
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2 | BOOST_CHECK(R0.isIdentity()); |
| 30 | |||
| 31 | // check the NAN case | ||
| 32 | #ifdef NDEBUG | ||
| 33 | Motion::Vector3 vec3_nan(Motion::Vector3::Constant(NAN)); | ||
| 34 | SE3::Matrix3 R_nan = exp3(vec3_nan); | ||
| 35 | BOOST_CHECK(R_nan != R_nan); | ||
| 36 | #endif | ||
| 37 | |||
| 38 |
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2 | M = exp6(v); |
| 39 | |||
| 40 |
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2 | BOOST_CHECK(R.isApprox(M.rotation())); |
| 41 | |||
| 42 |
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2 | Eigen::Matrix<double, 7, 1> q0; |
| 43 |
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2 | q0 << 0., 0., 0., 0., 0., 0., 1.; |
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2 | Eigen::Matrix<double, 7, 1> q = quaternion::exp6(v); |
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2 | Eigen::Quaterniond quat0(q.tail<4>()); |
| 46 |
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2 | BOOST_CHECK(R.isApprox(quat0.matrix())); |
| 47 | |||
| 48 | // check the NAN case | ||
| 49 | #ifdef NDEBUG | ||
| 50 | Motion::Vector6 vec6_nan(Motion::Vector6::Constant(NAN)); | ||
| 51 | SE3 M_nan = exp6(vec6_nan); | ||
| 52 | BOOST_CHECK(M_nan != M_nan); | ||
| 53 | #endif | ||
| 54 | |||
| 55 |
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2 | R = exp3(SE3::Vector3::Zero()); |
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2 | BOOST_CHECK(R.isIdentity()); |
| 57 | |||
| 58 | // Quaternion | ||
| 59 |
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2 | Eigen::Quaterniond quat; |
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2 | quaternion::exp3(v.angular(), quat); |
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2 | BOOST_CHECK(quat.toRotationMatrix().isApprox(M.rotation())); |
| 62 | |||
| 63 |
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2 | quaternion::exp3(SE3::Vector3::Zero(), quat); |
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2 | BOOST_CHECK(quat.toRotationMatrix().isIdentity()); |
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2 | BOOST_CHECK(quat.vec().isZero() && quat.coeffs().tail<1>().isOnes()); |
| 66 | |||
| 67 | // Check QuaternionMap | ||
| 68 |
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2 | Eigen::Vector4d vec4; |
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2 | Eigen::QuaternionMapd quat_map(vec4.data()); |
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2 | quaternion::exp3(v.angular(), quat_map); |
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2 | BOOST_CHECK(quat_map.toRotationMatrix().isApprox(M.rotation())); |
| 72 | 2 | } | |
| 73 | |||
| 74 |
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4 | BOOST_AUTO_TEST_CASE(renorm_rotation) |
| 75 | { | ||
| 76 |
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2 | SE3 M0, M1; |
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2 | SE3::Matrix3 R0, R1; |
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2 | SE3::Matrix3 R_normed; |
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2 | SE3::Matrix3 Id(SE3::Matrix3::Identity()); |
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2 | SE3::Vector3 vals; |
| 81 | double tr0, tr; | ||
| 82 | 2 | const size_t num_tries = 20; | |
| 83 | |||
| 84 |
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42 | for (size_t i = 0; i < num_tries; i++) |
| 85 | { | ||
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40 | M0.setRandom(); |
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40 | M1 = M0.actInv(M0); |
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40 | R1 = M1.rotation(); |
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40 | R_normed = pinocchio::renormalize_rotation_matrix(R1); |
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40 | BOOST_CHECK((R_normed.transpose() * R_normed).isApprox(Id)); |
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40 | tr0 = R1.trace(); |
| 92 | |||
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40 | tr = R_normed.trace(); |
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40 | vals = 2. * R_normed.diagonal().array() - tr + 1.; |
| 95 | } | ||
| 96 | 2 | } | |
| 97 | |||
| 98 |
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4 | BOOST_AUTO_TEST_CASE(log) |
| 99 | { | ||
| 100 |
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2 | SE3 M(SE3::Identity()); |
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2 | Motion v(Motion::Random()); |
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2 | v.linear().setZero(); |
| 103 | |||
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2 | SE3::Vector3 omega = log3(M.rotation()); |
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2 | BOOST_CHECK(omega.isZero()); |
| 106 | |||
| 107 | // check the NAN case | ||
| 108 | #ifdef NDEBUG | ||
| 109 | SE3::Matrix3 mat3_nan(SE3::Matrix3::Constant(NAN)); | ||
| 110 | SE3::Vector3 omega_nan = log3(mat3_nan); | ||
| 111 | BOOST_CHECK(omega_nan != omega_nan); | ||
| 112 | #endif | ||
| 113 | |||
