GCC Code Coverage Report


Directory: ./
File: unittest/spatial.cpp
Date: 2025-02-12 21:03:38
Exec Total Coverage
Lines: 681 681 100.0%
Branches: 3029 6030 50.2%

Line Branch Exec Source
1 //
2 // Copyright (c) 2015-2021 CNRS INRIA
3 //
4
5 #include <iostream>
6
7 #include "pinocchio/spatial/force.hpp"
8 #include "pinocchio/spatial/motion.hpp"
9 #include "pinocchio/spatial/se3.hpp"
10 #include "pinocchio/spatial/inertia.hpp"
11 #include "pinocchio/spatial/act-on-set.hpp"
12 #include "pinocchio/spatial/explog.hpp"
13 #include "pinocchio/spatial/skew.hpp"
14 #include "pinocchio/spatial/cartesian-axis.hpp"
15 #include "pinocchio/spatial/spatial-axis.hpp"
16
17 #include <boost/test/unit_test.hpp>
18 #include <boost/utility/binary.hpp>
19
20 BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE)
21
22
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4 BOOST_AUTO_TEST_CASE(test_SE3)
23 {
24 using namespace pinocchio;
25 typedef SE3::HomogeneousMatrixType HomogeneousMatrixType;
26 typedef SE3::ActionMatrixType ActionMatrixType;
27 typedef SE3::Vector3 Vector3;
28 typedef Eigen::Matrix<double, 4, 1> Vector4;
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2 const SE3 identity = SE3::Identity();
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32 typedef SE3::Quaternion Quaternion;
33 typedef SE3::Vector4 Vector4;
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2 Quaternion quat(Vector4::Random().normalized());
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2 SE3 m_from_quat(quat, Vector3::Random());
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2 SE3 amb = SE3::Random();
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2 SE3 bmc = SE3::Random();
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2 SE3 amc = amb * bmc;
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2 HomogeneousMatrixType aMb = amb;
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2 HomogeneousMatrixType bMc = bmc;
44
45 // Test internal product
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2 HomogeneousMatrixType aMc = amc;
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2 BOOST_CHECK(aMc.isApprox(aMb * bMc));
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2 HomogeneousMatrixType bMa = amb.inverse();
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2 BOOST_CHECK(bMa.isApprox(aMb.inverse()));
51
52 // Test point action
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2 Vector3 p = Vector3::Random();
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2 Vector4 p4;
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2 p4.head(3) = p;
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2 p4[3] = 1;
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2 Vector3 Mp = (aMb * p4).head(3);
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2 BOOST_CHECK(amb.act(p).isApprox(Mp));
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2 Vector3 Mip = (aMb.inverse() * p4).head(3);
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2 BOOST_CHECK(amb.actInv(p).isApprox(Mip));
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64 // Test action matrix
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2 ActionMatrixType aXb = amb;
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2 ActionMatrixType bXc = bmc;
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2 ActionMatrixType aXc = amc;
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2 BOOST_CHECK(aXc.isApprox(aXb * bXc));
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2 ActionMatrixType bXa = amb.inverse();
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2 BOOST_CHECK(bXa.isApprox(aXb.inverse()));
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2 ActionMatrixType X_identity = identity.toActionMatrix();
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2 BOOST_CHECK(X_identity.isIdentity());
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2 ActionMatrixType X_identity_inverse = identity.toActionMatrixInverse();
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2 BOOST_CHECK(X_identity_inverse.isIdentity());
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79 // Test dual action matrix
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2 BOOST_CHECK(aXb.inverse().transpose().isApprox(amb.toDualActionMatrix()));
81
82 // Test isIdentity
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2 BOOST_CHECK(identity.isIdentity());
84
85 // Test isApprox
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2 BOOST_CHECK(identity.isApprox(identity));
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88 // Test cast
89 typedef SE3Tpl<float> SE3f;
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2 SE3f::Matrix3 rot_float(amb.rotation().cast<float>());
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2 SE3f amb_float = amb.cast<float>();
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2 BOOST_CHECK(amb_float.isApprox(amb.cast<float>()));
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2 SE3f amb_float2(amb);
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2 BOOST_CHECK(amb_float.isApprox(amb_float2));
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97 // Test actInv
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2 const SE3 M = SE3::Random();
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2 const SE3 Minv = M.inverse();
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2 BOOST_CHECK(Minv.actInv(Minv).isIdentity());
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2 BOOST_CHECK(M.actInv(identity).isApprox(Minv));
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104 // Test normalization
105 {
106 2 const double prec = Eigen::NumTraits<double>::dummy_precision();
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2 SE3 M(SE3::Random());
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2 M.rotation() += prec * SE3::Matrix3::Random();
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2 BOOST_CHECK(!M.isNormalized());
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2 SE3 M_normalized = M.normalized();
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2 BOOST_CHECK(M_normalized.isNormalized());
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2 M.normalize();
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2 BOOST_CHECK(M.isNormalized());
116 }
117 2 }
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4 BOOST_AUTO_TEST_CASE(test_Motion)
120 {
121 using namespace pinocchio;
122 typedef SE3::ActionMatrixType ActionMatrixType;
123 typedef Motion::Vector6 Vector6;
124
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2 SE3 amb = SE3::Random();
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2 SE3 bmc = SE3::Random();
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2 SE3 amc = amb * bmc;
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2 Motion bv = Motion::Random();
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2 Motion bv2 = Motion::Random();
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132 typedef MotionBase<Motion> Base;
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2 Vector6 bv_vec = bv;
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2 Vector6 bv2_vec = bv2;
136
137 // std::stringstream
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2 std::stringstream ss;
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2 ss << bv << std::endl;
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2 BOOST_CHECK(!ss.str().empty());
141
142 // Test .+.
143
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2 Vector6 bvPbv2_vec = bv + bv2;
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2 BOOST_CHECK(bvPbv2_vec.isApprox(bv_vec + bv2_vec));
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2 Motion bplus = static_cast<Base &>(bv) + static_cast<Base &>(bv2);
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2 BOOST_CHECK((bv + bv2).isApprox(bplus));
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2 Motion v_not_zero(Vector6::Ones());
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2 BOOST_CHECK(!v_not_zero.isZero());
151
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2 Motion v_zero(Vector6::Zero());
153
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2 BOOST_CHECK(v_zero.isZero());
154
155 // Test == and !=
156
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2 BOOST_CHECK(bv == bv);
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2 BOOST_CHECK(!(bv != bv));
158
159 // Test -.
160
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2 Vector6 Mbv_vec = -bv;
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2 BOOST_CHECK(Mbv_vec.isApprox(-bv_vec));
162
163 // Test .+=.
