aba-derivatives.cpp
Go to the documentation of this file.
1 //
2 // Copyright (c) 2018-2020 CNRS INRIA
3 //
4 
5 #include "pinocchio/multibody/model.hpp"
6 #include "pinocchio/multibody/data.hpp"
7 #include "pinocchio/algorithm/jacobian.hpp"
8 #include "pinocchio/algorithm/joint-configuration.hpp"
9 #include "pinocchio/algorithm/kinematics.hpp"
10 #include "pinocchio/algorithm/kinematics-derivatives.hpp"
11 #include "pinocchio/algorithm/rnea.hpp"
12 #include "pinocchio/algorithm/rnea-derivatives.hpp"
13 #include "pinocchio/algorithm/aba.hpp"
14 #include "pinocchio/algorithm/aba-derivatives.hpp"
15 #include "pinocchio/algorithm/crba.hpp"
16 #include "pinocchio/parsers/sample-models.hpp"
17 
18 #include <iostream>
19 
20 #include <boost/test/unit_test.hpp>
21 #include <boost/utility/binary.hpp>
22 
23 BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE)
24 
25 BOOST_AUTO_TEST_CASE(test_aba_derivatives)
26 {
27  using namespace Eigen;
28  using namespace pinocchio;
29 
30  Model model;
31  buildModels::humanoidRandom(model);
32 
33  Data data(model), data_ref(model);
34 
35  model.lowerPositionLimit.head<3>().fill(-1.);
36  model.upperPositionLimit.head<3>().fill(1.);
37  VectorXd q = randomConfiguration(model);
38  VectorXd v(VectorXd::Random(model.nv));
39  VectorXd tau(VectorXd::Random(model.nv));
40  VectorXd a(aba(model,data_ref,q,v,tau));
41 
42  MatrixXd aba_partial_dq(model.nv,model.nv); aba_partial_dq.setZero();
43  MatrixXd aba_partial_dv(model.nv,model.nv); aba_partial_dv.setZero();
44  Data::RowMatrixXs aba_partial_dtau(model.nv,model.nv); aba_partial_dtau.setZero();
45 
46  computeABADerivatives(model, data, q, v, tau, aba_partial_dq, aba_partial_dv, aba_partial_dtau);
47  computeRNEADerivatives(model,data_ref,q,v,a);
48  for(Model::JointIndex k = 1; k < (Model::JointIndex)model.njoints; ++k)
49  {
50  BOOST_CHECK(data.oMi[k].isApprox(data_ref.oMi[k]));
51  BOOST_CHECK(data.v[k].isApprox(data_ref.v[k]));
52  BOOST_CHECK(data.ov[k].isApprox(data_ref.ov[k]));
53  BOOST_CHECK(data.oa_gf[k].isApprox(data_ref.oa_gf[k]));
54  BOOST_CHECK(data.of[k].isApprox(data_ref.of[k]));
55  BOOST_CHECK(data.oYcrb[k].isApprox(data_ref.oYcrb[k]));
56  BOOST_CHECK(data.doYcrb[k].isApprox(data_ref.doYcrb[k]));
57  }
58 
59  computeJointJacobians(model,data_ref,q);
60  BOOST_CHECK(data.J.isApprox(data_ref.J));
61 
62  aba(model,data_ref,q,v,tau);
63  BOOST_CHECK(data.ddq.isApprox(data_ref.ddq));
64 
65  computeMinverse(model,data_ref,q);
66  data_ref.Minv.triangularView<Eigen::StrictlyLower>()
67  = data_ref.Minv.transpose().triangularView<Eigen::StrictlyLower>();
68 
69  BOOST_CHECK(aba_partial_dtau.isApprox(data_ref.Minv));
70 
71  BOOST_CHECK(data.J.isApprox(data_ref.J));
72  BOOST_CHECK(data.dJ.isApprox(data_ref.dJ));
73  BOOST_CHECK(data.dVdq.isApprox(data_ref.dVdq));
74  BOOST_CHECK(data.dAdq.isApprox(data_ref.dAdq));
75  BOOST_CHECK(data.dAdv.isApprox(data_ref.dAdv));
76  BOOST_CHECK(data.dtau_dq.isApprox(data_ref.dtau_dq));
77  BOOST_CHECK(data.dtau_dv.isApprox(data_ref.dtau_dv));