| 114 |
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2 | M.setRandom(); |
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2 | M.translation().setZero(); |
| 116 | |||
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2 | v = log6(M); |
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2 | omega = log3(M.rotation()); |
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2 | BOOST_CHECK(omega.isApprox(v.angular())); |
| 120 | |||
| 121 | // check the NAN case | ||
| 122 | #ifdef NDEBUG | ||
| 123 | SE3::Matrix4 mat4_nan(SE3::Matrix4::Constant(NAN)); | ||
| 124 | Motion::Vector6 v_nan = log6(mat4_nan); | ||
| 125 | BOOST_CHECK(v_nan != v_nan); | ||
| 126 | #endif | ||
| 127 | |||
| 128 | // Quaternion | ||
| 129 |
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2 | Eigen::Quaterniond quat(SE3::Matrix3::Identity()); |
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2 | omega = quaternion::log3(quat); |
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2 | BOOST_CHECK(omega.isZero()); |
| 132 | |||
| 133 |
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2002 | for (int k = 0; k < 1e3; ++k) |
| 134 | { | ||
| 135 |
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2000 | SE3::Vector3 w; |
| 136 |
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2000 | w.setRandom(); |
| 137 |
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2000 | quaternion::exp3(w, quat); |
| 138 |
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2000 | SE3::Matrix3 rot = exp3(w); |
| 139 | |||
| 140 |
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2000 | BOOST_CHECK(quat.toRotationMatrix().isApprox(rot)); |
| 141 | double theta; | ||
| 142 |
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2000 | omega = quaternion::log3(quat, theta); |
| 143 | 2000 | const double PI_value = PI<double>(); | |
| 144 |
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2000 | BOOST_CHECK(omega.norm() <= PI_value); |
| 145 | double theta_ref; | ||
| 146 |
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2000 | SE3::Vector3 omega_ref = log3(quat.toRotationMatrix(), theta_ref); |
| 147 | |||
| 148 |
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2000 | BOOST_CHECK(omega.isApprox(omega_ref)); |
| 149 | } | ||
| 150 | |||
| 151 | // Check QuaternionMap | ||
| 152 |
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2 | Eigen::Vector4d vec4; |
| 153 |
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2 | Eigen::QuaternionMapd quat_map(vec4.data()); |
| 154 |
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2 | quat_map = SE3::Random().rotation(); |
| 155 |
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2 | BOOST_CHECK(quaternion::log3(quat_map).isApprox(log3(quat_map.toRotationMatrix()))); |
| 156 | 2 | } | |
| 157 | |||
| 158 |
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4 | BOOST_AUTO_TEST_CASE(explog3) |
| 159 | { | ||
| 160 |
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2 | SE3 M(SE3::Random()); |
| 161 |
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2 | SE3::Matrix3 M_res = exp3(log3(M.rotation())); |
| 162 |
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2 | BOOST_CHECK(M_res.isApprox(M.rotation())); |
| 163 | |||
| 164 |
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2 | Motion::Vector3 v; |
| 165 |
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2 | v.setRandom(); |
| 166 |
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2 | Motion::Vector3 v_res = log3(exp3(v)); |
| 167 |
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2 | BOOST_CHECK(v_res.isApprox(v)); |
| 168 | 2 | } | |
| 169 | |||
| 170 |
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4 | BOOST_AUTO_TEST_CASE(explog3_quaternion) |
| 171 | { | ||
| 172 |
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2 | SE3 M(SE3::Random()); |
| 173 |
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2 | Eigen::Quaterniond quat; |
| 174 |
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2 | quat = M.rotation(); |
| 175 |
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2 | Eigen::Quaterniond quat_res; |
| 176 |
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2 | quaternion::exp3(quaternion::log3(quat), quat_res); |
| 177 |
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2 | BOOST_CHECK(quat_res.isApprox(quat) || quat_res.coeffs().isApprox(-quat.coeffs())); |
| 178 | |||
| 179 |
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2 | Motion::Vector3 v; |
| 180 |
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2 | v.setRandom(); |
| 181 |
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2 | quaternion::exp3(v, quat); |
| 182 |
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2 | BOOST_CHECK(quaternion::log3(quat).isApprox(v)); |
| 183 | |||
| 184 |
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2 | SE3::Matrix3 R_next = M.rotation() * exp3(v); |
| 185 |
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2 | Motion::Vector3 v_est = log3(M.rotation().transpose() * R_next); |
| 186 |