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2 Motion bv3 = bv;
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2 bv3 += bv2;
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2 BOOST_CHECK(bv3.toVector().isApprox(bv_vec + bv2_vec));
167
168 // Test .=V6
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2 bv3 = bv2_vec;
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2 BOOST_CHECK(bv3.toVector().isApprox(bv2_vec));
171
172 // Test scalar*M6
173
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2 Motion twicebv(2. * bv);
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2 BOOST_CHECK(twicebv.isApprox(Motion(2. * bv.toVector())));
175
176 // Test M6*scalar
177
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2 Motion bvtwice(bv * 2.);
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2 BOOST_CHECK(bvtwice.isApprox(twicebv));
179
180 // Test M6/scalar
181
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2 Motion bvdividedbytwo(bvtwice / 2.);
182
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2 BOOST_CHECK(bvdividedbytwo.isApprox(bv));
183
184 // Test constructor from V6
185
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2 Motion bv4(bv2_vec);
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2 BOOST_CHECK(bv4.toVector().isApprox(bv2_vec));
187
188 // Test action
189
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2 ActionMatrixType aXb = amb;
190
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2 BOOST_CHECK(amb.act(bv).toVector().isApprox(aXb * bv_vec));
191
192 // Test action inverse
193
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2 ActionMatrixType bXc = bmc;
194
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2 BOOST_CHECK(bmc.actInv(bv).toVector().isApprox(bXc.inverse() * bv_vec));
195
196 // Test double action
197
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2 Motion cv = Motion::Random();
198
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2 bv = bmc.act(cv);
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2 BOOST_CHECK(amb.act(bv).toVector().isApprox(amc.act(cv).toVector()));
200
201 // Simple test for cross product vxv
202
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2 Motion vxv = bv.cross(bv);
203
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2 BOOST_CHECK_SMALL(
204 vxv.toVector().tail(3).norm(),
205 1e-3); // previously ensure that (vxv.toVector().tail(3).isMuchSmallerThan(1e-3));
206
207 // Test Action Matrix
208
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2 Motion v2xv = bv2.cross(bv);
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2 Motion::ActionMatrixType actv2 = bv2.toActionMatrix();
210
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2 BOOST_CHECK(v2xv.toVector().isApprox(actv2 * bv.toVector()));
212
213 // Test Dual Action Matrix
214
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2 Force f(bv.toVector());
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2 Force v2xf = bv2.cross(f);
216
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2 Motion::ActionMatrixType dualactv2 = bv2.toDualActionMatrix();
217
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2 BOOST_CHECK(v2xf.toVector().isApprox(dualactv2 * f.toVector()));
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2 BOOST_CHECK(dualactv2.isApprox(-actv2.transpose()));
220
221 // Simple test for cross product vxf
222
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2 Force vxf = bv.cross(f);
223
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2 BOOST_CHECK(vxf.linear().isApprox(bv.angular().cross(f.linear())));
224
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2 BOOST_CHECK_SMALL(
225 vxf.angular().norm(),
226 1e-3); // previously ensure that ( vxf.angular().isMuchSmallerThan(1e-3));
227
228 // Test frame change for vxf
229
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2 Motion av = Motion::Random();
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2 Force af = Force::Random();
231
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2 bv = amb.actInv(av);
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2 Force bf = amb.actInv(af);
233
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2 Force avxf = av.cross(af);
234
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2 Force bvxf = bv.cross(bf);
235
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2 BOOST_CHECK(avxf.toVector().isApprox(amb.act(bvxf).toVector()));
236
237 // Test frame change for vxv
238
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2 av = Motion::Random();
239
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2 Motion aw = Motion::Random();
240
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2 bv = amb.actInv(av);
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2 Motion bw = amb.actInv(aw);
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2 Motion avxw = av.cross(aw);
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2 Motion bvxw = bv.cross(bw);
244
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2 BOOST_CHECK(avxw.toVector().isApprox(amb.act(bvxw).toVector()));
245
246 // Test isApprox
247
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2 bv.toVector().setOnes();
248 2 const double eps = 1e-6;
249
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2 BOOST_CHECK(bv == bv);
250
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2 BOOST_CHECK(bv.isApprox(bv));
251
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2 Motion bv_approx(bv);
252
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2 bv_approx.linear()[0] += eps;
253
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2 BOOST_CHECK(bv_approx.isApprox(bv, eps));
254
255 // Test ref() method
256 {
257
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2 Motion a(Motion::Random());
258
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2 BOOST_CHECK(a.ref().isApprox(a));
259
260
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2 const Motion b(a);
261
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2 BOOST_CHECK(b.isApprox(a.ref()));
262 }
263
264 // Test cast
265 {
266 typedef MotionTpl<float> Motionf;
267
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2 Motion a(Motion::Random());
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2 Motionf a_float = a.cast<float>();
269
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2 BOOST_CHECK(a_float.isApprox(a.cast<float>()));
270
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2 Motionf a_float2(a);
272
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2 BOOST_CHECK(a_float.isApprox(a_float2));
273 }
274 2 }
275
276
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4 BOOST_AUTO_TEST_CASE(test_motion_ref)
277 {
278 using namespace pinocchio;
279 typedef Motion::Vector6 Vector6;
280
281 typedef MotionRef<Vector6> MotionV6;
282
283
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2 Motion v_ref(Motion::Random());
284
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2 MotionV6 v(v_ref.toVector());
285
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2 BOOST_CHECK(v_ref.isApprox(v));
287
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2 MotionV6::MotionPlain v2(v * 2.);
289
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2 Motion v2_ref(v_ref * 2.);
290
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2 BOOST_CHECK(v2_ref.isApprox(v2));
292
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2 v2 = v_ref + v;
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2 BOOST_CHECK(v2_ref.isApprox(v2));
295
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2 v = v2;
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2 BOOST_CHECK(v2.isApprox(v));
298
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2 v2 = v - v;
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2 BOOST_CHECK(v2.isApprox(Motion::Zero()));
301
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2 SE3 M(SE3::Identity());
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2 v2 = M.act(v);
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2 BOOST_CHECK(v2.isApprox(v));
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2 v2 = M.actInv(v);
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2 BOOST_CHECK(v2.isApprox(v));
308
309
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2 Motion v3(Motion::Random());
310
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2 v_ref.setRandom();
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2 v = v_ref;
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2 v2 = v.cross(v3);
313
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2 v2_ref = v_ref.cross(v3);
314
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2 BOOST_CHECK(v2.isApprox(v2_ref));
316
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2 v.setRandom();
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2 v.setZero();
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2 BOOST_CHECK(v.isApprox(Motion::Zero()));
320
321 // Test ref() method
322 {
323
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2 Vector6 v6(Vector6::Random());
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2 MotionV6 a(v6);
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2 BOOST_CHECK(a.ref().isApprox(a));
326
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2 const Motion b(a);
328
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2 BOOST_CHECK(b.isApprox(a.ref()));
329 }
330 2 }
331
332
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4 BOOST_AUTO_TEST_CASE(test_motion_zero)
333 {
334 using namespace pinocchio;
335
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2 Motion v((MotionZero()));
336
337
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2 BOOST_CHECK(v.toVector().isZero());
338
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2 BOOST_CHECK(MotionZero() == Motion::Zero());
339
340 // SE3.act
341
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2 SE3 m(SE3::Random());
342
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2 BOOST_CHECK(m.act(MotionZero()) == Motion::Zero());
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2 BOOST_CHECK(m.actInv(MotionZero()) == Motion::Zero());
344
345 // Motion.cross
346
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2 Motion v2(Motion::Random());
347
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2 BOOST_CHECK(v2.cross(MotionZero()) == Motion::Zero());
348 2 }
349
350
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4 BOOST_AUTO_TEST_CASE(test_Force)
351 {
352 using namespace pinocchio;
353 typedef SE3::ActionMatrixType ActionMatrixType;
354 typedef Force::Vector6 Vector6;
355
356
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2 SE3 amb = SE3::Random();
357
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2 SE3 bmc = SE3::Random();
358
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2 SE3 amc = amb * bmc;
359
360
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2 Force bf = Force::Random();
361
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2 Force bf2 = Force::Random();
362
363
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2 Vector6 bf_vec = bf;
364
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2 Vector6 bf2_vec = bf2;
365
366 // std::stringstream
367
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2 std::stringstream ss;
368
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2 ss << bf << std::endl;
369
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2 BOOST_CHECK(!ss.str().empty());
370
371 // Test .+.
