pinocchio  3.7.0
A fast and flexible implementation of Rigid Body Dynamics algorithms and their analytical derivatives
 
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explog.hpp
1//
2// Copyright (c) 2015-2023 CNRS INRIA
3// Copyright (c) 2015 Wandercraft, 86 rue de Paris 91400 Orsay, France.
4//
5
6#ifndef __pinocchio_spatial_explog_hpp__
7#define __pinocchio_spatial_explog_hpp__
8
9#include "pinocchio/fwd.hpp"
10#include "pinocchio/utils/static-if.hpp"
11#include "pinocchio/math/fwd.hpp"
12#include "pinocchio/math/sincos.hpp"
13#include "pinocchio/math/taylor-expansion.hpp"
14#include "pinocchio/spatial/motion.hpp"
15#include "pinocchio/spatial/skew.hpp"
16#include "pinocchio/spatial/se3.hpp"
17
18#include <Eigen/Geometry>
19
20#include "pinocchio/spatial/log.hpp"
21
22namespace pinocchio
23{
33 template<typename Vector3Like>
34 typename Eigen::
35 Matrix<typename Vector3Like::Scalar, 3, 3, PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3Like)::Options>
36 exp3(const Eigen::MatrixBase<Vector3Like> & v)
37 {
38 PINOCCHIO_ASSERT_MATRIX_SPECIFIC_SIZE(Vector3Like, v, 3, 1);
39
40 typedef typename Vector3Like::Scalar Scalar;
41 typedef typename PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3Like) Vector3LikePlain;
42 typedef Eigen::Matrix<Scalar, 3, 3, Vector3LikePlain::Options> Matrix3;
43 const static Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
44
45 const Scalar t2 = v.squaredNorm() + eps * eps;
46
47 const Scalar t = math::sqrt(t2);
48 Scalar ct, st;
49 SINCOS(t, &st, &ct);
50
51 const Scalar alpha_vxvx = internal::if_then_else(
52 internal::GT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(),
53 static_cast<Scalar>((1 - ct) / t2), static_cast<Scalar>(Scalar(1) / Scalar(2) - t2 / 24));
54 const Scalar alpha_vx = internal::if_then_else(
55 internal::GT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(),
56 static_cast<Scalar>((st) / t), static_cast<Scalar>(Scalar(1) - t2 / 6));
57 Matrix3 res(alpha_vxvx * v * v.transpose());
58 res.coeffRef(0, 1) -= alpha_vx * v[2];
59 res.coeffRef(1, 0) += alpha_vx * v[2];
60 res.coeffRef(0, 2) += alpha_vx * v[1];
61 res.coeffRef(2, 0) -= alpha_vx * v[1];
62 res.coeffRef(1, 2) -= alpha_vx * v[0];
63 res.coeffRef(2, 1) += alpha_vx * v[0];
64
65 ct = internal::if_then_else(
66 internal::GT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(), ct,
67 static_cast<Scalar>(Scalar(1) - t2 / 2));
68 res.diagonal().array() += ct;
69
70 return res;
71 }
72
80 template<typename Matrix3Like>
81 Eigen::
82 Matrix<typename Matrix3Like::Scalar, 3, 1, PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3Like)::Options>
83 log3(const Eigen::MatrixBase<Matrix3Like> & R, typename Matrix3Like::Scalar & theta)
84 {
85 typedef typename Matrix3Like::Scalar Scalar;
86 typedef Eigen::Matrix<Scalar, 3, 1, PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3Like)::Options> Vector3;
87 Vector3 res;
88 log3_impl<Scalar>::run(R, theta, res);
89 return res;
90 }
91
100 template<typename Matrix3Like>
101 Eigen::
102 Matrix<typename Matrix3Like::Scalar, 3, 1, PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3Like)::Options>
103 log3(const Eigen::MatrixBase<Matrix3Like> & R)
104 {
105 typename Matrix3Like::Scalar theta;
106 return log3(R.derived(), theta);
107 }
108
117 template<AssignmentOperatorType op, typename Vector3Like, typename Matrix3Like>
118 void Jexp3(const Eigen::MatrixBase<Vector3Like> & r, const Eigen::MatrixBase<Matrix3Like> & Jexp)
119 {
120 PINOCCHIO_ASSERT_MATRIX_SPECIFIC_SIZE(Vector3Like, r, 3, 1);
121 PINOCCHIO_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3Like, Jexp, 3, 3);