78 
79  MatrixXd aba_partial_dq_fd(model.nv,model.nv); aba_partial_dq_fd.setZero();
80  MatrixXd aba_partial_dv_fd(model.nv,model.nv); aba_partial_dv_fd.setZero();
81  MatrixXd aba_partial_dtau_fd(model.nv,model.nv); aba_partial_dtau_fd.setZero();
82 
83  Data data_fd(model);
84  VectorXd a0 = aba(model,data_fd,q,v,tau);
85  VectorXd v_eps(VectorXd::Zero(model.nv));
86  VectorXd q_plus(model.nq);
87  VectorXd a_plus(model.nv);
88  const double alpha = 1e-8;
89  for(int k = 0; k < model.nv; ++k)
90  {
91  v_eps[k] += alpha;
92  q_plus = integrate(model,q,v_eps);
93  a_plus = aba(model,data_fd,q_plus,v,tau);
94 
95  aba_partial_dq_fd.col(k) = (a_plus - a0)/alpha;
96  v_eps[k] -= alpha;
97  }
98  BOOST_CHECK(aba_partial_dq.isApprox(aba_partial_dq_fd,sqrt(alpha)));
99 
100  VectorXd v_plus(v);
101  for(int k = 0; k < model.nv; ++k)
102  {
103  v_plus[k] += alpha;
104  a_plus = aba(model,data_fd,q,v_plus,tau);
105 
106  aba_partial_dv_fd.col(k) = (a_plus - a0)/alpha;
107  v_plus[k] -= alpha;
108  }
109  BOOST_CHECK(aba_partial_dv.isApprox(aba_partial_dv_fd,sqrt(alpha)));
110 
111  VectorXd tau_plus(tau);
112  for(int k = 0; k < model.nv; ++k)
113  {
114  tau_plus[k] += alpha;
115  a_plus = aba(model,data_fd,q,v,tau_plus);
116 
117  aba_partial_dtau_fd.col(k) = (a_plus - a0)/alpha;
118  tau_plus[k] -= alpha;
119  }
120  BOOST_CHECK(aba_partial_dtau.isApprox(aba_partial_dtau_fd,sqrt(alpha)));
121 }
122 
123 BOOST_AUTO_TEST_CASE(test_aba_minimal_argument)
124 {
125  using namespace Eigen;
126  using namespace pinocchio;
127 
128  Model model;
129  buildModels::humanoidRandom(model);
130 
131  Data data(model), data_ref(model);
132 
133  model.lowerPositionLimit.head<3>().fill(-1.);
134  model.upperPositionLimit.head<3>().fill(1.);
135  VectorXd q = randomConfiguration(model);
136  VectorXd v(VectorXd::Random(model.nv));
137  VectorXd tau(VectorXd::Random(model.nv));
138  VectorXd a(aba(model,data_ref,q,v,tau));
139 
140  MatrixXd aba_partial_dq(model.nv,model.nv); aba_partial_dq.setZero();
141  MatrixXd aba_partial_dv(model.nv,model.nv); aba_partial_dv.setZero();
142  Data::RowMatrixXs aba_partial_dtau(model.nv,model.nv); aba_partial_dtau.setZero();
143 
144  computeABADerivatives(model, data_ref, q, v, tau, aba_partial_dq, aba_partial_dv, aba_partial_dtau);
145 
146  computeABADerivatives(model, data, q, v, tau);
147 
148  BOOST_CHECK(data.J.isApprox(data_ref.J));
149  BOOST_CHECK(data.dJ.isApprox(data_ref.dJ));
150  BOOST_CHECK(data.dVdq.isApprox(data_ref.dVdq));
151  BOOST_CHECK(data.dAdq.isApprox(data_ref.dAdq));
152  BOOST_CHECK(data.dAdv.isApprox(data_ref.dAdv));
153  BOOST_CHECK(data.dtau_dq.isApprox(data_ref.dtau_dq));
154  BOOST_CHECK(data.dtau_dv.isApprox(data_ref.dtau_dv));
155  BOOST_CHECK(data.Minv.isApprox(aba_partial_dtau));
156  BOOST_CHECK(data.ddq_dq.isApprox(aba_partial_dq));
157  BOOST_CHECK(data.ddq_dv.isApprox(aba_partial_dv));
158 }
159 
160 BOOST_AUTO_TEST_CASE(test_aba_derivatives_fext)
161 {
162  using namespace Eigen;