372
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2 Vector6 bfPbf2_vec = bf + bf2;
373
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2 BOOST_CHECK(bfPbf2_vec.isApprox(bf_vec + bf2_vec));
374
375 // Test -.
376
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2 Vector6 Mbf_vec = -bf;
377
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2 BOOST_CHECK(Mbf_vec.isApprox(-bf_vec));
378
379 // Test .+=.
380
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2 Force bf3 = bf;
381
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2 bf3 += bf2;
382
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2 BOOST_CHECK(bf3.toVector().isApprox(bf_vec + bf2_vec));
383
384 // Test .= V6
385
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2 bf3 = bf2_vec;
386
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2 BOOST_CHECK(bf3.toVector().isApprox(bf2_vec));
387
388 // Test constructor from V6
389
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2 Force bf4(bf2_vec);
390
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2 BOOST_CHECK(bf4.toVector().isApprox(bf2_vec));
391
392 // Test action
393
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2 ActionMatrixType aXb = amb;
394
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2 BOOST_CHECK(amb.act(bf).toVector().isApprox(aXb.inverse().transpose() * bf_vec));
395
396 // Test action inverse
397
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2 ActionMatrixType bXc = bmc;
398
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2 BOOST_CHECK(bmc.actInv(bf).toVector().isApprox(bXc.transpose() * bf_vec));
399
400 // Test double action
401
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2 Force cf = Force::Random();
402
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2 bf = bmc.act(cf);
403
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2 BOOST_CHECK(amb.act(bf).toVector().isApprox(amc.act(cf).toVector()));
404
405 // Simple test for cross product
406 // Force vxv = bf.cross(bf);
407 // ensure that (vxv.toVector().isMuchSmallerThan(bf.toVector()));
408
409
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2 Force f_not_zero(Vector6::Ones());
410
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2 BOOST_CHECK(!f_not_zero.isZero());
411
412
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2 Force f_zero(Vector6::Zero());
413
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2 BOOST_CHECK(f_zero.isZero());
414
415 // Test isApprox
416
417
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2 BOOST_CHECK(bf == bf);
418
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2 bf.setRandom();
419
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2 bf2.setZero();
420
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2 BOOST_CHECK(bf == bf);
421
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2 BOOST_CHECK(bf != bf2);
422
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2 BOOST_CHECK(bf.isApprox(bf));
423
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2 BOOST_CHECK(!bf.isApprox(bf2));
424
425 2 const double eps = 1e-6;
426
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2 Force bf_approx(bf);
427
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2 bf_approx.linear()[0] += 2. * eps;
428
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2 BOOST_CHECK(!bf_approx.isApprox(bf, eps));
429
430 // Test ref() method
431 {
432
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2 Force a(Force::Random());
433
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2 BOOST_CHECK(a.ref().isApprox(a));
434
435
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2 const Force b(a);
436
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2 BOOST_CHECK(b.isApprox(a.ref()));
437 }
438
439 // Test cast
440 {
441 typedef ForceTpl<float> Forcef;
442
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2 Force a(Force::Random());
443
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2 Forcef a_float = a.cast<float>();
444
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2 BOOST_CHECK(a_float.isApprox(a.cast<float>()));
445
446
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2 Forcef a_float2(a);
447
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2 BOOST_CHECK(a_float.isApprox(a_float2));
448 }
449
450 // Test scalar multiplication
451 2 const double alpha = 1.5;
452
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2 Force b(Force::Random());
453
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2 Force alpha_f = alpha * b;
454
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2 Force f_alpha = b * alpha;
455
456
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2 BOOST_CHECK(alpha_f == f_alpha);
457 2 }
458
459
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4 BOOST_AUTO_TEST_CASE(test_force_ref)
460 {
461 using namespace pinocchio;
462 typedef Force::Vector6 Vector6;
463
464 typedef ForceRef<Vector6> ForceV6;
465
466
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2 Force f_ref(Force::Random());
467
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2 ForceV6 f(f_ref.toVector());
468
469
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2 BOOST_CHECK(f_ref.isApprox(f));
470
471
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2 ForceV6::ForcePlain f2(f * 2.);
472
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2 Force f2_ref(f_ref * 2.);
473
474
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2 BOOST_CHECK(f2_ref.isApprox(f2));
475
476
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2 f2 = f_ref + f;
477
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2 BOOST_CHECK(f2_ref.isApprox(f2));
478
479
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2 f = f2;
480
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2 BOOST_CHECK(f2.isApprox(f));
481
482
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2 f2 = f - f;
483
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2 BOOST_CHECK(f2.isApprox(Force::Zero()));
484
485
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2 SE3 M(SE3::Identity());
486
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2 f2 = M.act(f);
487
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2 BOOST_CHECK(f2.isApprox(f));
488
489
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2 f2 = M.actInv(f);
490
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2 BOOST_CHECK(f2.isApprox(f));
491
492
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2 Motion v(Motion::Random());
493
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2 f_ref.setRandom();
494
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2 f = f_ref;
495
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2 f2 = v.cross(f);
496
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2 f2_ref = v.cross(f_ref);
497
498
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2 BOOST_CHECK(f2.isApprox(f2_ref));
499
500
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2 f.setRandom();
501
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2 f.setZero();
502
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2 BOOST_CHECK(f.isApprox(Force::Zero()));
503
504 // Test ref() method
505 {
506
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2 Vector6 v6(Vector6::Random());
507
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2 ForceV6 a(v6);
508
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2 BOOST_CHECK(a.ref().isApprox(a));
509
510
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2 const Force b(a);
511
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2 BOOST_CHECK(b.isApprox(a.ref()));
512 }
513 2 }
514
515
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4 BOOST_AUTO_TEST_CASE(test_Inertia)
516 {
517 using namespace pinocchio;
518 typedef Inertia::Matrix6 Matrix6;
519
520
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2 Inertia aI = Inertia::Random();
521
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2 Matrix6 matI = aI;
522
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2 BOOST_CHECK_EQUAL(matI(0, 0), aI.mass());
523
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2 BOOST_CHECK_EQUAL(matI(1, 1), aI.mass());
524
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2 BOOST_CHECK_EQUAL(matI(2, 2), aI.mass()); // 1,1 before unifying
525
526
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2 BOOST_CHECK_SMALL(
527 (matI - matI.transpose()).norm(),
528 matI.norm()); // previously ensure that( (matI-matI.transpose()).isMuchSmallerThan(matI) );
529
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2 BOOST_CHECK_SMALL(
530 (matI.topRightCorner<3, 3>() * aI.lever()).norm(),
531 aI.lever().norm()); // previously ensure that(
