unittest/frames.cpp

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//
// Copyright (c) 2016-2024 CNRS INRIA
//
 
#include "pinocchio/multibody/model.hpp"
#include "pinocchio/multibody/data.hpp"
#include "pinocchio/algorithm/model.hpp"
#include "pinocchio/algorithm/jacobian.hpp"
#include "pinocchio/algorithm/frames.hpp"
#include "pinocchio/algorithm/rnea.hpp"
#include "pinocchio/algorithm/crba.hpp"
#include "pinocchio/spatial/act-on-set.hpp"
#include "pinocchio/multibody/sample-models.hpp"
#include "pinocchio/utils/timer.hpp"
#include "pinocchio/algorithm/joint-configuration.hpp"
 
#include <iostream>
 
#include <boost/test/unit_test.hpp>
#include <boost/utility/binary.hpp>
 
#include "utils/model-generator.hpp"
 
template<typename Derived>
inline bool isFinite(const Eigen::MatrixBase<Derived> & x)
{
  return ((x - x).array() == (x - x).array()).all();
}
 
BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE)
 
BOOST_AUTO_TEST_CASE(frame_basic)
{
  using namespace pinocchio;
  Model model;
  buildModels::humanoidRandom(model);
 
  BOOST_CHECK(model.frames.size() >= size_t(model.njoints));
  for (Model::FrameVector::const_iterator it = model.frames.begin(); it != model.frames.end(); ++it)
  {
    const Frame & frame = *it;
    BOOST_CHECK(frame == frame);
    Frame frame_copy(frame);
    BOOST_CHECK(frame_copy == frame);
  }
 
  Frame frame1("toto", 0, 0, SE3::Random(), OP_FRAME);
  std::ostringstream os;
  os << frame1 << std::endl;
  BOOST_CHECK(!os.str().empty());
 
  // Check other signature
  Frame frame2("toto", 0, frame1.placement, OP_FRAME);
  BOOST_CHECK(frame1 == frame2);
}
 
BOOST_AUTO_TEST_CASE(cast)
{
  using namespace pinocchio;
  Frame frame("toto", 0, 0, SE3::Random(), OP_FRAME);
 
  BOOST_CHECK(frame.cast<double>() == frame);
  BOOST_CHECK(frame.cast<double>().cast<long double>() == frame.cast<long double>());
 
  typedef FrameTpl<long double> Frameld;
  Frameld frame2(frame);
 
  BOOST_CHECK(frame2 == frame.cast<long double>());
}
 
BOOST_AUTO_TEST_CASE(test_kinematics)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  pinocchio::Model model;
  pinocchio::buildModels::humanoidRandom(model);
  Model::Index parent_idx = model.existJointName("rarm2_joint") ? model.getJointId("rarm2_joint")
                                                                : (Model::Index)(model.njoints - 1);
  const std::string & frame_name = std::string(model.names[parent_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  model.addFrame(Frame(frame_name, parent_idx, 0, framePlacement, OP_FRAME));
  pinocchio::Data data(model);
 
  VectorXd q = VectorXd::Ones(model.nq);
  q.middleRows<4>(3).normalize();
  framesForwardKinematics(model, data, q);
 
  BOOST_CHECK(
    data.oMf[model.getFrameId(frame_name)].isApprox(data.oMi[parent_idx] * framePlacement));
}
 
BOOST_AUTO_TEST_CASE(test_update_placements)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  pinocchio::Model model;
  pinocchio::buildModels::humanoidRandom(model);
  Model::Index parent_idx = model.existJointName("rarm2_joint") ? model.getJointId("rarm2_joint")
                                                                : (Model::Index)(model.njoints - 1);
  const std::string & frame_name = std::string(model.names[parent_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  Model::FrameIndex frame_idx =
    model.addFrame(Frame(frame_name, parent_idx, 0, framePlacement, OP_FRAME));
  pinocchio::Data data(model);
  pinocchio::Data data_ref(model);
 
  VectorXd q = VectorXd::Ones(model.nq);
  q.middleRows<4>(3).normalize();
 
  forwardKinematics(model, data, q);
  updateFramePlacements(model, data);
 
  framesForwardKinematics(model, data_ref, q);
 