163  using namespace pinocchio;
164 
165  Model model;
166  buildModels::humanoidRandom(model);
167 
168  Data data(model), data_ref(model);
169 
170  model.lowerPositionLimit.head<3>().fill(-1.);
171  model.upperPositionLimit.head<3>().fill(1.);
172  VectorXd q = randomConfiguration(model);
173  VectorXd v(VectorXd::Random(model.nv));
174  VectorXd tau(VectorXd::Random(model.nv));
175  VectorXd a(aba(model,data_ref,q,v,tau));
176 
177  typedef PINOCCHIO_ALIGNED_STD_VECTOR(Force) ForceVector;
178  ForceVector fext((size_t)model.njoints);
179  for(ForceVector::iterator it = fext.begin(); it != fext.end(); ++it)
180  (*it).setRandom();
181 
182  MatrixXd aba_partial_dq(model.nv,model.nv); aba_partial_dq.setZero();
183  MatrixXd aba_partial_dv(model.nv,model.nv); aba_partial_dv.setZero();
184  Data::RowMatrixXs aba_partial_dtau(model.nv,model.nv); aba_partial_dtau.setZero();
185 
186  computeABADerivatives(model, data, q, v, tau, fext,
187  aba_partial_dq, aba_partial_dv, aba_partial_dtau);
188 
189  aba(model,data_ref,q,v,tau,fext);
190 // updateGlobalPlacements(model, data_ref);
191 // for(size_t k =1; k < (size_t)model.njoints; ++k)
192 // {
193 // BOOST_CHECK(data.oMi[k].isApprox(data_ref.oMi[k]));
194 // BOOST_CHECK(daita.of[k].isApprox(data_ref.oMi[k].act(data.f[k])));
195 //
196 // }
197  BOOST_CHECK(data.ddq.isApprox(data_ref.ddq));
198 
199  computeABADerivatives(model,data_ref,q,v,tau);
200  BOOST_CHECK(aba_partial_dv.isApprox(data_ref.ddq_dv));
201  BOOST_CHECK(aba_partial_dtau.isApprox(data_ref.Minv));
202 
203  MatrixXd aba_partial_dq_fd(model.nv,model.nv); aba_partial_dq_fd.setZero();
204  MatrixXd aba_partial_dv_fd(model.nv,model.nv); aba_partial_dv_fd.setZero();
205  MatrixXd aba_partial_dtau_fd(model.nv,model.nv); aba_partial_dtau_fd.setZero();
206 
207  Data data_fd(model);
208  const VectorXd a0 = aba(model,data_fd,q,v,tau,fext);
209  VectorXd v_eps(VectorXd::Zero(model.nv));
210  VectorXd q_plus(model.nq);
211  VectorXd a_plus(model.nv);
212  const double alpha = 1e-8;
213  for(int k = 0; k < model.nv; ++k)
214  {
215  v_eps[k] += alpha;
216  q_plus = integrate(model,q,v_eps);
217  a_plus = aba(model,data_fd,q_plus,v,tau,fext);
218 
219  aba_partial_dq_fd.col(k) = (a_plus - a0)/alpha;
220  v_eps[k] -= alpha;
221  }
222  BOOST_CHECK(aba_partial_dq.isApprox(aba_partial_dq_fd,sqrt(alpha)));
223 
224  VectorXd v_plus(v);
225  for(int k = 0; k < model.nv; ++k)
226  {
227  v_plus[k] += alpha;
228  a_plus = aba(model,data_fd,q,v_plus,tau,fext);
229 
230  aba_partial_dv_fd.col(k) = (a_plus - a0)/alpha;
231  v_plus[k] -= alpha;
232  }
233  BOOST_CHECK(aba_partial_dv.isApprox(aba_partial_dv_fd,sqrt(alpha)));
234 
235  VectorXd tau_plus(tau);
236  for(int k = 0; k < model.nv; ++k)
237  {
238  tau_plus[k] += alpha;
239  a_plus = aba(model,data_fd,q,v,tau_plus,fext);
240 
241  aba_partial_dtau_fd.col(k) = (a_plus - a0)/alpha;
242  tau_plus[k] -= alpha;
243  }
244  BOOST_CHECK(aba_partial_dtau.isApprox(aba_partial_dtau_fd,sqrt(alpha)));
245 
246  // test the shortcut