532 // (matI.topRightCorner<3,3>()*aI.lever()).isMuchSmallerThan(aI.lever()) );
533
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2 Inertia I1 = Inertia::Identity();
535
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2 BOOST_CHECK(I1.matrix().isApprox(Matrix6::Identity()));
536
537 // Test motion-to-force map
538
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2 Motion v = Motion::Random();
539
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2 Force f = I1 * v;
540
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2 BOOST_CHECK(f.toVector().isApprox(v.toVector()));
541
542 // Test Inertia group application
543
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2 SE3 bma = SE3::Random();
544
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2 Inertia bI = bma.act(aI);
545
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2 Matrix6 bXa = bma;
546
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2 BOOST_CHECK((bma.rotation() * aI.inertia().matrix() * bma.rotation().transpose())
547 .isApprox(bI.inertia().matrix()));
548
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2 BOOST_CHECK((bXa.transpose().inverse() * aI.matrix() * bXa.inverse()).isApprox(bI.matrix()));
549
550 // Test inverse action
551
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2 BOOST_CHECK((bXa.transpose() * bI.matrix() * bXa).isApprox(bma.actInv(bI).matrix()));
552
553 // Test vxIv cross product
554
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2 v = Motion::Random();
555
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2 f = aI * v;
556
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2 Force vxf = v.cross(f);
557
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2 Force vxIv = aI.vxiv(v);
558
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2 BOOST_CHECK(vxf.toVector().isApprox(vxIv.toVector()));
559
560 // Test operator+
561
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2 I1 = Inertia::Random();
562
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2 Inertia I2 = Inertia::Random();
563
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2 BOOST_CHECK((I1.matrix() + I2.matrix()).isApprox((I1 + I2).matrix()));
564
565 // Test operator-
566 {
567
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2 I1 = Inertia::Random();
568
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2 Inertia I2 = Inertia::Random();
569
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2 Inertia Isum = I1 + I2;
570
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2 Inertia I1_other = Isum - I2;
571
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2 BOOST_CHECK(I1_other.matrix().isApprox(I1.matrix()));
572 }
573
574 // Test operator +=
575
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2 Inertia I12 = I1;
576
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2 I12 += I2;
577
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2 BOOST_CHECK((I1.matrix() + I2.matrix()).isApprox(I12.matrix()));
578
579 // Test operator -=
580 {
581
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2 Inertia I2 = Inertia::Random();
582
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2 Inertia Isum = I1 + I2;
583
584
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2 Inertia I1_other = Isum;
585
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2 I1_other -= I2;
586
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2 BOOST_CHECK((I1_other.matrix()).isApprox(I1.matrix()));
587 }
588
589 // Test operator vtiv
590
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2 double kinetic_ref = v.toVector().transpose() * aI.matrix() * v.toVector();
591
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2 double kinetic = aI.vtiv(v);
592
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2 BOOST_CHECK_SMALL(kinetic_ref - kinetic, 1e-12);
593
594 // Test constructor (Matrix6)
595
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2 Inertia I1_bis(I1.matrix());
596
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2 BOOST_CHECK(I1.matrix().isApprox(I1_bis.matrix()));
597
598 // Test Inertia from ellipsoid
599 2 const double sphere_mass = 5.;
600 2 const double sphere_radius = 2.;
601
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2 I1 = Inertia::FromSphere(sphere_mass, sphere_radius);
602 2 const double L_sphere = 2. / 5. * sphere_mass * sphere_radius * sphere_radius;
603
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2 BOOST_CHECK_SMALL(I1.mass() - sphere_mass, 1e-12);
604
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2 BOOST_CHECK(I1.lever().isZero());
605
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2 BOOST_CHECK(
606 I1.inertia().matrix().isApprox(Symmetric3(L_sphere, 0., L_sphere, 0., 0., L_sphere).matrix()));
607
608 // Test Inertia from ellipsoid
609
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2 I1 = Inertia::FromEllipsoid(2., 3., 4., 5.);
610
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2 BOOST_CHECK_SMALL(I1.mass() - 2, 1e-12);
611
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2 BOOST_CHECK_SMALL(I1.lever().norm(), 1e-12);
612
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2 BOOST_CHECK(I1.inertia().matrix().isApprox(Symmetric3(16.4, 0., 13.6, 0., 0., 10.).matrix()));
613
614 // Test Inertia from Cylinder
615
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2 I1 = Inertia::FromCylinder(2., 4., 6.);
616
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2 BOOST_CHECK_SMALL(I1.mass() - 2, 1e-12);
617
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2 BOOST_CHECK_SMALL(I1.lever().norm(), 1e-12);
618
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2 BOOST_CHECK(I1.inertia().matrix().isApprox(Symmetric3(14., 0., 14., 0., 0., 16.).matrix()));
619
620 // Test Inertia from Box
621
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2 I1 = Inertia::FromBox(2., 6., 12., 18.);
622
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2 BOOST_CHECK_SMALL(I1.mass() - 2, 1e-12);
623
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2 BOOST_CHECK_SMALL(I1.lever().norm(), 1e-12);
624
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2 BOOST_CHECK(I1.inertia().matrix().isApprox(Symmetric3(78., 0., 60., 0., 0., 30.).matrix()));
625
626 // Test Inertia From Capsule
627
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2 I1 = Inertia::FromCapsule(1., 2., 3);
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2 BOOST_CHECK_SMALL(I1.mass() - 1, 1e-12);
629
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2 BOOST_CHECK_SMALL(I1.lever().norm(), 1e-12);
630
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2 BOOST_CHECK(I1.inertia().matrix().isApprox(
631 Symmetric3(3.79705882, 0., 3.79705882, 0., 0., 1.81176471).matrix(),
632 1e-5)); // Computed with hppfcl::Capsule
633
634 // Copy operator
635
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2 Inertia aI_copy(aI);
636
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2 BOOST_CHECK(aI_copy == aI);
637
638 // Test isZero
639
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2 Inertia I_not_zero = Inertia::Identity();
640
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2 BOOST_CHECK(!I_not_zero.isZero());
641
642
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2 Inertia I_zero = Inertia::Zero();
643
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2 BOOST_CHECK(I_zero.isZero());
644
645 // Test isApprox
646 2 const double eps = 1e-6;
647
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2 BOOST_CHECK(aI == aI);
648
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2 BOOST_CHECK(aI.isApprox(aI));
649
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2 Inertia aI_approx(aI);
650 2 aI_approx.mass() += eps / 2.;
651
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2 BOOST_CHECK(aI_approx.isApprox(aI, eps));
652
653 // Test Variation
654
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2 Inertia::Matrix6 aIvariation = aI.variation(v);
655
656
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2 Motion::ActionMatrixType vAction = v.toActionMatrix();
657
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2 Motion::ActionMatrixType vDualAction = v.toDualActionMatrix();
658
659
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2 Inertia::Matrix6 aImatrix = aI.matrix();
660
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2 Inertia::Matrix6 aIvariation_ref = vDualAction * aImatrix - aImatrix * vAction;
661
662
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2 BOOST_CHECK(aIvariation.isApprox(aIvariation_ref));
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2 BOOST_CHECK(vxIv.isApprox(Force(aIvariation * v.toVector())));
664
665 // Test vxI operator
666 {