  BOOST_CHECK(data.oMf[frame_idx].isApprox(data_ref.oMf[frame_idx]));
}
 
BOOST_AUTO_TEST_CASE(test_update_single_placement)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  pinocchio::Model model;
  pinocchio::buildModels::humanoidRandom(model);
  Model::Index parent_idx = model.existJointName("rarm2_joint") ? model.getJointId("rarm2_joint")
                                                                : (Model::Index)(model.njoints - 1);
  const std::string & frame_name = std::string(model.names[parent_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  Model::FrameIndex frame_idx =
    model.addFrame(Frame(frame_name, parent_idx, 0, framePlacement, OP_FRAME));
  pinocchio::Data data(model);
  pinocchio::Data data_ref(model);
 
  VectorXd q = VectorXd::Ones(model.nq);
  q.middleRows<4>(3).normalize();
 
  forwardKinematics(model, data, q);
  updateFramePlacement(model, data, frame_idx);
 
  framesForwardKinematics(model, data_ref, q);
 
  BOOST_CHECK(data.oMf[frame_idx].isApprox(data_ref.oMf[frame_idx]));
}
 
BOOST_AUTO_TEST_CASE(test_velocity)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  pinocchio::Model model;
  pinocchio::buildModels::humanoidRandom(model);
  Model::Index parent_idx = model.existJointName("rarm2_joint") ? model.getJointId("rarm2_joint")
                                                                : (Model::Index)(model.njoints - 1);
  const std::string & frame_name = std::string(model.names[parent_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  Model::FrameIndex frame_idx =
    model.addFrame(Frame(frame_name, parent_idx, 0, framePlacement, OP_FRAME));
  pinocchio::Data data(model);
 
  VectorXd q = VectorXd::Ones(model.nq);
  q.middleRows<4>(3).normalize();
  VectorXd v = VectorXd::Ones(model.nv);
  forwardKinematics(model, data, q, v);
 
  Motion vf = getFrameVelocity(model, data, frame_idx);
 
  BOOST_CHECK(vf.isApprox(framePlacement.actInv(data.v[parent_idx])));
 
  pinocchio::Data data_ref(model);
  forwardKinematics(model, data_ref, q, v);
  updateFramePlacements(model, data_ref);
  Motion v_ref = getFrameVelocity(model, data_ref, frame_idx);
 
  BOOST_CHECK(v_ref.isApprox(getFrameVelocity(model, data, frame_idx)));
  BOOST_CHECK(v_ref.isApprox(getFrameVelocity(model, data, frame_idx, LOCAL)));
  BOOST_CHECK(
    data_ref.oMf[frame_idx].act(v_ref).isApprox(getFrameVelocity(model, data, frame_idx, WORLD)));
  BOOST_CHECK(SE3(data_ref.oMf[frame_idx].rotation(), Eigen::Vector3d::Zero())
                .act(v_ref)
                .isApprox(getFrameVelocity(model, data, frame_idx, LOCAL_WORLD_ALIGNED)));
}
 
BOOST_AUTO_TEST_CASE(test_acceleration)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  pinocchio::Model model;
  pinocchio::buildModels::humanoidRandom(model);
  Model::Index parent_idx = model.existJointName("rarm2_joint") ? model.getJointId("rarm2_joint")
                                                                : (Model::Index)(model.njoints - 1);
  const std::string & frame_name = std::string(model.names[parent_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  Model::FrameIndex frame_idx =
    model.addFrame(Frame(frame_name, parent_idx, 0, framePlacement, OP_FRAME));
  pinocchio::Data data(model);
 
  VectorXd q = VectorXd::Ones(model.nq);
  q.middleRows<4>(3).normalize();
  VectorXd v = VectorXd::Ones(model.nv);
  VectorXd a = VectorXd::Ones(model.nv);
  forwardKinematics(model, data, q, v, a);
 
  Motion af = getFrameAcceleration(model, data, frame_idx);
 
  BOOST_CHECK(af.isApprox(framePlacement.actInv(data.a[parent_idx])));
 
  pinocchio::Data data_ref(model);
  forwardKinematics(model, data_ref, q, v, a);
  updateFramePlacements(model, data_ref);
  Motion a_ref = getFrameAcceleration(model, data_ref, frame_idx);
 