247  Data data_shortcut(model);
248  computeABADerivatives(model,data_shortcut,q,v,tau,fext);
249  BOOST_CHECK(data_shortcut.ddq_dq.isApprox(aba_partial_dq));
250  BOOST_CHECK(data_shortcut.ddq_dv.isApprox(aba_partial_dv));
251  BOOST_CHECK(data_shortcut.Minv.isApprox(aba_partial_dtau));
252 }
253 
254 BOOST_AUTO_TEST_CASE(test_multiple_calls)
255 {
256  using namespace Eigen;
257  using namespace pinocchio;
258 
259  Model model;
260  buildModels::humanoidRandom(model);
261 
262  Data data1(model), data2(model);
263 
264  model.lowerPositionLimit.head<3>().fill(-1.);
265  model.upperPositionLimit.head<3>().fill(1.);
266  VectorXd q = randomConfiguration(model);
267  VectorXd v(VectorXd::Random(model.nv));
268  VectorXd tau(VectorXd::Random(model.nv));
269 
270  computeABADerivatives(model,data1,q,v,tau);
271  data2 = data1;
272 
273  for(int k = 0; k < 20; ++k)
274  {
275  computeABADerivatives(model,data1,q,v,tau);
276  }
277 
278  BOOST_CHECK(data1.J.isApprox(data2.J));
279  BOOST_CHECK(data1.dJ.isApprox(data2.dJ));
280  BOOST_CHECK(data1.dVdq.isApprox(data2.dVdq));
281  BOOST_CHECK(data1.dAdq.isApprox(data2.dAdq));
282  BOOST_CHECK(data1.dAdv.isApprox(data2.dAdv));
283 
284  BOOST_CHECK(data1.dFdq.isApprox(data2.dFdq));
285  BOOST_CHECK(data1.dFdv.isApprox(data2.dFdv));
286 
287  BOOST_CHECK(data1.dtau_dq.isApprox(data2.dtau_dq));
288  BOOST_CHECK(data1.dtau_dv.isApprox(data2.dtau_dv));
289 
290  BOOST_CHECK(data1.ddq_dq.isApprox(data2.ddq_dq));
291  BOOST_CHECK(data1.ddq_dv.isApprox(data2.ddq_dv));
292  BOOST_CHECK(data1.Minv.isApprox(data2.Minv));
293 }
294 
295 BOOST_AUTO_TEST_CASE(test_aba_derivatives_vs_kinematics_derivatives)
296 {
297  using namespace Eigen;
298  using namespace pinocchio;
299 
300  Model model;
301  buildModels::humanoidRandom(model);
302 
303  Data data(model), data_ref(model);
304 
305  model.lowerPositionLimit.head<3>().fill(-1.);
306  model.upperPositionLimit.head<3>().fill(1.);
307  VectorXd q = randomConfiguration(model);
308  VectorXd v(VectorXd::Random(model.nv));
309  VectorXd a(VectorXd::Random(model.nv));
310 
311  VectorXd tau = rnea(model,data_ref,q,v,a);
312 
314  MatrixXd aba_partial_dq(model.nv,model.nv); aba_partial_dq.setZero();
315  MatrixXd aba_partial_dv(model.nv,model.nv); aba_partial_dv.setZero();
316  MatrixXd aba_partial_dtau(model.nv,model.nv); aba_partial_dtau.setZero();
317 
318  computeABADerivatives(model,data,q,v,tau,aba_partial_dq,aba_partial_dv,aba_partial_dtau);
319  computeForwardKinematicsDerivatives(model,data_ref,q,v,a);
320 
321  BOOST_CHECK(data.J.isApprox(data_ref.J));
322  BOOST_CHECK(data.dJ.isApprox(data_ref.dJ));
323 
324  for(size_t k = 1; k < (size_t)model.njoints; ++k)
325  {
326  BOOST_CHECK(data.oMi[k].isApprox(data_ref.oMi[k]));
327  BOOST_CHECK(data.ov[k].isApprox(data_ref.ov[k]));
328  BOOST_CHECK(data.oa[k].isApprox(data_ref.oa[k]));
329  }
330 }
331 
332 BOOST_AUTO_TEST_SUITE_END()
pinocchio::DataTpl::dJ
Matrix6x dJ
Derivative of the Jacobian with respect to the time.