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2 | BOOST_CHECK(v_est.isApprox(v)); |
| 187 | |||
| 188 |
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2 | SE3::Quaternion quat_v; |
| 189 |
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2 | quaternion::exp3(v, quat_v); |
| 190 |
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2 | SE3::Quaternion quat_next = quat * quat_v; |
| 191 |
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2 | v_est = quaternion::log3(quat.conjugate() * quat_next); |
| 192 |
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2 | BOOST_CHECK(v_est.isApprox(v)); |
| 193 | 2 | } | |
| 194 | |||
| 195 |
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4 | BOOST_AUTO_TEST_CASE(Jlog3_fd) |
| 196 | { | ||
| 197 |
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2 | SE3 M(SE3::Random()); |
| 198 |
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2 | SE3::Matrix3 R(M.rotation()); |
| 199 | |||
| 200 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 201 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 202 |
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2 | SE3::Matrix3 Jfd, Jlog; |
| 203 |
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2 | Jlog3(R, Jlog); |
| 204 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 205 |
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2 | Jfd.setZero(); |
| 206 | |||
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2 | Motion::Vector3 dR; |
| 208 |
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2 | dR.setZero(); |
| 209 | 2 | const double eps = 1e-8; | |
| 210 |
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8 | for (int i = 0; i < 3; ++i) |
| 211 | { | ||
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6 | dR[i] = eps; |
| 213 |
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6 | SE3::Matrix3 R_dR_plus = R * exp3(dR); |
| 214 |
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6 | SE3::Matrix3 R_dR_minus = R * exp3(-dR); |
| 215 |
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6 | Jfd.col(i) = (log3(R_dR_plus) - log3(R_dR_minus)) / (2 * eps); |
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6 | dR[i] = 0; |
| 217 | } | ||
| 218 |
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2 | BOOST_CHECK(Jfd.isApprox(Jlog, std::sqrt(eps))); |
| 219 | 2 | } | |
| 220 | |||
| 221 |
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4 | BOOST_AUTO_TEST_CASE(Jexp3_fd) |
| 222 | { | ||
| 223 |
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2 | SE3 M(SE3::Random()); |
| 224 |
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2 | SE3::Matrix3 R(M.rotation()); |
| 225 | |||
| 226 |
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2 | Motion::Vector3 v = log3(R); |
| 227 | |||
| 228 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 229 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 230 |
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2 | SE3::Matrix3 Jexp_fd, Jexp; |
| 231 | |||
| 232 |
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2 | Jexp3(Motion::Vector3::Zero(), Jexp); |
| 233 |
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2 | BOOST_CHECK(Jexp.isIdentity()); |
| 234 | |||
| 235 |
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2 | Jexp3(v, Jexp); |
| 236 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 237 | |||
| 238 |
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2 | Motion::Vector3 dv; |
| 239 |
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2 | dv.setZero(); |
| 240 | 2 | const double eps = 1e-3; | |
| 241 |
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8 | for (int i = 0; i < 3; ++i) |
| 242 | { | ||
| 243 |
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6 | dv[i] = eps; |
| 244 |
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6 | SE3::Matrix3 R_next = exp3(v + dv); |
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6 | SE3::Matrix3 R_prev = exp3(v - dv); |
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6 | SE3::Matrix3 Rpn = R_prev.transpose() * R_next; |
| 247 |
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6 | Jexp_fd.col(i) = log3(Rpn) / (2. * eps); |
| 248 |
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6 | dv[i] = 0; |
| 249 | } | ||
| 250 |
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2 | BOOST_CHECK(Jexp_fd.isApprox(Jexp, std::sqrt(eps))); |
| 251 | 2 | } | |
| 252 | |||
| 253 | template<typename QuaternionLike, typename Matrix43Like> | ||
| 254 | 2 | void Jexp3QuatLocal( | |
| 255 | const Eigen::QuaternionBase<QuaternionLike> & quat, const Eigen::MatrixBase<Matrix43Like> & Jexp) | ||
| 256 | { | ||
| 257 | 2 | Matrix43Like & Jout = PINOCCHIO_EIGEN_CONST_CAST(Matrix43Like, Jexp); | |
| 258 | |||
| 259 |
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2 | skew(0.5 * quat.vec(), Jout.template topRows<3>()); |
| 260 |
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2 | Jout.template topRows<3>().diagonal().array() += 0.5 * quat.w(); |
| 261 |
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2 | Jout.template bottomRows<1>() = -0.5 * quat.vec().transpose(); |