122
123 Matrix3Like & Jout = PINOCCHIO_EIGEN_CONST_CAST(Matrix3Like, Jexp);
124 typedef typename Matrix3Like::Scalar Scalar;
125
126 const Scalar n2 = r.squaredNorm();
127 const Scalar n = math::sqrt(n2);
128 const Scalar n_inv = Scalar(1) / n;
129 const Scalar n2_inv = n_inv * n_inv;
130 Scalar cn, sn;
131 SINCOS(n, &sn, &cn);
132
133 const Scalar a = internal::if_then_else(
134 internal::LT, n, TaylorSeriesExpansion<Scalar>::template precision<3>(),
135 static_cast<Scalar>(Scalar(1) - n2 / Scalar(6)), static_cast<Scalar>(sn * n_inv));
136 const Scalar b = internal::if_then_else(
137 internal::LT, n, TaylorSeriesExpansion<Scalar>::template precision<3>(),
138 static_cast<Scalar>(-Scalar(1) / Scalar(2) - n2 / Scalar(24)),
139 static_cast<Scalar>(-(1 - cn) * n2_inv));
140 const Scalar c = internal::if_then_else(
141 internal::LT, n, TaylorSeriesExpansion<Scalar>::template precision<3>(),
142 static_cast<Scalar>(Scalar(1) / Scalar(6) - n2 / Scalar(120)),
143 static_cast<Scalar>(n2_inv * (1 - a)));
144
145 switch (op)
146 {
147 case SETTO:
148 Jout.diagonal().setConstant(a);
149 Jout(0, 1) = -b * r[2];
150 Jout(1, 0) = -Jout(0, 1);
151 Jout(0, 2) = b * r[1];
152 Jout(2, 0) = -Jout(0, 2);
153 Jout(1, 2) = -b * r[0];
154 Jout(2, 1) = -Jout(1, 2);
155 Jout.noalias() += c * r * r.transpose();
156 break;
157 case ADDTO:
158 Jout.diagonal().array() += a;
159 Jout(0, 1) += -b * r[2];
160 Jout(1, 0) += b * r[2];
161 Jout(0, 2) += b * r[1];
162 Jout(2, 0) += -b * r[1];
163 Jout(1, 2) += -b * r[0];
164 Jout(2, 1) += b * r[0];
165 Jout.noalias() += c * r * r.transpose();
166 break;
167 case RMTO:
168 Jout.diagonal().array() -= a;
169 Jout(0, 1) -= -b * r[2];
170 Jout(1, 0) -= b * r[2];
171 Jout(0, 2) -= b * r[1];
172 Jout(2, 0) -= -b * r[1];
173 Jout(1, 2) -= -b * r[0];
174 Jout(2, 1) -= b * r[0];
175 Jout.noalias() -= c * r * r.transpose();
176 break;
177 default:
178 assert(false && "Wrong Op requesed value");
179 break;
180 }
181 }
182
191 template<typename Vector3Like, typename Matrix3Like>
192 void Jexp3(const Eigen::MatrixBase<Vector3Like> & r, const Eigen::MatrixBase<Matrix3Like> & Jexp)
193 {
194 Jexp3<SETTO>(r, Jexp);
195 }
196
239 template<typename Scalar, typename Vector3Like, typename Matrix3Like>
240 void Jlog3(
241 const Scalar & theta,
242 const Eigen::MatrixBase<Vector3Like> & log,
243 const Eigen::MatrixBase<Matrix3Like> & Jlog)
244 {
245 Jlog3_impl<Scalar>::run(theta, log, PINOCCHIO_EIGEN_CONST_CAST(Matrix3Like, Jlog));
246 }
247
260 template<typename Matrix3Like1, typename Matrix3Like2>
261 void
262 Jlog3(const Eigen::MatrixBase<Matrix3Like1> & R, const Eigen::MatrixBase<Matrix3Like2> & Jlog)
263 {
264 typedef typename Matrix3Like1::Scalar Scalar;
265 typedef Eigen::Matrix<Scalar, 3, 1, PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3Like1)::Options> Vector3;
266
267 Scalar t;
268 Vector3 w(log3(R, t));
269 Jlog3(t, w, PINOCCHIO_EIGEN_CONST_CAST(Matrix3Like2, Jlog));
270 }
271
272 template<typename Scalar, typename Vector3Like1, typename Vector3Like2, typename Matrix3Like>
273 void Hlog3(
274 const Scalar & theta,
275 const Eigen::MatrixBase<Vector3Like1> & log,
276 const Eigen::MatrixBase<Vector3Like2> & v,
277 const Eigen::MatrixBase<Matrix3Like> & vt_Hlog)
278 {
279 typedef Eigen::Matrix<Scalar, 3, 1, PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3Like)::Options> Vector3;
280 Matrix3Like & vt_Hlog_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3Like, vt_Hlog);
281
282 // theta = (log^T * log)^.5
283 // dt/dl = .5 * 2 * log^T * (log^T * log)^-.5
284 // = log^T / theta
285 // dt_dl = log / theta