  BOOST_CHECK(a_ref.isApprox(getFrameAcceleration(model, data, frame_idx)));
  BOOST_CHECK(a_ref.isApprox(getFrameAcceleration(model, data, frame_idx, LOCAL)));
  BOOST_CHECK(data_ref.oMf[frame_idx].act(a_ref).isApprox(
    getFrameAcceleration(model, data, frame_idx, WORLD)));
  BOOST_CHECK(SE3(data_ref.oMf[frame_idx].rotation(), Eigen::Vector3d::Zero())
                .act(a_ref)
                .isApprox(getFrameAcceleration(model, data, frame_idx, LOCAL_WORLD_ALIGNED)));
}
 
BOOST_AUTO_TEST_CASE(test_classic_acceleration)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  pinocchio::Model model;
  pinocchio::buildModels::humanoidRandom(model);
  Model::Index parent_idx = model.existJointName("rarm2_joint") ? model.getJointId("rarm2_joint")
                                                                : (Model::Index)(model.njoints - 1);
  const std::string & frame_name = std::string(model.names[parent_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  Model::FrameIndex frame_idx =
    model.addFrame(Frame(frame_name, parent_idx, 0, framePlacement, OP_FRAME));
  pinocchio::Data data(model);
 
  VectorXd q = VectorXd::Ones(model.nq);
  q.middleRows<4>(3).normalize();
  VectorXd v = VectorXd::Ones(model.nv);
  VectorXd a = VectorXd::Ones(model.nv);
  forwardKinematics(model, data, q, v, a);
 
  Motion vel = framePlacement.actInv(data.v[parent_idx]);
  Motion acc = framePlacement.actInv(data.a[parent_idx]);
  Vector3d linear;
 
  Motion acc_classical_local = acc;
  linear = acc.linear() + vel.angular().cross(vel.linear());
  acc_classical_local.linear() = linear;
 
  Motion af = getFrameClassicalAcceleration(model, data, frame_idx);
 
  BOOST_CHECK(af.isApprox(acc_classical_local));
 
  pinocchio::Data data_ref(model);
  forwardKinematics(model, data_ref, q, v, a);
  updateFramePlacements(model, data_ref);
 
  SE3 T_ref = data_ref.oMf[frame_idx];
  Motion v_ref = getFrameVelocity(model, data_ref, frame_idx);
  Motion a_ref = getFrameAcceleration(model, data_ref, frame_idx);
 
  Motion acc_classical_local_ref = a_ref;
  linear = a_ref.linear() + v_ref.angular().cross(v_ref.linear());
  acc_classical_local_ref.linear() = linear;
 
  BOOST_CHECK(
    acc_classical_local_ref.isApprox(getFrameClassicalAcceleration(model, data, frame_idx)));
  BOOST_CHECK(
    acc_classical_local_ref.isApprox(getFrameClassicalAcceleration(model, data, frame_idx, LOCAL)));
 
  Motion vel_world_ref = T_ref.act(v_ref);
  Motion acc_classical_world_ref = T_ref.act(a_ref);
  linear = acc_classical_world_ref.linear() + vel_world_ref.angular().cross(vel_world_ref.linear());
  acc_classical_world_ref.linear() = linear;
 
  BOOST_CHECK(
    acc_classical_world_ref.isApprox(getFrameClassicalAcceleration(model, data, frame_idx, WORLD)));
 
  Motion vel_aligned_ref = SE3(T_ref.rotation(), Eigen::Vector3d::Zero()).act(v_ref);
  Motion acc_classical_aligned_ref = SE3(T_ref.rotation(), Eigen::Vector3d::Zero()).act(a_ref);
  linear =
    acc_classical_aligned_ref.linear() + vel_aligned_ref.angular().cross(vel_aligned_ref.linear());
  acc_classical_aligned_ref.linear() = linear;
 
  BOOST_CHECK(acc_classical_aligned_ref.isApprox(
    getFrameClassicalAcceleration(model, data, frame_idx, LOCAL_WORLD_ALIGNED)));
}
 