Definition: src/multibody/data.hpp:286
pinocchio::aba
const DataTpl< Scalar, Options, JointCollectionTpl >::TangentVectorType & aba(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< ConfigVectorType > &q, const Eigen::MatrixBase< TangentVectorType1 > &v, const Eigen::MatrixBase< TangentVectorType2 > &tau)
The Articulated-Body algorithm. It computes the forward dynamics, aka the joint accelerations given t...
q
q
pinocchio::DataTpl::RowMatrixXs
Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor|Options > RowMatrixXs
Definition: src/multibody/data.hpp:79
pinocchio::DataTpl::J
Matrix6x J
Jacobian of joint placements.
Definition: src/multibody/data.hpp:283
pinocchio::computeMinverse
const DataTpl< Scalar, Options, JointCollectionTpl >::RowMatrixXs & computeMinverse(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< ConfigVectorType > &q)
Computes the inverse of the joint space inertia matrix using Articulated Body formulation.
pinocchio::DataTpl::dtau_dv
MatrixXs dtau_dv
Partial derivative of the joint torque vector with respect to the joint velocity. ...
Definition: src/multibody/data.hpp:312
pinocchio::DataTpl::dAdv
Matrix6x dAdv
Variation of the spatial acceleration set with respect to the joint velocity.
Definition: src/multibody/data.hpp:306
pinocchio::rnea
void rnea(const int num_threads, ModelPoolTpl< Scalar, Options, JointCollectionTpl > &pool, const Eigen::MatrixBase< ConfigVectorPool > &q, const Eigen::MatrixBase< TangentVectorPool1 > &v, const Eigen::MatrixBase< TangentVectorPool2 > &a, const Eigen::MatrixBase< TangentVectorPool3 > &tau)
The Recursive Newton-Euler algorithm. It computes the inverse dynamics, aka the joint torques accordi...
Definition: parallel/rnea.hpp:32
pinocchio::integrate
void integrate(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const Eigen::MatrixBase< ConfigVectorType > &q, const Eigen::MatrixBase< TangentVectorType > &v, const Eigen::MatrixBase< ReturnType > &qout)
Integrate a configuration vector for the specified model for a tangent vector during one unit time...
Definition: joint-configuration.hpp:54
pinocchio::ModelTpl::njoints
int njoints
Number of joints.
Definition: src/multibody/model.hpp:82
pinocchio::ModelTpl::lowerPositionLimit
ConfigVectorType lowerPositionLimit
Lower joint configuration limit.
Definition: src/multibody/model.hpp:139
pinocchio::randomConfiguration
void randomConfiguration(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const Eigen::MatrixBase< ConfigVectorIn1 > &lowerLimits, const Eigen::MatrixBase< ConfigVectorIn2 > &upperLimits, const Eigen::MatrixBase< ReturnType > &qout)
Generate a configuration vector uniformly sampled among provided limits.
Definition: joint-configuration.hpp:224
pinocchio::DataTpl::dtau_dq
MatrixXs dtau_dq
Partial derivative of the joint torque vector with respect to the joint configuration.
Definition: src/multibody/data.hpp:309
fill
fill
pinocchio::DataTpl::Minv
RowMatrixXs Minv
The inverse of the joint space inertia matrix (a square matrix of dim model.nv).
Definition: src/multibody/data.hpp:156
pinocchio::DataTpl::ddq_dq
MatrixXs ddq_dq
Partial derivative of the joint acceleration vector with respect to the joint configuration.