286 Scalar ctheta, stheta;
287 SINCOS(theta, &stheta, &ctheta);
288
289 Scalar denom = .5 / (1 - ctheta), a = theta * stheta * denom,
290 da_dt = (stheta - theta) * denom, // da / dtheta
291 b = (1 - a) / (theta * theta),
292 // db_dt = - (2 * (1 - a) / theta + da_dt ) / theta**2; // db / dtheta
293 db_dt = -(2 / theta - (theta + stheta) * denom) / (theta * theta); // db / dtheta
294
295 // Compute dl_dv_v = Jlog * v
296 // Jlog = a I3 + .5 [ log ] + b * log * log^T
297 // if v == log, then Jlog * v == v
298 Vector3 dl_dv_v(a * v + .5 * log.cross(v) + b * log * log.transpose() * v);
299
300 Scalar dt_dv_v = log.dot(dl_dv_v) / theta;
301
302 // Derivative of b * log * log^T
303 vt_Hlog_.noalias() = db_dt * dt_dv_v * log * log.transpose();
304 vt_Hlog_.noalias() += b * dl_dv_v * log.transpose();
305 vt_Hlog_.noalias() += b * log * dl_dv_v.transpose();
306 // Derivative of .5 * [ log ]
307 addSkew(.5 * dl_dv_v, vt_Hlog_);
308 // Derivative of a * I3
309 vt_Hlog_.diagonal().array() += da_dt * dt_dv_v;
310 }
311
320 template<typename Matrix3Like1, typename Vector3Like, typename Matrix3Like2>
321 void Hlog3(
322 const Eigen::MatrixBase<Matrix3Like1> & R,
323 const Eigen::MatrixBase<Vector3Like> & v,
324 const Eigen::MatrixBase<Matrix3Like2> & vt_Hlog)
325 {
326 typedef typename Matrix3Like1::Scalar Scalar;
327 typedef Eigen::Matrix<Scalar, 3, 1, PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3Like1)::Options> Vector3;
328
329 Scalar t;
330 Vector3 w(log3(R, t));
331 Hlog3(t, w, v, PINOCCHIO_EIGEN_CONST_CAST(Matrix3Like2, vt_Hlog));
332 }
333
343 template<typename MotionDerived>
344 SE3Tpl<
345 typename MotionDerived::Scalar,
346 PINOCCHIO_EIGEN_PLAIN_TYPE(typename MotionDerived::Vector3)::Options>
347 exp6(const MotionDense<MotionDerived> & nu)
348 {
349 typedef typename MotionDerived::Scalar Scalar;
350 enum
351 {
352 Options = PINOCCHIO_EIGEN_PLAIN_TYPE(typename MotionDerived::Vector3)::Options
353 };
354
355 typedef SE3Tpl<Scalar, Options> SE3;
356
357 SE3 res;
358 typename SE3::LinearType & trans = res.translation();
359 typename SE3::AngularType & rot = res.rotation();
360
361 const typename MotionDerived::ConstAngularType & w = nu.angular();
362 const typename MotionDerived::ConstLinearType & v = nu.linear();
363 const static Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
364
365 Scalar alpha_wxv, alpha_v, alpha_w, diagonal_term;
366 const Scalar t2 = w.squaredNorm() + eps * eps;
367 const Scalar t = math::sqrt(t2);
368 Scalar ct, st;
369 SINCOS(t, &st, &ct);
370 const Scalar inv_t2 = Scalar(1) / t2;
371
372 alpha_wxv = internal::if_then_else(
373 internal::LT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(),
374 static_cast<Scalar>(Scalar(1) / Scalar(2) - t2 / 24),
375 static_cast<Scalar>((Scalar(1) - ct) * inv_t2));
376
377 alpha_v = internal::if_then_else(
378 internal::LT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(),
379 static_cast<Scalar>(Scalar(1) - t2 / 6), static_cast<Scalar>((st) / t));
380
381 alpha_w = internal::if_then_else(
382 internal::LT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(),
383 static_cast<Scalar>((Scalar(1) / Scalar(6) - t2 / 120)),
384 static_cast<Scalar>((Scalar(1) - alpha_v) * inv_t2));
385
386 diagonal_term = internal::if_then_else(
387 internal::LT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(),
388 static_cast<Scalar>(Scalar(1) - t2 / 2), ct);
389
390 // Linear
391 trans.noalias() = (alpha_v * v + (alpha_w * w.dot(v)) * w + alpha_wxv * w.cross(v));
392
393 // Rotational
394 rot.noalias() = alpha_wxv * w * w.transpose();
395 rot.coeffRef(0, 1) -= alpha_v * w[2];