BOOST_AUTO_TEST_CASE(test_frame_getters)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  // Build a simple 1R planar model
  Model model;
  JointIndex parentId = model.addJoint(0, JointModelRZ(), SE3::Identity(), "Joint1");
  FrameIndex frameId = model.addFrame(
    Frame("Frame1", parentId, 0, SE3(Matrix3d::Identity(), Vector3d(1.0, 0.0, 0.0)), OP_FRAME));
 
  Data data(model);
 
  // Predetermined configuration values
  VectorXd q(model.nq);
  q << M_PI / 2;
 
  VectorXd v(model.nv);
  v << 1.0;
 
  VectorXd a(model.nv);
  a << 0.0;
 
  // Expected velocity
  Motion v_local;
  v_local.linear() = Vector3d(0.0, 1.0, 0.0);
  v_local.angular() = Vector3d(0.0, 0.0, 1.0);
 
  Motion v_world;
  v_world.linear() = Vector3d::Zero();
  v_world.angular() = Vector3d(0.0, 0.0, 1.0);
 
  Motion v_align;
  v_align.linear() = Vector3d(-1.0, 0.0, 0.0);
  v_align.angular() = Vector3d(0.0, 0.0, 1.0);
 
  // Expected classical acceleration
  Motion ac_local;
  ac_local.linear() = Vector3d(-1.0, 0.0, 0.0);
  ac_local.angular() = Vector3d::Zero();
 
  Motion ac_world = Motion::Zero();
 
  Motion ac_align;
  ac_align.linear() = Vector3d(0.0, -1.0, 0.0);
  ac_align.angular() = Vector3d::Zero();
 
  // Perform kinematics
  forwardKinematics(model, data, q, v, a);
 
  // Check output velocity
  BOOST_CHECK(v_local.isApprox(getFrameVelocity(model, data, frameId)));
  BOOST_CHECK(v_local.isApprox(getFrameVelocity(model, data, frameId, LOCAL)));
  BOOST_CHECK(v_world.isApprox(getFrameVelocity(model, data, frameId, WORLD)));
  BOOST_CHECK(v_align.isApprox(getFrameVelocity(model, data, frameId, LOCAL_WORLD_ALIGNED)));
 
  // Check output acceleration (all zero)
  BOOST_CHECK(getFrameAcceleration(model, data, frameId).isZero());
  BOOST_CHECK(getFrameAcceleration(model, data, frameId, LOCAL).isZero());
  BOOST_CHECK(getFrameAcceleration(model, data, frameId, WORLD).isZero());
  BOOST_CHECK(getFrameAcceleration(model, data, frameId, LOCAL_WORLD_ALIGNED).isZero());
 
  // Check output classical acceleration
  BOOST_CHECK(ac_local.isApprox(getFrameClassicalAcceleration(model, data, frameId)));
  BOOST_CHECK(ac_local.isApprox(getFrameClassicalAcceleration(model, data, frameId, LOCAL)));
  BOOST_CHECK(ac_world.isApprox(getFrameClassicalAcceleration(model, data, frameId, WORLD)));
  BOOST_CHECK(
    ac_align.isApprox(getFrameClassicalAcceleration(model, data, frameId, LOCAL_WORLD_ALIGNED)));
}
 
// Test getFrameJacobian
// Jacobian is calculated in LOCAL, WORLD and LOCAL_WORLD_ALIGNED and tested against velocity.
void test_get_frame_jacobian_impl(
  const pinocchio::Model & input_model, pinocchio::JointIndex joint_idx)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  Model model(input_model);
  const std::string & frame_name = std::string(model.names[joint_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  auto frame_idx = model.addFrame(Frame(frame_name, joint_idx, 0, framePlacement, OP_FRAME));
 
  pinocchio::Data data(model);
  // data_ref is used to compute the frame velocity
  pinocchio::Data data_ref(model);
 
  model.lowerPositionLimit.head<7>().fill(-1.);
  model.upperPositionLimit.head<7>().fill(1.);
  VectorXd q = randomConfiguration(model);
  VectorXd v = VectorXd::Random(model.nv);
 
  computeJointJacobians(model, data, q);
  updateFramePlacement(model, data, frame_idx);
 
  forwardKinematics(model, data_ref, q, v);
  updateFramePlacement(model, data_ref, frame_idx);
 