| 262 | 2 | } | |
| 263 | |||
| 264 |
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4 | BOOST_AUTO_TEST_CASE(Jexp3_quat_fd) |
| 265 | { | ||
| 266 | typedef double Scalar; | ||
| 267 |
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2 | SE3::Vector3 w; |
| 268 |
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2 | w.setRandom(); |
| 269 |
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2 | SE3::Quaternion quat; |
| 270 |
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2 | quaternion::exp3(w, quat); |
| 271 | |||
| 272 | typedef Eigen::Matrix<Scalar, 4, 3> Matrix43; | ||
| 273 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 274 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 275 |
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2 | Matrix43 Jexp3, Jexp3_fd; |
| 276 |
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2 | quaternion::Jexp3CoeffWise(w, Jexp3); |
| 277 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 278 |
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2 | SE3::Vector3 dw; |
| 279 |
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2 | dw.setZero(); |
| 280 | 2 | const double eps = 1e-8; | |
| 281 | |||
| 282 |
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8 | for (int i = 0; i < 3; ++i) |
| 283 | { | ||
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6 | dw[i] = eps; |
| 285 |
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6 | SE3::Quaternion quat_plus; |
| 286 |
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6 | quaternion::exp3(w + dw, quat_plus); |
| 287 |
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6 | Jexp3_fd.col(i) = (quat_plus.coeffs() - quat.coeffs()) / eps; |
| 288 |
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6 | dw[i] = 0; |
| 289 | } | ||
| 290 |
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2 | BOOST_CHECK(Jexp3.isApprox(Jexp3_fd, sqrt(eps))); |
| 291 | |||
| 292 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 293 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 294 |
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2 | SE3::Matrix3 Jlog; |
| 295 |
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2 | pinocchio::Jlog3(quat.toRotationMatrix(), Jlog); |
| 296 | |||
| 297 |
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2 | Matrix43 Jexp_quat_local; |
| 298 |
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2 | Jexp3QuatLocal(quat, Jexp_quat_local); |
| 299 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 300 | |||
| 301 |
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2 | Matrix43 Jcompositon = Jexp3 * Jlog; |
| 302 |
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2 | BOOST_CHECK(Jcompositon.isApprox(Jexp_quat_local)); |
| 303 | // std::cout << "Jcompositon\n" << Jcompositon << std::endl; | ||
| 304 | // std::cout << "Jexp_quat_local\n" << Jexp_quat_local << std::endl; | ||
| 305 | |||
| 306 | // Arount zero | ||
| 307 |
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2 | w.setZero(); |
| 308 |
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2 | w.fill(1e-6); |
| 309 |
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2 | quaternion::exp3(w, quat); |
| 310 |
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2 | quaternion::Jexp3CoeffWise(w, Jexp3); |
| 311 |
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8 | for (int i = 0; i < 3; ++i) |
| 312 | { | ||
| 313 |
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6 | dw[i] = eps; |
| 314 |
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6 | SE3::Quaternion quat_plus; |
| 315 |
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6 | quaternion::exp3(w + dw, quat_plus); |
| 316 |
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6 | Jexp3_fd.col(i) = (quat_plus.coeffs() - quat.coeffs()) / eps; |
| 317 |
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6 | dw[i] = 0; |
| 318 | } | ||
| 319 |
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2 | BOOST_CHECK(Jexp3.isApprox(Jexp3_fd, sqrt(eps))); |
| 320 | 2 | } | |
| 321 | |||
| 322 |
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4 | BOOST_AUTO_TEST_CASE(Jexp3_quat) |
| 323 | { | ||
| 324 |
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2 | SE3 M(SE3::Random()); |
| 325 |
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2 | SE3::Quaternion quat(M.rotation()); |
| 326 | |||
| 327 |
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2 | Motion dv(Motion::Zero()); |
| 328 | 2 | const double eps = 1e-8; | |
| 329 | |||
| 330 | typedef Eigen::Matrix<double, 7, 6> Matrix76; | ||
| 331 |
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2 | Matrix76 Jexp6_fd, Jexp6_quat; |
| 332 |
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2 | Jexp6_quat.setZero(); |
| 333 | typedef Eigen::Matrix<double, 4, 3> Matrix43; | ||
| 334 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 335 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 336 |
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2 | Matrix43 Jexp3_quat; |
| 337 |