396 rot.coeffRef(1, 0) += alpha_v * w[2];
397 rot.coeffRef(0, 2) += alpha_v * w[1];
398 rot.coeffRef(2, 0) -= alpha_v * w[1];
399 rot.coeffRef(1, 2) -= alpha_v * w[0];
400 rot.coeffRef(2, 1) += alpha_v * w[0];
401 rot.diagonal().array() += diagonal_term;
402
403 return res;
404 }
405
415 template<typename Vector6Like>
416 SE3Tpl<typename Vector6Like::Scalar, PINOCCHIO_EIGEN_PLAIN_TYPE(Vector6Like)::Options>
417 exp6(const Eigen::MatrixBase<Vector6Like> & v)
418 {
419 PINOCCHIO_ASSERT_MATRIX_SPECIFIC_SIZE(Vector6Like, v, 6, 1);
420
421 MotionRef<const Vector6Like> nu(v.derived());
422 return exp6(nu);
423 }
424
434 template<typename Scalar, int Options>
442
453 template<typename Vector3Like, typename QuaternionLike>
454 MotionTpl<typename Vector3Like::Scalar, Vector3Like::Options> log6(
455 const Eigen::QuaternionBase<QuaternionLike> & quat, const Eigen::MatrixBase<Vector3Like> & vec)
456 {
457 typedef typename Vector3Like::Scalar Scalar;
458 typedef MotionTpl<Scalar, Vector3Like::Options> Motion;
459 Motion mout;
460 log6_impl<Scalar>::run(quat, vec, mout);
461 return mout;
462 }
463
473 template<typename Matrix4Like>
474 MotionTpl<typename Matrix4Like::Scalar, Eigen::internal::traits<Matrix4Like>::Options>
475 log6(const Eigen::MatrixBase<Matrix4Like> & M)
476 {
477 PINOCCHIO_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix4Like, M, 4, 4);
478
479 typedef typename Matrix4Like::Scalar Scalar;
480 enum
481 {
482 Options = Eigen::internal::traits<Matrix4Like>::Options
483 };
484 typedef MotionTpl<Scalar, Options> Motion;
485 typedef SE3Tpl<Scalar, Options> SE3;
486
487 SE3 m(M);
488 Motion mout;
489 log6_impl<Scalar>::run(m, mout);
490 return mout;
491 }
492
495 template<AssignmentOperatorType op, typename MotionDerived, typename Matrix6Like>
496 void Jexp6(const MotionDense<MotionDerived> & nu, const Eigen::MatrixBase<Matrix6Like> & Jexp)
497 {
498 PINOCCHIO_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix6Like, Jexp, 6, 6);
499
500 typedef typename MotionDerived::Scalar Scalar;
501 typedef typename MotionDerived::Vector3 Vector3;
502 typedef Eigen::Matrix<Scalar, 3, 3, Vector3::Options> Matrix3;
503 Matrix6Like & Jout = PINOCCHIO_EIGEN_CONST_CAST(Matrix6Like, Jexp);
504
505 const typename MotionDerived::ConstLinearType & v = nu.linear();
506 const typename MotionDerived::ConstAngularType & w = nu.angular();
507 const Scalar t2 = w.squaredNorm();
508 const Scalar t = math::sqrt(t2);
509
510 const Scalar tinv = Scalar(1) / t, t2inv = tinv * tinv;
511 Scalar st, ct;
512 SINCOS(t, &st, &ct);
513 const Scalar inv_2_2ct = Scalar(1) / (Scalar(2) * (Scalar(1) - ct));
514
515 const Scalar beta = internal::if_then_else(
516 internal::LT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(),
517 static_cast<Scalar>(Scalar(1) / Scalar(12) + t2 / Scalar(720)),
518 static_cast<Scalar>(t2inv - st * tinv * inv_2_2ct));
519
520 const Scalar beta_dot_over_theta = internal::if_then_else(
521 internal::LT, t, TaylorSeriesExpansion<Scalar>::template precision<3>(),
522 static_cast<Scalar>(Scalar(1) / Scalar(360)),
523 static_cast<Scalar>(
524 -Scalar(2) * t2inv * t2inv + (Scalar(1) + st * tinv) * t2inv * inv_2_2ct));
525
526 switch (op)
527 {
528 case SETTO: {
529 Jexp3<SETTO>(w, Jout.template bottomRightCorner<3, 3>());
530 Jout.template topLeftCorner<3, 3>() = Jout.template bottomRightCorner<3, 3>();
531 const Vector3 p = Jout.template topLeftCorner<3, 3>().transpose() * v;
532 const Scalar wTp(w.dot(p));
533 const Matrix3 J(
534 alphaSkew(.5, p) + (beta_dot_over_theta * wTp) * w * w.transpose()