  // In LOCAL frame
  Data::Matrix6x J_local(Data::Matrix6x::Zero(6, model.nv));
  getFrameJacobian(model, data, frame_idx, LOCAL, J_local);
  auto frame_velocity_local = getFrameVelocity(model, data_ref, frame_idx, LOCAL);
  BOOST_CHECK((J_local * v).isApprox(frame_velocity_local.toVector()));
 
  // In WORLD frame
  Data::Matrix6x J_world(Data::Matrix6x::Zero(6, model.nv));
  getFrameJacobian(model, data, frame_idx, WORLD, J_world);
  auto frame_velocity_world = getFrameVelocity(model, data_ref, frame_idx, WORLD);
  BOOST_CHECK((J_world * v).isApprox(frame_velocity_world.toVector()));
 
  // In LOCAL_WORLD_ALIGNED frame
  Data::Matrix6x J_local_world_aligned(Data::Matrix6x::Zero(6, model.nv));
  getFrameJacobian(model, data, frame_idx, LOCAL_WORLD_ALIGNED, J_local_world_aligned);
  auto frame_velocity_local_world_aligned =
    getFrameVelocity(model, data_ref, frame_idx, LOCAL_WORLD_ALIGNED);
  BOOST_CHECK((J_local_world_aligned * v).isApprox(frame_velocity_local_world_aligned.toVector()));
}
 
// Test getFrameJacobian on normal models
BOOST_AUTO_TEST_CASE(test_get_frame_jacobian)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  Model model;
  buildModels::humanoidRandom(model);
  for (int j = 1; j < model.njoints; j++)
  {
    test_get_frame_jacobian_impl(model, static_cast<pinocchio::JointIndex>(j));
  }
}
 
// Test getFrameJacobian on model with mimic joint
BOOST_AUTO_TEST_CASE(test_get_frame_jacobian_mimic)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  for (int i = 0; i < pinocchio::MimicTestCases::N_CASES; i++)
  {
    const pinocchio::MimicTestCases mimic_test_case(i);
    const pinocchio::Model & model_mimic = mimic_test_case.model_mimic;
    for (int j = 1; j < model_mimic.njoints; j++)
    {
      test_get_frame_jacobian_impl(model_mimic, static_cast<pinocchio::JointIndex>(j));
    }
  }
}
 
// Test computeFrameJacobian
// Jacobian is calculated in LOCAL, WORLD and LOCAL_WORLD_ALIGNED and tested against velocity.
void test_compute_frame_jacobian_impl(
  const pinocchio::Model & input_model, pinocchio::JointIndex joint_idx)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  Model model(input_model);
  const std::string & frame_name = std::string(model.names[joint_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  auto frame_idx = model.addFrame(Frame(frame_name, joint_idx, 0, framePlacement, OP_FRAME));
 
  pinocchio::Data data(model);
  // data_ref is used to compute the frame velocity
  pinocchio::Data data_ref(model);
 
  model.lowerPositionLimit.head<7>().fill(-1.);
  model.upperPositionLimit.head<7>().fill(1.);
  VectorXd q = randomConfiguration(model);
  VectorXd v = VectorXd::Random(model.nv);
 
  forwardKinematics(model, data_ref, q, v);
  updateFramePlacement(model, data_ref, frame_idx);
 
  // In LOCAL frame
  Data::Matrix6x J_local(Data::Matrix6x::Zero(6, model.nv));
  computeFrameJacobian(model, data, q, frame_idx, LOCAL, J_local);
  auto frame_velocity_local = getFrameVelocity(model, data_ref, frame_idx, LOCAL);
  BOOST_CHECK((J_local * v).isApprox(frame_velocity_local.toVector()));
 
  // In WORLD frame
  Data::Matrix6x J_world(Data::Matrix6x::Zero(6, model.nv));
  computeFrameJacobian(model, data, q, frame_idx, WORLD, J_world);
  auto frame_velocity_world = getFrameVelocity(model, data_ref, frame_idx, WORLD);
  BOOST_CHECK((J_world * v).isApprox(frame_velocity_world.toVector()));
 