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2 | Jexp3QuatLocal(quat, Jexp3_quat); |
| 338 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 339 |
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2 | SE3 M_next; |
| 340 | |||
| 341 |
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2 | Jexp6_quat.middleRows<3>(Motion::LINEAR).middleCols<3>(Motion::LINEAR) = M.rotation(); |
| 342 |
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2 | Jexp6_quat.middleRows<4>(Motion::ANGULAR).middleCols<3>(Motion::ANGULAR) = |
| 343 |
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2 | Jexp3_quat; // * Jlog6_SE3.middleRows<3>(Motion::ANGULAR); |
| 344 |
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14 | for (int i = 0; i < 6; ++i) |
| 345 | { | ||
| 346 |
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12 | dv.toVector()[i] = eps; |
| 347 |
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12 | M_next = M * exp6(dv); |
| 348 |
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12 | const SE3::Quaternion quat_next(M_next.rotation()); |
| 349 |
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12 | Jexp6_fd.middleRows<3>(Motion::LINEAR).col(i) = (M_next.translation() - M.translation()) / eps; |
| 350 |
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12 | Jexp6_fd.middleRows<4>(Motion::ANGULAR).col(i) = (quat_next.coeffs() - quat.coeffs()) / eps; |
| 351 |
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12 | dv.toVector()[i] = 0.; |
| 352 | } | ||
| 353 | |||
| 354 |
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2 | BOOST_CHECK(Jexp6_quat.isApprox(Jexp6_fd, sqrt(eps))); |
| 355 | 2 | } | |
| 356 | |||
| 357 |
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4 | BOOST_AUTO_TEST_CASE(Jexplog3) |
| 358 | { | ||
| 359 |
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2 | Motion v(Motion::Random()); |
| 360 | |||
| 361 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 362 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 363 |
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2 | Eigen::Matrix3d R(exp3(v.angular())), Jexp, Jlog; |
| 364 |
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2 | Jexp3(v.angular(), Jexp); |
| 365 |
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2 | Jlog3(R, Jlog); |
| 366 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 367 | |||
| 368 |
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2 | BOOST_CHECK((Jlog * Jexp).isIdentity()); |
| 369 | |||
| 370 |
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2 | SE3 M(SE3::Random()); |
| 371 |
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2 | R = M.rotation(); |
| 372 |
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2 | v.angular() = log3(R); |
| 373 |
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2 | Jlog3(R, Jlog); |
| 374 |
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2 | Jexp3(v.angular(), Jexp); |
| 375 | |||
| 376 |
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2 | BOOST_CHECK((Jexp * Jlog).isIdentity()); |
| 377 | 2 | } | |
| 378 | |||
| 379 |
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|
4 | BOOST_AUTO_TEST_CASE(Jlog3_quat) |
| 380 | { | ||
| 381 |
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2 | SE3::Vector3 w; |
| 382 |
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2 | w.setRandom(); |
| 383 |
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2 | SE3::Quaternion quat; |
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2 | quaternion::exp3(w, quat); |
| 385 | |||
| 386 |
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2 | SE3::Matrix3 R(quat.toRotationMatrix()); |
| 387 | |||
| 388 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 389 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 390 |
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2 | SE3::Matrix3 res, res_ref; |
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2 | quaternion::Jlog3(quat, res); |
| 392 |
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2 | Jlog3(R, res_ref); |
| 393 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 394 | |||
| 395 |
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2 | BOOST_CHECK(res.isApprox(res_ref)); |
| 396 | 2 | } | |
| 397 | |||
| 398 |
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|
4 | BOOST_AUTO_TEST_CASE(explog6) |
| 399 | { | ||
| 400 |
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2 | SE3 M(SE3::Random()); |
| 401 |
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2 | SE3 M_res = exp6(log6(M)); |
| 402 |
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2 | BOOST_CHECK(M_res.isApprox(M)); |
| 403 | |||
| 404 |
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2 | Motion v(Motion::Random()); |
| 405 |
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2 | Motion v_res = log6(exp6(v)); |
| 406 |
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2 | BOOST_CHECK(v_res.toVector().isApprox(v.toVector())); |
| 407 | 2 | } | |
| 408 | |||
| 409 |
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|
4 | BOOST_AUTO_TEST_CASE(Jlog6_fd) |