667 typedef Inertia::Matrix6 Matrix6;
668
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2 Inertia I(Inertia::Random());
669
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2 Motion v(Motion::Random());
670
671
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2 const Matrix6 M_ref(v.toDualActionMatrix() * I.matrix());
672
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2 Matrix6 M;
673
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2 Inertia::vxi(v, I, M);
674
675
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2 BOOST_CHECK(M.isApprox(M_ref));
676
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2 BOOST_CHECK(I.vxi(v).isApprox(M_ref));
677 }
678
679 // Test Ivx operator
680 {
681 typedef Inertia::Matrix6 Matrix6;
682
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2 Inertia I(Inertia::Random());
683
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2 Motion v(Motion::Random());
684
685
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2 const Matrix6 M_ref(I.matrix() * v.toActionMatrix());
686
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2 Matrix6 M;
687
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2 Inertia::ivx(v, I, M);
688
689
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2 BOOST_CHECK(M.isApprox(M_ref));
690
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2 BOOST_CHECK(I.ivx(v).isApprox(M_ref));
691 }
692
693 // Test variation against vxI - Ivx operator
694 {
695 typedef Inertia::Matrix6 Matrix6;
696
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2 Inertia I(Inertia::Random());
697
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2 Motion v(Motion::Random());
698
699
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2 Matrix6 Ivariation = I.variation(v);
700
701
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2 Matrix6 M1;
702
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2 Inertia::vxi(v, I, M1);
703
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2 Matrix6 M2;
704
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2 Inertia::ivx(v, I, M2);
705
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2 Matrix6 M3(M1 - M2);
706
707
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2 BOOST_CHECK(M3.isApprox(Ivariation));
708 }
709
710 // Test inverse
711 {
712
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2 Inertia I(Inertia::Random());
713
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2 Inertia::Matrix6 I_inv = I.inverse();
714
715
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2 BOOST_CHECK(I_inv.isApprox(I.matrix().inverse()));
716 }
717
718 // Test dynamic parameters
719 {
720
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2 Inertia I(Inertia::Random());
721
722
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2 Inertia::Vector10 v = I.toDynamicParameters();
723
724
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2 BOOST_CHECK_CLOSE(v[0], I.mass(), 1e-12);
725
726
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2 BOOST_CHECK(v.segment<3>(1).isApprox(I.mass() * I.lever()));
727
728
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2 Eigen::Matrix3d I_o = I.inertia() + I.mass() * skew(I.lever()).transpose() * skew(I.lever());
729
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2 Eigen::Matrix3d I_ov;
730
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2 I_ov << v[4], v[5], v[7], v[5], v[6], v[8], v[7], v[8], v[9];
731
732
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2 BOOST_CHECK(I_o.isApprox(I_ov));
733
734
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2 Inertia I2 = Inertia::FromDynamicParameters(v);
735
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2 BOOST_CHECK(I2.isApprox(I));
736 }
737
738 // Test disp
739
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2 std::cout << aI << std::endl;
740
741 // Test Inertia parametrizations
742 {
743 typedef LogCholeskyParametersTpl<double, 0> LogCholeskyParameters;
744 typedef PseudoInertiaTpl<double, 0> PseudoInertia;
745
746
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2 Inertia::Vector10 eta;
747
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2 eta.setRandom();
748
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2 LogCholeskyParameters log_cholesky = LogCholeskyParameters(eta);
749
750 // Convert logcholesky parametrization to pseudo-inertia
751
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2 PseudoInertia pseudo = log_cholesky.toPseudoInertia();
752
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2 Eigen::Matrix4d pseudo_matrix = pseudo.toMatrix();
753 // Convert logcholesky to inertia tpl
754
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2 Inertia I_from_log_cholesky = Inertia::FromLogCholeskyParameters(log_cholesky);
755
756 // Check if conversion from inertia tpl to pseudo inertia gives same result as from logcholesky
757 // parametrization to pseudo-inertia
758
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2 Eigen::Matrix4d pseudo_from_inertia = I_from_log_cholesky.toPseudoInertia().toMatrix();
759
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2 BOOST_CHECK(pseudo_matrix.isApprox(pseudo_from_inertia, 1e-10));
760
761 // // Check if log-cholesky parametrization to pseudo-inertia gives same result as their
762 // calculations
763
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2 double alpha = log_cholesky.parameters[0];
764
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2 double d1 = log_cholesky.parameters[1];
765
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2 double d2 = log_cholesky.parameters[2];
766
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2 double d3 = log_cholesky.parameters[3];
767
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2 double s12 = log_cholesky.parameters[4];
768
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2 double s23 = log_cholesky.parameters[5];
769
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2 double s13 = log_cholesky.parameters[6];
770
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2 double t1 = log_cholesky.parameters[7];
771
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2 double t2 = log_cholesky.parameters[8];
772
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2 double t3 = log_cholesky.parameters[9];
773
774 2 double exp_alpha = std::exp(alpha);
775 2 double exp_d1 = std::exp(d1);
776 2 double exp_d2 = std::exp(d2);
777 2 double exp_d3 = std::exp(d3);
778
779
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2 Eigen::Matrix4d U;
780 // clang-format off
781
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2 U << exp_d1, s12, s13, t1,
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2 0, exp_d2, s23, t2,
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2 0, 0, exp_d3, t3,
784
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2 0, 0, 0, 1;
785 // clang-format on
786
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2 U *= exp_alpha;
787
788
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2 Eigen::Matrix4d pseudo_chol = U * U.transpose();
789
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2 BOOST_CHECK(pseudo_matrix.isApprox(pseudo_chol, 1e-10));
790
791 // Additional checks: Convert back from pseudo-inertia to inertia and validate
792
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2 Inertia I_back = pseudo.toInertia();
793
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2 BOOST_CHECK_CLOSE(I_back.mass(), I_from_log_cholesky.mass(), 1e-12);
794
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2 BOOST_CHECK(I_back.lever().isApprox(I_from_log_cholesky.lever(), 1e-12));
795
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2 BOOST_CHECK(I_back.inertia().isApprox(I_from_log_cholesky.inertia(), 1e-12));
796
797 // Convert Inertia to dynamic parameters
798
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2 Inertia::Vector10 dynamic_params_inertia = I_from_log_cholesky.toDynamicParameters();
799
800 // Convert log Cholesky to dynamic parameters
801
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2 Inertia::Vector10 dynamic_params_log_cholesky = log_cholesky.toDynamicParameters();
802
803 // Compare dynamic parameters from Inertia and log Cholesky
804
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2 BOOST_CHECK(dynamic_params_inertia.isApprox(dynamic_params_log_cholesky, 1e-10));
805
806 // Convert Pseudo Inertia to dynamic parameters
807
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2 PseudoInertia pseudo_inertia = PseudoInertia::FromMatrix(pseudo_matrix);
808
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2 Inertia::Vector10 dynamic_params_pseudo_inertia = pseudo_inertia.toDynamicParameters();
809
810 // Compare dynamic parameters from Inertia and Pseudo Inertia