  // In LOCAL_WORLD_ALIGNED frame
  Data::Matrix6x J_local_world_aligned(Data::Matrix6x::Zero(6, model.nv));
  computeFrameJacobian(model, data, q, frame_idx, LOCAL_WORLD_ALIGNED, J_local_world_aligned);
  auto frame_velocity_local_world_aligned =
    getFrameVelocity(model, data_ref, frame_idx, LOCAL_WORLD_ALIGNED);
  BOOST_CHECK((J_local_world_aligned * v).isApprox(frame_velocity_local_world_aligned.toVector()));
}
 
// Test computeFrameJacobian on normal models
BOOST_AUTO_TEST_CASE(test_compute_frame_jacobian)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  Model model;
  buildModels::humanoidRandom(model);
  for (int j = 1; j < model.njoints; j++)
  {
    test_compute_frame_jacobian_impl(model, static_cast<pinocchio::JointIndex>(j));
  }
}
 
// Test computeFrameJacobian on model with mimic joint
BOOST_AUTO_TEST_CASE(test_compute_frame_jacobian_mimic)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  for (int i = 0; i < pinocchio::MimicTestCases::N_CASES; i++)
  {
    const pinocchio::MimicTestCases mimic_test_case(i, true);
    const pinocchio::Model & model_mimic = mimic_test_case.model_mimic;
    for (int j = 1; j < model_mimic.njoints; j++)
    {
      test_compute_frame_jacobian_impl(model_mimic, static_cast<pinocchio::JointIndex>(j));
    }
  }
}
 
BOOST_AUTO_TEST_CASE(test_frame_jacobian_time_variation)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  pinocchio::Model model;
  pinocchio::buildModels::humanoidRandom(model);
  Model::Index parent_idx = model.existJointName("rarm2_joint") ? model.getJointId("rarm2_joint")
                                                                : (Model::Index)(model.njoints - 1);
  const std::string & frame_name = std::string(model.names[parent_idx] + "_frame");
  const SE3 & framePlacement = SE3::Random();
  model.addFrame(Frame(frame_name, parent_idx, 0, framePlacement, OP_FRAME));
  pinocchio::Data data(model);
  pinocchio::Data data_ref(model);
 
  VectorXd q = randomConfiguration(
    model, -1 * Eigen::VectorXd::Ones(model.nq), Eigen::VectorXd::Ones(model.nq));
  VectorXd v = VectorXd::Random(model.nv);
  VectorXd a = VectorXd::Random(model.nv);
 
  computeJointJacobiansTimeVariation(model, data, q, v);
  updateFramePlacements(model, data);
 
  forwardKinematics(model, data_ref, q, v, a);
  updateFramePlacements(model, data_ref);
 
  BOOST_CHECK(isFinite(data.dJ));
 
  Model::Index idx = model.getFrameId(frame_name);
  const Frame & frame = model.frames[idx];
  BOOST_CHECK(frame.placement.isApprox_impl(framePlacement));
 
  Data::Matrix6x J(6, model.nv);
  J.fill(0.);
  Data::Matrix6x dJ(6, model.nv);
  dJ.fill(0.);
 
  // Regarding to the WORLD origin
  getFrameJacobian(model, data, idx, WORLD, J);
  getFrameJacobianTimeVariation(model, data, idx, WORLD, dJ);
 
  Motion v_idx(J * v);
  const Motion & v_ref_local = frame.placement.actInv(data_ref.v[parent_idx]);
  const Motion & v_ref = data_ref.oMf[idx].act(v_ref_local);
 
  const SE3 wMf = SE3(data_ref.oMf[idx].rotation(), SE3::Vector3::Zero());
  const Motion v_ref_local_world_aligned = wMf.act(v_ref_local);
  BOOST_CHECK(v_idx.isApprox(v_ref));
 
  Motion a_idx(J * a + dJ * v);
  const Motion a_ref_local = frame.placement.actInv(data_ref.a[parent_idx]);
  const Motion a_ref = data_ref.oMf[idx].act(a_ref_local);
  const Motion a_ref_local_world_aligned = wMf.act(a_ref_local);
  BOOST_CHECK(a_idx.isApprox(a_ref));
 