535 - (t2 * beta_dot_over_theta + Scalar(2) * beta) * p * w.transpose()
536 + wTp * beta * Matrix3::Identity() + beta * w * p.transpose());
537 Jout.template topRightCorner<3, 3>().noalias() = -Jout.template topLeftCorner<3, 3>() * J;
538 Jout.template bottomLeftCorner<3, 3>().setZero();
539 break;
540 }
541 case ADDTO: {
542 PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH
543 PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED
544 Matrix3 Jtmp3;
545 Jexp3<SETTO>(w, Jtmp3);
546 PINOCCHIO_COMPILER_DIAGNOSTIC_POP
547 Jout.template bottomRightCorner<3, 3>() += Jtmp3;
548 Jout.template topLeftCorner<3, 3>() += Jtmp3;
549 const Vector3 p = Jtmp3.transpose() * v;
550 const Scalar wTp(w.dot(p));
551 const Matrix3 J(
552 alphaSkew(.5, p) + (beta_dot_over_theta * wTp) * w * w.transpose()
553 - (t2 * beta_dot_over_theta + Scalar(2) * beta) * p * w.transpose()
554 + wTp * beta * Matrix3::Identity() + beta * w * p.transpose());
555 Jout.template topRightCorner<3, 3>().noalias() += -Jtmp3 * J;
556 break;
557 }
558 case RMTO: {
559 PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH
560 PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_MAYBE_UNINITIALIZED
561 Matrix3 Jtmp3;
562 Jexp3<SETTO>(w, Jtmp3);
563 PINOCCHIO_COMPILER_DIAGNOSTIC_POP
564 Jout.template bottomRightCorner<3, 3>() -= Jtmp3;
565 Jout.template topLeftCorner<3, 3>() -= Jtmp3;
566 const Vector3 p = Jtmp3.transpose() * v;
567 const Scalar wTp(w.dot(p));
568 const Matrix3 J(
569 alphaSkew(.5, p) + (beta_dot_over_theta * wTp) * w * w.transpose()
570 - (t2 * beta_dot_over_theta + Scalar(2) * beta) * p * w.transpose()
571 + wTp * beta * Matrix3::Identity() + beta * w * p.transpose());
572 Jout.template topRightCorner<3, 3>().noalias() -= -Jtmp3 * J;
573 break;
574 }
575 default:
576 assert(false && "Wrong Op requesed value");
577 break;
578 }
579 }
580
583 template<typename MotionDerived, typename Matrix6Like>
584 void Jexp6(const MotionDense<MotionDerived> & nu, const Eigen::MatrixBase<Matrix6Like> & Jexp)
585 {
586 Jexp6<SETTO>(nu, Jexp);
587 }
588
591 template<typename MotionDerived>
592 Eigen::Matrix<typename MotionDerived::Scalar, 6, 6, MotionDerived::Options>
593 Jexp6(const MotionDense<MotionDerived> & nu)
594 {
595 typedef typename MotionDerived::Scalar Scalar;
596 enum
597 {
598 Options = MotionDerived::Options
599 };
600 typedef Eigen::Matrix<Scalar, 6, 6, Options> ReturnType;
601
602 ReturnType res;
603 Jexp6(nu, res);
604 return res;
605 }
606
667 template<typename Scalar, int Options, typename Matrix6Like>
668 void Jlog6(const SE3Tpl<Scalar, Options> & M, const Eigen::MatrixBase<Matrix6Like> & Jlog)
669 {
670 Jlog6_impl<Scalar>::run(M, PINOCCHIO_EIGEN_CONST_CAST(Matrix6Like, Jlog));
671 }
672
678 template<typename Scalar, int Options>
679 Eigen::Matrix<Scalar, 6, 6, Options> Jlog6(const SE3Tpl<Scalar, Options> & M)
680 {
681 typedef Eigen::Matrix<Scalar, 6, 6, Options> ReturnType;
682
683 ReturnType res;
684 Jlog6(M, res);
685 return res;
686 }
687
688 template<typename Scalar, int Options>
689 template<typename OtherScalar>
690 SE3Tpl<Scalar, Options> SE3Tpl<Scalar, Options>::Interpolate(
691 const SE3Tpl & A, const SE3Tpl & B, const OtherScalar & alpha)
692 {
693 typedef SE3Tpl<Scalar, Options> ReturnType;
694 typedef MotionTpl<Scalar, Options> Motion;
695
696 Motion dv = log6(A.actInv(B));
697 ReturnType res = A * exp6(alpha * dv);
698 return res;
699 }
700
701} // namespace pinocchio
702
703#include "pinocchio/spatial/explog-quaternion.hpp"
704#include "pinocchio/spatial/log.hxx"
705
706#endif // #ifndef __pinocchio_spatial_explog_hpp__
pinocchio
Main pinocchio namespace.