811
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2 BOOST_CHECK(dynamic_params_inertia.isApprox(dynamic_params_pseudo_inertia, 1e-10));
812
813 // Compare dynamic parameters from log Cholesky and Pseudo Inertia
814
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2 BOOST_CHECK(dynamic_params_log_cholesky.isApprox(dynamic_params_pseudo_inertia, 1e-10));
815
816 // Calculate Jacobian of logcholesky parametrization
817
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2 Eigen::Matrix<double, 10, 10> jacobian = log_cholesky.calculateJacobian();
818
819 // Check if determinant is non-zero
820
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2 BOOST_CHECK(std::abs(jacobian.determinant()) > 1e-10);
821
822 // Check physical consistency by positive definiteness of pseudo inertia
823
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2 Eigen::SelfAdjointEigenSolver<Eigen::Matrix4d> eigensolver(pseudo_matrix);
824
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2 BOOST_CHECK((eigensolver.eigenvalues().array() > 0).all());
825
826 // Test disp
827
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2 std::cout << I_from_log_cholesky << std::endl;
828
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2 std::cout << log_cholesky << std::endl;
829
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2 std::cout << pseudo_inertia << std::endl;
830 }
831 2 }
832
833
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4 BOOST_AUTO_TEST_CASE(cast_inertia)
834 {
835 using namespace pinocchio;
836
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2 Inertia Y(Inertia::Random());
837
838 typedef InertiaTpl<long double> Inertiald;
839
840
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2 BOOST_CHECK(Y.cast<double>() == Y);
841
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2 BOOST_CHECK(Y.cast<long double>().cast<double>() == Y);
842
843
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2 Inertiald Y2(Y);
844
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2 BOOST_CHECK(Y2.isApprox(Y.cast<long double>()));
845 2 }
846
847
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4 BOOST_AUTO_TEST_CASE(test_ActOnSet)
848 {
849 using namespace pinocchio;
850 2 const int N = 20;
851 typedef Eigen::Matrix<double, 6, N> Matrix6N;
852
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2 SE3 jMi = SE3::Random();
853
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2 Motion v = Motion::Random();
854
855 // Forcet SET
856 PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH
857 PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED
858
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2 Matrix6N iF = Matrix6N::Random(), jF, jFinv, jF_ref, jFinv_ref;
859
860 // forceSet::se3Action
861
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2 forceSet::se3Action(jMi, iF, jF);
862
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42 for (int k = 0; k < N; ++k)
863
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40 BOOST_CHECK(jMi.act(Force(iF.col(k))).toVector().isApprox(jF.col(k)));
864
865
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2 jF_ref = jMi.toDualActionMatrix() * iF;
866
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2 BOOST_CHECK(jF_ref.isApprox(jF));
867
868
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2 forceSet::se3ActionInverse(jMi.inverse(), iF, jFinv);
869
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2 BOOST_CHECK(jFinv.isApprox(jF));
870 PINOCCHIO_COMPILER_DIAGNOSTIC_POP
871
872
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2 Matrix6N iF2 = Matrix6N::Random();
873
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2 jF_ref += jMi.toDualActionMatrix() * iF2;
874
875
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2 forceSet::se3Action<ADDTO>(jMi, iF2, jF);
876
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2 BOOST_CHECK(jF.isApprox(jF_ref));
877
878
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2 Matrix6N iF3 = Matrix6N::Random();
879
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2 jF_ref -= jMi.toDualActionMatrix() * iF3;
880
881
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2 forceSet::se3Action<RMTO>(jMi, iF3, jF);
882
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2 BOOST_CHECK(jF.isApprox(jF_ref));
883
884 // forceSet::se3ActionInverse
885
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2 forceSet::se3ActionInverse(jMi, iF, jFinv);
886
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2 jFinv_ref = jMi.inverse().toDualActionMatrix() * iF;
887
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2 BOOST_CHECK(jFinv_ref.isApprox(jFinv));
888
889
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2 jFinv_ref += jMi.inverse().toDualActionMatrix() * iF2;
890
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2 forceSet::se3ActionInverse<ADDTO>(jMi, iF2, jFinv);
891
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2 BOOST_CHECK(jFinv.isApprox(jFinv_ref));
892
893
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2 jFinv_ref -= jMi.inverse().toDualActionMatrix() * iF3;
894
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2 forceSet::se3ActionInverse<RMTO>(jMi, iF3, jFinv);
895
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2 BOOST_CHECK(jFinv.isApprox(jFinv_ref));
896
897 // forceSet::motionAction
898
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2 forceSet::motionAction(v, iF, jF);
899
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42 for (int k = 0; k < N; ++k)
900
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40 BOOST_CHECK(v.cross(Force(iF.col(k))).toVector().isApprox(jF.col(k)));
901
902
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2 jF_ref = v.toDualActionMatrix() * iF;
903
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2 BOOST_CHECK(jF.isApprox(jF_ref));
904
905
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2 jF_ref += v.toDualActionMatrix() * iF2;
906
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2 forceSet::motionAction<ADDTO>(v, iF2, jF);
907
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2 BOOST_CHECK(jF.isApprox(jF_ref));
908
909
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2 jF_ref -= v.toDualActionMatrix() * iF3;
910
1/2
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2 forceSet::motionAction<RMTO>(v, iF3, jF);
911
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2 BOOST_CHECK(jF.isApprox(jF_ref));
912
913 // Motion SET
914 PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH
915 PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED
916
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2 Matrix6N iV = Matrix6N::Random(), jV, jV_ref, jVinv, jVinv_ref;
917
918 // motionSet::se3Action
919
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2 motionSet::se3Action(jMi, iV, jV);
920
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42 for (int k = 0; k < N; ++k)
921
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40 BOOST_CHECK(jMi.act(Motion(iV.col(k))).toVector().isApprox(jV.col(k)));
922
923
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2 jV_ref = jMi.toActionMatrix() * iV;
924
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2 BOOST_CHECK(jV.isApprox(jV_ref));
925
926
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2 motionSet::se3ActionInverse(jMi.inverse(), iV, jVinv);
927
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2 BOOST_CHECK(jVinv.isApprox(jV));
928 PINOCCHIO_COMPILER_DIAGNOSTIC_POP
929
930
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2 Matrix6N iV2 = Matrix6N::Random();
931
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2 jV_ref += jMi.toActionMatrix() * iV2;
932
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2 motionSet::se3Action<ADDTO>(jMi, iV2, jV);
933
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2 BOOST_CHECK(jV.isApprox(jV_ref));
934
935
2/4
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2 Matrix6N iV3 = Matrix6N::Random();
936
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2 jV_ref -= jMi.toActionMatrix() * iV3;
937
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2 motionSet::se3Action<RMTO>(jMi, iV3, jV);
938
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2 BOOST_CHECK(jV.isApprox(jV_ref));
939
940 // motionSet::se3ActionInverse
941
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2 motionSet::se3ActionInverse(jMi, iV, jVinv);
942
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2 jVinv_ref = jMi.inverse().toActionMatrix() * iV;
943
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2 BOOST_CHECK(jVinv.isApprox(jVinv_ref));
944
945
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2 jVinv_ref += jMi.inverse().toActionMatrix() * iV2;
