GCC Code Coverage Report


Directory: ./
File: unittest/explog.cpp
Date: 2025-02-12 21:03:38
Exec Total Coverage
Lines: 385 385 100.0%
Branches: 1662 3296 50.4%

Line Branch Exec Source
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 {
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2 SE3 M(SE3::Random());
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2 Motion v(Motion::Random());
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2 v.linear().setZero();
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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()));
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2 SE3::Matrix3 R0 = exp3(SE3::Vector3::Zero());
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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
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2 M = exp6(v);
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2 BOOST_CHECK(R.isApprox(M.rotation()));
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2 Eigen::Matrix<double, 7, 1> q0;
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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>());
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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
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2 R = exp3(SE3::Vector3::Zero());
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2 BOOST_CHECK(R.isIdentity());
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58 // Quaternion
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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()));
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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());
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67 // Check QuaternionMap
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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 }
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4 BOOST_AUTO_TEST_CASE(renorm_rotation)
75 {
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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;
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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();
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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 }
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4 BOOST_AUTO_TEST_CASE(log)
99 {
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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();
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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
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2 M.setRandom();
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2 M.translation().setZero();
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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
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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());
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2002 for (int k = 0; k < 1e3; ++k)
134 {
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2000 SE3::Vector3 w;
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2000 w.setRandom();
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2000 quaternion::exp3(w, quat);
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2000 SE3::Matrix3 rot = exp3(w);
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2000 BOOST_CHECK(quat.toRotationMatrix().isApprox(rot));
141 double theta;
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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
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2 Eigen::Vector4d vec4;
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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 {
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2 SE3 M(SE3::Random());
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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
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2 Motion::Vector3 v;
165
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2 v.setRandom();
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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 {
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2 SE3 M(SE3::Random());
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2 Eigen::Quaterniond quat;
174
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2 quat = M.rotation();
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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();
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2 quaternion::exp3(v, quat);
182
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2 BOOST_CHECK(quaternion::log3(quat).isApprox(v));
183
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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
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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);
216
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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
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2 Jexp3(v, Jexp);
236 PINOCCHIO_COMPILER_DIAGNOSTIC_POP
237
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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 {
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6 dv[i] = eps;
244
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6 SE3::Matrix3 R_next = exp3(v + dv);
245
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6 SE3::Matrix3 R_prev = exp3(v - dv);
246
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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>());
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2 Jout.template topRows<3>().diagonal().array() += 0.5 * quat.w();
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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;
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2 w.setRandom();
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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
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8 for (int i = 0; i < 3; ++i)
283 {
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6 dw[i] = eps;
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6 SE3::Quaternion quat_plus;
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6 quaternion::exp3(w + dw, quat_plus);
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6 Jexp3_fd.col(i) = (quat_plus.coeffs() - quat.coeffs()) / eps;
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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
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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;
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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();
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2 w.fill(1e-6);
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2 quaternion::exp3(w, quat);
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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;
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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;
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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
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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
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2 BOOST_CHECK((Jlog * Jexp).isIdentity());
369
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2 SE3 M(SE3::Random());
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2 R = M.rotation();
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2 v.angular() = log3(R);
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2 Jlog3(R, Jlog);
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2 Jexp3(v.angular(), Jexp);
375
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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;
384
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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;
391
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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
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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
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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();
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2 Jb = Jlog;
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2 Jfda.setZero();
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2 Jfdb.setZero();
503
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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;
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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
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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
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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
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2 A_bis = SE3::Interpolate(A, A, 1.);
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2 BOOST_CHECK(A_bis.isApprox(A));
626
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2 B_bis = SE3::Interpolate(B, B, 1.);
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2 BOOST_CHECK(B_bis.isApprox(B));
629
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2 SE3 C = SE3::Interpolate(A, B, 0.5);
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2 SE3 D = SE3::Interpolate(B, A, 0.5);
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2 BOOST_CHECK(D.isApprox(C));
633 2 }
634
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4 BOOST_AUTO_TEST_CASE(test_Jlog6_robustness)
636 {
637 2 const int num_tests = 1e1;
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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();
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20 SE3::Matrix6 res = Jlog6(M.actInv(M));
642
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20 BOOST_CHECK(res.isIdentity());
644 }
645 2 }
646
647 BOOST_AUTO_TEST_SUITE_END()
648