Definition treeview.dox:11
pinocchio::Jlog3
void Jlog3(const Scalar &theta, const Eigen::MatrixBase< Vector3Like > &log, const Eigen::MatrixBase< Matrix3Like > &Jlog)
Derivative of log3.
Definition explog.hpp:240
pinocchio::SINCOS
void SINCOS(const S1 &a, S2 *sa, S3 *ca)
Computes sin/cos values of a given input scalar.
Definition sincos.hpp:27
pinocchio::log3
Eigen::Matrix< typename Matrix3Like::Scalar, 3, 1, Matrix3Like ::Options > log3(const Eigen::MatrixBase< Matrix3Like > &R, typename Matrix3Like::Scalar &theta)
Same as log3.
Definition explog.hpp:83
pinocchio::exp3
Eigen::Matrix< typename Vector3Like::Scalar, 3, 3, Vector3Like ::Options > exp3(const Eigen::MatrixBase< Vector3Like > &v)
Exp: so3 -> SO3.
Definition explog.hpp:36
pinocchio::addSkew
void addSkew(const Eigen::MatrixBase< Vector3Like > &v, const Eigen::MatrixBase< Matrix3Like > &M)
Add skew matrix represented by a 3d vector to a given matrix, i.e. add the antisymmetric matrix repre...
Definition skew.hpp:68
pinocchio::log6
MotionTpl< Scalar, Options > log6(const SE3Tpl< Scalar, Options > &M)
Log: SE3 -> se3.
Definition explog.hpp:435
pinocchio::exp6
SE3Tpl< typename MotionDerived::Scalar, typename MotionDerived::Vector3 ::Options > exp6(const MotionDense< MotionDerived > &nu)
Exp: se3 -> SE3.
Definition explog.hpp:347
pinocchio::alphaSkew
void alphaSkew(const Scalar alpha, const Eigen::MatrixBase< Vector3 > &v, const Eigen::MatrixBase< Matrix3 > &M)
Computes the skew representation of a given 3d vector multiplied by a given scalar....
Definition skew.hpp:134
pinocchio::Jlog6
void Jlog6(const SE3Tpl< Scalar, Options > &M, const Eigen::MatrixBase< Matrix6Like > &Jlog)
Derivative of log6.
Definition explog.hpp:668
pinocchio::Jexp6
void Jexp6(const MotionDense< MotionDerived > &nu, const Eigen::MatrixBase< Matrix6Like > &Jexp)
Derivative of exp6 Computed as the inverse of Jlog6.
Definition explog.hpp:496
pinocchio::Jexp3
void Jexp3(const Eigen::MatrixBase< Vector3Like > &r, const Eigen::MatrixBase< Matrix3Like > &Jexp)
Derivative of .
Definition explog.hpp:118
pinocchio::Jlog3_impl
Definition log.hpp:13
pinocchio::Jlog6_impl
Definition log.hpp:18
pinocchio::SE3Tpl::Interpolate
static SE3Tpl Interpolate(const SE3Tpl &A, const SE3Tpl &B, const OtherScalar &alpha)
Linear interpolation on the SE3 manifold.
pinocchio::log3_impl
Definition log.hpp:11
pinocchio::log6_impl
Definition log.hpp:16