946
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2 motionSet::se3ActionInverse<ADDTO>(jMi, iV2, jVinv);
947
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2 BOOST_CHECK(jVinv.isApprox(jVinv_ref));
948
949
4/8
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2 jVinv_ref -= jMi.inverse().toActionMatrix() * iV3;
950
1/2
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2 motionSet::se3ActionInverse<RMTO>(jMi, iV3, jVinv);
951
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2 BOOST_CHECK(jVinv.isApprox(jVinv_ref));
952
953 // motionSet::motionAction
954
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2 motionSet::motionAction(v, iV, jV);
955
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42 for (int k = 0; k < N; ++k)
956
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40 BOOST_CHECK(v.cross(Motion(iV.col(k))).toVector().isApprox(jV.col(k)));
957
958
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2 jV_ref = v.toActionMatrix() * iV;
959
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2 BOOST_CHECK(jV.isApprox(jV_ref));
960
961
3/6
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2 jV_ref += v.toActionMatrix() * iV2;
962
1/2
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2 motionSet::motionAction<ADDTO>(v, iV2, jV);
963
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2 BOOST_CHECK(jV.isApprox(jV_ref));
964
965
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2 jV_ref -= v.toActionMatrix() * iV3;
966
1/2
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2 motionSet::motionAction<RMTO>(v, iV3, jV);
967
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2 BOOST_CHECK(jV.isApprox(jV_ref));
968
969 // motionSet::inertiaAction
970
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2 const Inertia I(Inertia::Random());
971
1/2
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2 motionSet::inertiaAction(I, iV, jV);
972
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42 for (int k = 0; k < N; ++k)
973
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40 BOOST_CHECK((I * (Motion(iV.col(k)))).toVector().isApprox(jV.col(k)));
974
975
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2 jV_ref = I.matrix() * iV;
976
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2 BOOST_CHECK(jV.isApprox(jV_ref));
977
978
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2 jV_ref += I.matrix() * iV2;
979
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2 motionSet::inertiaAction<ADDTO>(I, iV2, jV);
980
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2 BOOST_CHECK(jV.isApprox(jV_ref));
981
982
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2 jV_ref -= I.matrix() * iV3;
983
1/2
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2 motionSet::inertiaAction<RMTO>(I, iV3, jV);
984
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2 BOOST_CHECK(jV.isApprox(jV_ref));
985
986 // motionSet::act
987
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2 Force f = Force::Random();
988
1/2
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2 motionSet::act(iV, f, jF);
989
2/2
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42 for (int k = 0; k < N; ++k)
990
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40 BOOST_CHECK(Motion(iV.col(k)).cross(f).toVector().isApprox(jF.col(k)));
991
992
2/2
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42 for (int k = 0; k < N; ++k)
993
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40 jF_ref.col(k) = Force(Motion(iV.col(k)).cross(f)).toVector();
994
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2 BOOST_CHECK(jF.isApprox(jF_ref));
995
996
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42 for (int k = 0; k < N; ++k)
997
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40 jF_ref.col(k) += Force(Motion(iV2.col(k)).cross(f)).toVector();
998
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2 motionSet::act<ADDTO>(iV2, f, jF);
999
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2 BOOST_CHECK(jF.isApprox(jF_ref));
1000
1001
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42 for (int k = 0; k < N; ++k)
1002
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40 jF_ref.col(k) -= Force(Motion(iV3.col(k)).cross(f)).toVector();
1003
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2 motionSet::act<RMTO>(iV3, f, jF);
1004
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2 BOOST_CHECK(jF.isApprox(jF_ref));
1005 2 }
1006
1007
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4 BOOST_AUTO_TEST_CASE(test_skew)
1008 {
1009 using namespace pinocchio;
1010 typedef SE3::Vector3 Vector3;
1011 typedef Motion::Vector6 Vector6;
1012
1013
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2 Vector3 v3(Vector3::Random());
1014
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2 Vector6 v6(Vector6::Random());
1015
1016
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2 Vector3 res1 = unSkew(skew(v3));
1017
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2 BOOST_CHECK(res1.isApprox(v3));
1018
1019
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2 Vector3 res2 = unSkew(skew(v6.head<3>()));
1020
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2 BOOST_CHECK(res2.isApprox(v6.head<3>()));
1021
1022
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2 Vector3 res3 = skew(v3) * v3;
1023
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2 BOOST_CHECK(res3.isZero());
1024
1025
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2 Vector3 rhs(Vector3::Random());
1026
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2 Vector3 res41 = skew(v3) * rhs;
1027
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2 Vector3 res42 = v3.cross(rhs);
1028
1029
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2 BOOST_CHECK(res41.isApprox(res42));
1030 2 }
1031
1032
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4 BOOST_AUTO_TEST_CASE(test_addSkew)
1033 {
1034 using namespace pinocchio;
1035 typedef SE3::Vector3 Vector3;
1036 typedef SE3::Matrix3 Matrix3;
1037
1038
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2 Vector3 v(Vector3::Random());
1039
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2 Matrix3 M(Matrix3::Random());
1040
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2 Matrix3 Mcopy(M);
1041
1042
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2 addSkew(v, M);
1043
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2 Matrix3 Mref = Mcopy + skew(v);
1044
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2 BOOST_CHECK(M.isApprox(Mref));
1045
1046
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2 Mref += skew(-v);
1047
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2 addSkew(-v, M);
1048
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2 BOOST_CHECK(M.isApprox(Mcopy));
1049
1050
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2 M.setZero();
1051
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2 addSkew(v, M);
1052
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2 BOOST_CHECK(M.isApprox(skew(v)));
1053 2 }
1054
1055
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4 BOOST_AUTO_TEST_CASE(test_skew_square)
1056 {
1057 using namespace pinocchio;
1058 typedef SE3::Vector3 Vector3;
1059 typedef SE3::Matrix3 Matrix3;
1060
1061
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2 Vector3 u(Vector3::Random());
1062
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2 Vector3 v(Vector3::Random());
1063
1064
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2 Matrix3 ref = skew(u) * skew(v);
1065
1066
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2 Matrix3 res = skewSquare(u, v);
1067
1068
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2 BOOST_CHECK(res.isApprox(ref));
1069 2 }
1070
1071 template<int axis>
1072 struct test_scalar_multiplication_cartesian_axis
1073 {
1074 typedef pinocchio::CartesianAxis<axis> Axis;
1075 typedef double Scalar;
1076 typedef Eigen::Matrix<Scalar, 3, 1> Vector3;
1077
1078 6 static void run()
1079 {
1080 6 const Scalar alpha = static_cast<Scalar>(rand()) / static_cast<Scalar>(RAND_MAX);
1081
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6 const Vector3 r1 = Axis() * alpha;
1082
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6 const Vector3 r2 = alpha * Axis();
1083
1084
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6 BOOST_CHECK(r1.isApprox(r2));
1085
1086
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24 for (int k = 0; k < Axis::dim; ++k)
1087 {
1088
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18 if (k == axis)
1089 {
1090
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6 BOOST_CHECK(r1[k] == alpha);
1091