| 410 | { | ||
| 411 |
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2 | SE3 M(SE3::Random()); |
| 412 | |||
| 413 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 414 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 415 |
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2 | SE3::Matrix6 Jfd, Jlog; |
| 416 |
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2 | Jlog6(M, Jlog); |
| 417 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 418 |
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2 | Jfd.setZero(); |
| 419 | |||
| 420 |
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2 | Motion dM; |
| 421 |
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2 | dM.setZero(); |
| 422 | 2 | double step = 1e-8; | |
| 423 |
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14 | for (int i = 0; i < 6; ++i) |
| 424 | { | ||
| 425 |
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12 | dM.toVector()[i] = step; |
| 426 |
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12 | SE3 M_dM = M * exp6(dM); |
| 427 |
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12 | Jfd.col(i) = (log6(M_dM).toVector() - log6(M).toVector()) / step; |
| 428 |
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12 | dM.toVector()[i] = 0; |
| 429 | } | ||
| 430 | |||
| 431 |
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2 | BOOST_CHECK(Jfd.isApprox(Jlog, sqrt(step))); |
| 432 | |||
| 433 |
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2 | SE3::Matrix6 Jlog2 = Jlog6(M); |
| 434 |
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2 | BOOST_CHECK(Jlog2.isApprox(Jlog)); |
| 435 | 2 | } | |
| 436 | |||
| 437 |
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|
4 | BOOST_AUTO_TEST_CASE(Jlog6_singular) |
| 438 | { | ||
| 439 |
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32 | for (size_t i = 0; i < 15; i++) |
| 440 | { | ||
| 441 |
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30 | SE3 M0; |
| 442 |
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30 | if (i == 0) |
| 443 | { | ||
| 444 |
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2 | M0 = SE3::Identity(); |
| 445 | } | ||
| 446 | else | ||
| 447 | { | ||
| 448 |
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28 | M0 = SE3::Random(); |
| 449 | } | ||
| 450 |
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30 | SE3 dM(M0.actInv(M0)); |
| 451 | |||
| 452 |
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30 | BOOST_CHECK(dM.isApprox(SE3::Identity())); |
| 453 |
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30 | SE3::Matrix6 J0(SE3::Matrix6::Identity()); |
| 454 | |||
| 455 |
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30 | SE3::Matrix6 J_val = Jlog6(dM); |
| 456 |
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30 | BOOST_CHECK(J0.isApprox(J_val)); |
| 457 | } | ||
| 458 | 2 | } | |
| 459 | |||
| 460 |
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|
4 | BOOST_AUTO_TEST_CASE(Jexp6_fd) |
| 461 | { | ||
| 462 |
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2 | SE3 M(SE3::Random()); |
| 463 | |||
| 464 |
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2 | const Motion v = log6(M); |
| 465 | |||
| 466 |
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2 | SE3::Matrix6 Jexp_fd, Jexp; |
| 467 | |||
| 468 |
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2 | Jexp6(Motion::Zero(), Jexp); |
| 469 |
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2 | BOOST_CHECK(Jexp.isIdentity()); |
| 470 | |||
| 471 |
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2 | Jexp6(v, Jexp); |
| 472 | |||
| 473 |
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2 | Motion::Vector6 dv; |
| 474 |
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2 | dv.setZero(); |
| 475 | 2 | const double eps = 1e-8; | |
| 476 |
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14 | for (int i = 0; i < 6; ++i) |
| 477 | { | ||
| 478 |
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12 | dv[i] = eps; |
| 479 |
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12 | SE3 M_next = exp6(v + Motion(dv)); |
| 480 |
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12 | Jexp_fd.col(i) = log6(M.actInv(M_next)).toVector() / eps; |
| 481 |
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12 | dv[i] = 0; |
| 482 | } | ||
| 483 |
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2 | BOOST_CHECK(Jexp_fd.isApprox(Jexp, std::sqrt(eps))); |
| 484 | |||
| 485 |
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2 | SE3::Matrix6 Jexp2 = Jexp6(v); |
| 486 |
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2 | BOOST_CHECK(Jexp2.isApprox(Jexp)); |
| 487 | 2 | } | |
| 488 | |||
| 489 |
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|
4 | BOOST_AUTO_TEST_CASE(Jlog6_of_product_fd) |
| 490 | { | ||
| 491 |
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2 | SE3 Ma(SE3::Random()); |
| 492 |
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2 | SE3 Mb(SE3::Random()); |
| 493 | |||