Definition: src/multibody/data.hpp:315
pinocchio::DataTpl::dFdq
Matrix6x dFdq
Variation of the forceset with respect to the joint configuration.
Definition: src/multibody/data.hpp:165
pinocchio::DataTpl::dAdq
Matrix6x dAdq
Variation of the spatial acceleration set with respect to the joint configuration.
Definition: src/multibody/data.hpp:303
pinocchio::python::computeRNEADerivatives
bp::tuple computeRNEADerivatives(const Model &model, Data &data, const Eigen::VectorXd &q, const Eigen::VectorXd &v, const Eigen::VectorXd &a)
Definition: expose-rnea-derivatives.cpp:36
PINOCCHIO_ALIGNED_STD_VECTOR
#define PINOCCHIO_ALIGNED_STD_VECTOR(Type)
Definition: container/aligned-vector.hpp:11
pinocchio::ModelTpl::JointIndex
pinocchio::JointIndex JointIndex
Definition: src/multibody/model.hpp:49
pinocchio::computeForwardKinematicsDerivatives
void computeForwardKinematicsDerivatives(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< ConfigVectorType > &q, const Eigen::MatrixBase< TangentVectorType1 > &v, const Eigen::MatrixBase< TangentVectorType2 > &a)
Computes all the terms required to compute the derivatives of the placement, spatial velocity and acc...
a
Vec3f a
pinocchio::DataTpl::ddq
TangentVectorType ddq
The joint accelerations computed from ABA.
Definition: src/multibody/data.hpp:209
pinocchio::DataTpl::dFdv
Matrix6x dFdv
Variation of the forceset with respect to the joint velocity.
Definition: src/multibody/data.hpp:168
BOOST_AUTO_TEST_CASE
BOOST_AUTO_TEST_CASE(test_aba_derivatives)
Definition: aba-derivatives.cpp:25
pinocchio::DataTpl::ddq_dv
MatrixXs ddq_dv
Partial derivative of the joint acceleration vector with respect to the joint velocity.
Definition: src/multibody/data.hpp:318
pinocchio
Main pinocchio namespace.
Definition: timings.cpp:28
pinocchio::JointIndex
Index JointIndex
Definition: src/multibody/fwd.hpp:28
pinocchio::computeJointJacobians
const DataTpl< Scalar, Options, JointCollectionTpl >::Matrix6x & computeJointJacobians(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< ConfigVectorType > &q)
Computes the full model Jacobian, i.e. the stack of all motion subspace expressed in the world frame...
pinocchio::ModelTpl::nv
int nv
Dimension of the velocity vector space.
Definition: src/multibody/model.hpp:79
pinocchio::ModelTpl::upperPositionLimit
ConfigVectorType upperPositionLimit
Upper joint configuration limit.
Definition: src/multibody/model.hpp:142
pinocchio::computeABADerivatives
void computeABADerivatives(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< ConfigVectorType > &q, const Eigen::MatrixBase< TangentVectorType1 > &v, const Eigen::MatrixBase< TangentVectorType2 > &tau, const Eigen::MatrixBase< MatrixType1 > &aba_partial_dq, const Eigen::MatrixBase< MatrixType2 > &aba_partial_dv, const Eigen::MatrixBase< MatrixType3 > &aba_partial_dtau)
The derivatives of the Articulated-Body algorithm.
pinocchio::buildModels::humanoidRandom
void humanoidRandom(ModelTpl< Scalar, Options, JointCollectionTpl > &model, bool usingFF=true)
Create a humanoid kinematic tree with 6-DOF limbs and random joint placements.
pinocchio::python::VectorXd
Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > VectorXd
Definition: conversions.cpp:14
pinocchio::ModelTpl::nq
int nq
Dimension of the configuration vector representation.
Definition: src/multibody/model.hpp:76
pinocchio::DataTpl::dVdq
Matrix6x dVdq
Variation of the spatial velocity set with respect to the joint configuration.
Definition: src/multibody/data.hpp:300

pinocchio
Author(s):
autogenerated on Fri Jun 23 2023 02:38:28