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6 BOOST_CHECK(r2[k] == alpha);
1092 }
1093 else
1094 {
1095
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12 BOOST_CHECK(r1[k] == Scalar(0));
1096
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12 BOOST_CHECK(r2[k] == Scalar(0));
1097 }
1098 }
1099 6 }
1100 };
1101
1102
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4 BOOST_AUTO_TEST_CASE(test_cartesian_axis)
1103 {
1104 using namespace Eigen;
1105 using namespace pinocchio;
1106
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2 Vector3d v(Vector3d::Random());
1107 2 const double alpha = 3;
1108
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2 Vector3d v2(alpha * v);
1109
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2 BOOST_CHECK(XAxis::cross(v).isApprox(Vector3d::Unit(0).cross(v)));
1111
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2 BOOST_CHECK(YAxis::cross(v).isApprox(Vector3d::Unit(1).cross(v)));
1112
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2 BOOST_CHECK(ZAxis::cross(v).isApprox(Vector3d::Unit(2).cross(v)));
1113
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2 BOOST_CHECK(XAxis::alphaCross(alpha, v).isApprox(Vector3d::Unit(0).cross(v2)));
1114
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2 BOOST_CHECK(YAxis::alphaCross(alpha, v).isApprox(Vector3d::Unit(1).cross(v2)));
1115
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2 BOOST_CHECK(ZAxis::alphaCross(alpha, v).isApprox(Vector3d::Unit(2).cross(v2)));
1116
1117
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2 test_scalar_multiplication_cartesian_axis<0>::run();
1118
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2 test_scalar_multiplication_cartesian_axis<1>::run();
1119
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2 test_scalar_multiplication_cartesian_axis<2>::run();
1120
1121 // test Vector value
1122
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2 BOOST_CHECK(XAxis::vector() == Vector3d::UnitX());
1123
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2 BOOST_CHECK(YAxis::vector() == Vector3d::UnitY());
1124
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2 BOOST_CHECK(ZAxis::vector() == Vector3d::UnitZ());
1125 2 }
1126
1127 template<int axis>
1128 struct test_scalar_multiplication
1129 {
1130 typedef pinocchio::SpatialAxis<axis> Axis;
1131 typedef double Scalar;
1132 typedef pinocchio::MotionTpl<Scalar> Motion;
1133
1134 12 static void run()
1135 {
1136 12 const Scalar alpha = static_cast<Scalar>(rand()) / static_cast<Scalar>(RAND_MAX);
1137
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12 const Motion r1 = Axis() * alpha;
1138
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12 const Motion r2 = alpha * Axis();
1139
1140
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12 BOOST_CHECK(r1.isApprox(r2));
1141
1142
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84 for (int k = 0; k < Axis::dim; ++k)
1143 {
1144
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72 if (k == axis)
1145 {
1146
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12 BOOST_CHECK(r1.toVector()[k] == alpha);
1147
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12 BOOST_CHECK(r2.toVector()[k] == alpha);
1148 }
1149 else
1150 {
1151
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60 BOOST_CHECK(r1.toVector()[k] == Scalar(0));
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60 BOOST_CHECK(r2.toVector()[k] == Scalar(0));
1153 }
1154 }
1155 12 }
1156 };
1157
1158
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4 BOOST_AUTO_TEST_CASE(test_spatial_axis)
1159 {
1160 using namespace pinocchio;
1161
1162
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2 Motion v(Motion::Random());
1163
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2 Force f(Force::Random());
1164
1165
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2 Motion vaxis;
1166
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2 vaxis << AxisVX();
1167
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2 BOOST_CHECK(AxisVX::cross(v).isApprox(vaxis.cross(v)));
1168
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2 BOOST_CHECK(v.cross(AxisVX()).isApprox(v.cross(vaxis)));
1169
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2 BOOST_CHECK(AxisVX::cross(f).isApprox(vaxis.cross(f)));
1170
1171
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2 vaxis << AxisVY();
1172
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2 BOOST_CHECK(AxisVY::cross(v).isApprox(vaxis.cross(v)));
1173
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2 BOOST_CHECK(v.cross(AxisVY()).isApprox(v.cross(vaxis)));
1174
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2 BOOST_CHECK(AxisVY::cross(f).isApprox(vaxis.cross(f)));
1175
1176
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2 vaxis << AxisVZ();
1177
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2 BOOST_CHECK(AxisVZ::cross(v).isApprox(vaxis.cross(v)));
1178
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2 BOOST_CHECK(v.cross(AxisVZ()).isApprox(v.cross(vaxis)));
1179
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2 BOOST_CHECK(AxisVZ::cross(f).isApprox(vaxis.cross(f)));
1180
1181
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2 vaxis << AxisWX();
1182
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2 BOOST_CHECK(AxisWX::cross(v).isApprox(vaxis.cross(v)));
1183
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2 BOOST_CHECK(v.cross(AxisWX()).isApprox(v.cross(vaxis)));
1184
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2 BOOST_CHECK(AxisWX::cross(f).isApprox(vaxis.cross(f)));
1185
1186
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2 vaxis << AxisWY();
1187
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2 BOOST_CHECK(AxisWY::cross(v).isApprox(vaxis.cross(v)));
1188
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2 BOOST_CHECK(v.cross(AxisWY()).isApprox(v.cross(vaxis)));
1189
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2 BOOST_CHECK(AxisWY::cross(f).isApprox(vaxis.cross(f)));
1190
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2 vaxis << AxisWZ();
1192
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2 BOOST_CHECK(AxisWZ::cross(v).isApprox(vaxis.cross(v)));
1193
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2 BOOST_CHECK(v.cross(AxisWZ()).isApprox(v.cross(vaxis)));
1194
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2 BOOST_CHECK(AxisWZ::cross(f).isApprox(vaxis.cross(f)));
1195
1196 // Test operation Axis * Scalar
1197
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2 test_scalar_multiplication<0>::run();
1198
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2 test_scalar_multiplication<1>::run();
1199
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2 test_scalar_multiplication<2>::run();
1200
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2 test_scalar_multiplication<3>::run();
1201
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2 test_scalar_multiplication<4>::run();
1202
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2 test_scalar_multiplication<5>::run();
1203
1204 // Operations of Constraint on forces Sxf
1205 typedef Motion::ActionMatrixType ActionMatrixType;
1206 typedef ActionMatrixType::ColXpr ColType;
1207 typedef ForceRef<ColType> ForceRefOnColType;
1208 typedef MotionRef<ColType> MotionRefOnColType;
1209
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2 ActionMatrixType Sxf, Sxf_ref;
1210
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2 ActionMatrixType S(ActionMatrixType::Identity());
1211
1212
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2 SpatialAxis<0>::cross(f, ForceRefOnColType(Sxf.col(0)));
1213
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2 SpatialAxis<1>::cross(f, ForceRefOnColType(Sxf.col(1)));
1214
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2 SpatialAxis<2>::cross(f, ForceRefOnColType(Sxf.col(2)));
1215
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2 SpatialAxis<3>::cross(f, ForceRefOnColType(Sxf.col(3)));
1216
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2 SpatialAxis<4>::cross(f, ForceRefOnColType(Sxf.col(4)));
1217
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2 SpatialAxis<5>::cross(f, ForceRefOnColType(Sxf.col(5)));
1218
1219
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14 for (int k = 0; k < 6; ++k)
1220 {
1221
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12 MotionRefOnColType Scol(S.col(k));
1222
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12 ForceRefOnColType(Sxf_ref.col(k)) = Scol.cross(f);
1223 }
1224
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2 BOOST_CHECK(Sxf.isApprox(Sxf_ref));
1226 2 }
1227
1228 BOOST_AUTO_TEST_SUITE_END()
1229