| 494 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 495 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED | ||
| 496 |
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2 | SE3::Matrix6 Jlog, Ja, Jb, Jfda, Jfdb; |
| 497 |
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2 | Jlog6(Ma.inverse() * Mb, Jlog); |
| 498 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 499 |
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2 | Ja = -Jlog * (Ma.inverse() * Mb).toActionMatrixInverse(); |
| 500 |
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2 | Jb = Jlog; |
| 501 |
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2 | Jfda.setZero(); |
| 502 |
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2 | Jfdb.setZero(); |
| 503 | |||
| 504 |
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2 | Motion dM; |
| 505 |
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2 | dM.setZero(); |
| 506 | 2 | double step = 1e-8; | |
| 507 |
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14 | for (int i = 0; i < 6; ++i) |
| 508 | { | ||
| 509 |
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12 | dM.toVector()[i] = step; |
| 510 |
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12 | Jfda.col(i) = |
| 511 |
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24 | (log6((Ma * exp6(dM)).inverse() * Mb).toVector() - log6(Ma.inverse() * Mb).toVector()) / step; |
| 512 |
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12 | Jfdb.col(i) = |
| 513 |
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24 | (log6(Ma.inverse() * Mb * exp6(dM)).toVector() - log6(Ma.inverse() * Mb).toVector()) / step; |
| 514 |
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12 | dM.toVector()[i] = 0; |
| 515 | } | ||
| 516 | |||
| 517 |
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2 | BOOST_CHECK(Jfda.isApprox(Ja, sqrt(step))); |
| 518 |
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2 | BOOST_CHECK(Jfdb.isApprox(Jb, sqrt(step))); |
| 519 | 2 | } | |
| 520 | |||
| 521 |
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|
4 | BOOST_AUTO_TEST_CASE(Jexplog6) |
| 522 | { | ||
| 523 |
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2 | Motion v(Motion::Random()); |
| 524 | |||
| 525 |
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2 | SE3 M(exp6(v)); |
| 526 | { | ||
| 527 |
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2 | Eigen::Matrix<double, 6, 6, Eigen::RowMajor> Jexp, Jlog; |
| 528 |
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2 | Jexp6(v, Jexp); |
| 529 |
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2 | Jlog6(M, Jlog); |
| 530 | |||
| 531 |
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2 | BOOST_CHECK((Jlog * Jexp).isIdentity()); |
| 532 | } | ||
| 533 | |||
| 534 |
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2 | M.setRandom(); |
| 535 | |||
| 536 |
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2 | v = log6(M); |
| 537 | { | ||
| 538 |
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2 | Eigen::Matrix<double, 6, 6> Jexp, Jlog; |
| 539 |
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2 | Jlog6(M, Jlog); |
| 540 |
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2 | Jexp6(v, Jexp); |
| 541 | |||
| 542 |
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2 | BOOST_CHECK((Jexp * Jlog).isIdentity()); |
| 543 | } | ||
| 544 | 2 | } | |
| 545 | |||
| 546 |
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|
4 | BOOST_AUTO_TEST_CASE(Hlog3_fd) |
| 547 | { | ||
| 548 | typedef SE3::Vector3 Vector3; | ||
| 549 | typedef SE3::Matrix3 Matrix3; | ||
| 550 |
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2 | SE3::Quaternion q; |
| 551 |
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2 | quaternion::uniformRandom(q); |
| 552 |
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2 | 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 |
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2 | Vector3 dR; |
| 557 |
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2 | dR.setZero(); |
| 558 | 2 | double step = 1e-8; | |
| 559 |
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8 | for (int k = 0; k < 3; ++k) |
| 560 | { | ||
| 561 |
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6 | Vector3 e_k(Vector3::Zero()); |
| 562 |
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6 | e_k[k] = 1.; |
| 563 | |||
| 564 |
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6 | Matrix3 Hlog_e_k; |
| 565 |
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6 | Hlog3(R, e_k, Hlog_e_k); |
| 566 | |||
| 567 |
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6 | Matrix3 R_dR = R * exp3(step * e_k); |
| 568 |
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6 | Matrix3 Jlog_R, Jlog_R_dR; |
| 569 |
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6 | Jlog3(R, Jlog_R); |
| 570 |
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6 | Jlog3(R_dR, Jlog_R_dR); |
| 571 | |||
| 572 |
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6 | Matrix3 Hlog_e_k_fd = (Jlog_R_dR - Jlog_R) / step; |
| 573 | |||
| 574 |