  J.fill(0.);
  dJ.fill(0.);
  // Regarding to the LOCAL frame
  getFrameJacobian(model, data, idx, LOCAL, J);
  getFrameJacobianTimeVariation(model, data, idx, LOCAL, dJ);
 
  v_idx = (Motion::Vector6)(J * v);
  BOOST_CHECK(v_idx.isApprox(v_ref_local));
 
  a_idx = (Motion::Vector6)(J * a + dJ * v);
  BOOST_CHECK(a_idx.isApprox(a_ref_local));
 
  // Regarding to the LOCAL_WORLD_ALIGNED frame
  getFrameJacobian(model, data, idx, LOCAL_WORLD_ALIGNED, J);
  getFrameJacobianTimeVariation(model, data, idx, LOCAL_WORLD_ALIGNED, dJ);
  Data::Motion world_v_frame = data.ov[parent_idx];
  world_v_frame.linear().setZero();
 
  v_idx = (Motion::Vector6)(J * v);
  BOOST_CHECK(v_idx.isApprox(v_ref_local_world_aligned));
 
  a_idx = (Motion::Vector6)(J * a + dJ * v);
  BOOST_CHECK(
    a_idx.isApprox(world_v_frame.cross(wMf.act(v_ref_local)) + a_ref_local_world_aligned));
 
  // compare to finite differencies
  {
    Data data_ref(model), data_ref_plus(model);
 
    const double alpha = 1e-8;
    Eigen::VectorXd q_plus(model.nq);
    q_plus = integrate(model, q, alpha * v);
 
    // data_ref
    Data::Matrix6x J_ref_world(6, model.nv), J_ref_local(6, model.nv),
      J_ref_local_world_aligned(6, model.nv);
    J_ref_world.fill(0.);
    J_ref_local.fill(0.);
    J_ref_local_world_aligned.fill(0.);
    computeJointJacobians(model, data_ref, q);
    updateFramePlacements(model, data_ref);
    getFrameJacobian(model, data_ref, idx, WORLD, J_ref_world);
    getFrameJacobian(model, data_ref, idx, LOCAL, J_ref_local);
    getFrameJacobian(model, data_ref, idx, LOCAL_WORLD_ALIGNED, J_ref_local_world_aligned);
 
    // data_ref_plus
    Data::Matrix6x J_ref_plus_world(6, model.nv), J_ref_plus_local(6, model.nv),
      J_ref_plus_local_world_aligned(6, model.nv);
    J_ref_plus_world.fill(0.);
    J_ref_plus_local.fill(0.);
    J_ref_plus_local_world_aligned.fill(0.);
    computeJointJacobians(model, data_ref_plus, q_plus);
    updateFramePlacements(model, data_ref_plus);
    getFrameJacobian(model, data_ref_plus, idx, WORLD, J_ref_plus_world);
    getFrameJacobian(model, data_ref_plus, idx, LOCAL, J_ref_plus_local);
    getFrameJacobian(
      model, data_ref_plus, idx, LOCAL_WORLD_ALIGNED, J_ref_plus_local_world_aligned);
 
    Data::Matrix6x dJ_ref_world(6, model.nv), dJ_ref_local(6, model.nv),
      dJ_ref_local_world_aligned(6, model.nv);
    dJ_ref_world.fill(0.);
    dJ_ref_local.fill(0.);
    dJ_ref_local_world_aligned.fill(0.);
    dJ_ref_world = (J_ref_plus_world - J_ref_world) / alpha;
    dJ_ref_local = (J_ref_plus_local - J_ref_local) / alpha;
    dJ_ref_local_world_aligned =
      (J_ref_plus_local_world_aligned - J_ref_local_world_aligned) / alpha;
 