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6 | BOOST_CHECK(Hlog_e_k.isApprox(Hlog_e_k_fd, sqrt(step))); |
| 575 | } | ||
| 576 | 2 | } | |
| 577 | |||
| 578 |
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4 | 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 | 2 | const double EPSILON = 1e-12; | |
| 586 | |||
| 587 | // exp3 and log3. | ||
| 588 |
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2 | Vector3 v3(Vector3::Random()); |
| 589 |
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2 | Matrix3 R(pinocchio::exp3(v3)); |
| 590 |
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2 | BOOST_CHECK(R.transpose().isApprox(R.inverse(), EPSILON)); |
| 591 |
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2 | BOOST_CHECK_SMALL(R.determinant() - 1.0, EPSILON); |
| 592 |
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2 | Vector3 v3FromLog(pinocchio::log3(R)); |
| 593 |
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2 | BOOST_CHECK(v3.isApprox(v3FromLog, EPSILON)); |
| 594 | |||
| 595 | // exp6 and log6. | ||
| 596 |
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2 | pinocchio::Motion nu = pinocchio::Motion::Random(); |
| 597 |
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2 | pinocchio::SE3 m = pinocchio::exp6(nu); |
| 598 |
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2 | BOOST_CHECK(m.rotation().transpose().isApprox(m.rotation().inverse(), EPSILON)); |
| 599 |
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2 | BOOST_CHECK_SMALL(m.rotation().determinant() - 1.0, EPSILON); |
| 600 |
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2 | pinocchio::Motion nuFromLog(pinocchio::log6(m)); |
| 601 |
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2 | BOOST_CHECK(nu.linear().isApprox(nuFromLog.linear(), EPSILON)); |
| 602 |
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2 | BOOST_CHECK(nu.angular().isApprox(nuFromLog.angular(), EPSILON)); |
| 603 | |||
| 604 |
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2 | Vector6 v6(Vector6::Random()); |
| 605 |
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2 | pinocchio::SE3 m2(pinocchio::exp6(v6)); |
| 606 |
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2 | BOOST_CHECK(m2.rotation().transpose().isApprox(m2.rotation().inverse(), EPSILON)); |
| 607 |
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2 | BOOST_CHECK_SMALL(m2.rotation().determinant() - 1.0, EPSILON); |
| 608 |
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2 | Matrix4 M = m2.toHomogeneousMatrix(); |
| 609 |
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2 | pinocchio::Motion nu2FromLog(pinocchio::log6(M)); |
| 610 |
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2 | Vector6 v6FromLog(nu2FromLog.toVector()); |
| 611 |
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2 | BOOST_CHECK(v6.isApprox(v6FromLog, EPSILON)); |
| 612 | 2 | } | |
| 613 | |||
| 614 |
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4 | BOOST_AUTO_TEST_CASE(test_SE3_interpolate) |
| 615 | { | ||
| 616 |
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2 | SE3 A = SE3::Random(); |
| 617 |
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2 | SE3 B = SE3::Random(); |
| 618 | |||
| 619 |
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2 | SE3 A_bis = SE3::Interpolate(A, B, 0.); |
| 620 |
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2 | BOOST_CHECK(A_bis.isApprox(A)); |
| 621 |
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2 | SE3 B_bis = SE3::Interpolate(A, B, 1.); |
| 622 |
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2 | BOOST_CHECK(B_bis.isApprox(B)); |
| 623 | |||
| 624 |
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2 | A_bis = SE3::Interpolate(A, A, 1.); |
| 625 |
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2 | BOOST_CHECK(A_bis.isApprox(A)); |
| 626 | |||
| 627 |
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2 | B_bis = SE3::Interpolate(B, B, 1.); |
| 628 |
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2 | BOOST_CHECK(B_bis.isApprox(B)); |
| 629 | |||
| 630 |
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2 | SE3 C = SE3::Interpolate(A, B, 0.5); |
| 631 |
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2 | SE3 D = SE3::Interpolate(B, A, 0.5); |
| 632 |
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2 | BOOST_CHECK(D.isApprox(C)); |
| 633 | 2 | } | |
| 634 | |||
| 635 |
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4 | BOOST_AUTO_TEST_CASE(test_Jlog6_robustness) |
| 636 | { | ||
| 637 | 2 | const int num_tests = 1e1; | |
| 638 |
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22 | for (int k = 0; k < num_tests; ++k) |
| 639 | { | ||
| 640 |
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20 | const SE3 M = SE3::Random(); |
| 641 |
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20 | SE3::Matrix6 res = Jlog6(M.actInv(M)); |
| 642 | |||
| 643 |
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20 | BOOST_CHECK(res.isIdentity()); |
| 644 | } | ||
| 645 | 2 | } | |
| 646 | |||
| 647 | BOOST_AUTO_TEST_SUITE_END() | ||
| 648 |