    // data
    computeJointJacobiansTimeVariation(model, data, q, v);
    forwardKinematics(model, data, q, v);
    updateFramePlacements(model, data);
    Data::Matrix6x dJ_world(6, model.nv), dJ_local(6, model.nv),
      dJ_local_world_aligned(6, model.nv);
    dJ_world.fill(0.);
    dJ_local.fill(0.);
    dJ_local_world_aligned.fill(0.);
    getFrameJacobianTimeVariation(model, data, idx, WORLD, dJ_world);
    getFrameJacobianTimeVariation(model, data, idx, LOCAL, dJ_local);
    getFrameJacobianTimeVariation(model, data, idx, LOCAL_WORLD_ALIGNED, dJ_local_world_aligned);
 
    BOOST_CHECK(dJ_world.isApprox(dJ_ref_world, sqrt(alpha)));
    BOOST_CHECK(dJ_local.isApprox(dJ_ref_local, sqrt(alpha)));
    BOOST_CHECK(dJ_local_world_aligned.isApprox(dJ_ref_local_world_aligned, sqrt(alpha)));
  }
}
 
BOOST_AUTO_TEST_CASE(test_supported_inertia_and_force)
{
  using namespace Eigen;
  using namespace pinocchio;
 
  // Create a humanoid robot
  Model model_free;
  pinocchio::buildModels::humanoid(model_free, true);
  Data data_free(model_free);
 
  // Set freeflyer limits to allow for randomConfiguration
  model_free.lowerPositionLimit.segment(0, 3) << Vector3d::Constant(-1);
  model_free.upperPositionLimit.segment(0, 3) << Vector3d::Constant(1);
 
  // Joint of interest (that will be converted to frame)
  const std::string joint_name = "chest2_joint";
  const JointIndex joint_id = model_free.getJointId(joint_name);
 
  // Duplicate of the model with the joint of interest fixed (to make a frame)
  pinocchio::Model model_fix = buildReducedModel(model_free, {joint_id}, neutral(model_free));
  Data data_fix(model_fix);
  const FrameIndex frame_id = model_fix.getFrameId(joint_name);
 
  // Const variable to help convert q, v, a from one model to another
  const int joint_idx_q(model_free.joints[joint_id].idx_q());
  const int joint_idx_v(model_free.joints[joint_id].idx_v());
 
  // Pick random q, v, a
  VectorXd q_free = randomConfiguration(model_free);
  VectorXd v_free(VectorXd::Random(model_free.nv));
  VectorXd a_free(VectorXd::Random(model_free.nv));
 
  // Set joint of interest to q, v, a = 0 to mimic the fixed joint
  q_free[joint_idx_q] = 0;
  v_free[joint_idx_v] = 0;
  a_free[joint_idx_v] = 0;
 
  // Adapt configuration for fixed joint model
  VectorXd q_fix(model_fix.nq);
  q_fix << q_free.head(joint_idx_q), q_free.tail(model_free.nq - joint_idx_q - 1);
  VectorXd v_fix(model_fix.nv);
  v_fix << v_free.head(joint_idx_v), v_free.tail(model_free.nv - joint_idx_v - 1);
  VectorXd a_fix(model_fix.nv);
  a_fix << a_free.head(joint_idx_v), a_free.tail(model_free.nv - joint_idx_v - 1);
 
  // Compute inertia/force for both models differently
  forwardKinematics(model_fix, data_fix, q_fix, v_fix, a_fix);
  crba(model_free, data_free, q_free, Convention::WORLD);
 
  Inertia inertia_fix = computeSupportedInertiaByFrame(model_fix, data_fix, frame_id, false);
  Inertia inertia_free(model_free.inertias[joint_id]);
  BOOST_CHECK(inertia_fix.isApprox(inertia_free));
 
  inertia_fix = computeSupportedInertiaByFrame(model_fix, data_fix, frame_id, true);
  inertia_free = data_free.oMi[joint_id].actInv(data_free.oYcrb[joint_id]);
  BOOST_CHECK(inertia_fix.isApprox(inertia_free));
 
  rnea(model_fix, data_fix, q_fix, v_fix, a_fix);
  rnea(model_free, data_free, q_free, v_free, a_free);
 
  Force force_fix = computeSupportedForceByFrame(model_fix, data_fix, frame_id);
  Force force_free(data_free.f[joint_id]);
  BOOST_CHECK(force_fix.isApprox(force_free));
}
BOOST_AUTO_TEST_SUITE_END()