rbdlsim/3rdparty/rbdl/tests/SparseFactorizationTests.cc

#include <UnitTest++.h>

#include <iostream>

#include "Fixtures.h"
#include "rbdl/rbdl_mathutils.h"
#include "rbdl/rbdl_utils.h"
#include "rbdl/Logging.h"

#include "rbdl/Model.h"
#include "rbdl/Kinematics.h"
#include "rbdl/Dynamics.h"

using namespace std;
using namespace RigidBodyDynamics;
using namespace RigidBodyDynamics::Math;

const double TEST_PREC = 1.0e-12;

TEST_FIXTURE (FloatingBase12DoF, TestSparseFactorizationLTL) {
  for (unsigned int i = 0; i < model->q_size; i++) {
    Q[i] = static_cast<double> (i + 1) * 0.1;
  }

  MatrixNd H (MatrixNd::Zero (model->qdot_size, model->qdot_size));

  CompositeRigidBodyAlgorithm (*model, Q, H);

  MatrixNd L (H);
  SparseFactorizeLTL (*model, L);
  MatrixNd LTL = L.transpose() * L;

  CHECK_ARRAY_CLOSE (H.data(), LTL.data(), model->qdot_size * model->qdot_size, TEST_PREC);
}

TEST_FIXTURE (FloatingBase12DoF, TestSparseSolveLx) {
  for (unsigned int i = 0; i < model->q_size; i++) {
    Q[i] = static_cast<double> (i + 1) * 0.1;
  }

  MatrixNd H (MatrixNd::Zero (model->qdot_size, model->qdot_size));

  CompositeRigidBodyAlgorithm (*model, Q, H);

  MatrixNd L (H);
  SparseFactorizeLTL (*model, L);
  VectorNd x = L * Q;

  SparseSolveLx (*model, L, x);

  CHECK_ARRAY_CLOSE (Q.data(), x.data(), model->qdot_size, TEST_PREC);
}

TEST_FIXTURE (FloatingBase12DoF, TestSparseSolveLTx) {
  for (unsigned int i = 0; i < model->q_size; i++) {
    Q[i] = static_cast<double> (i + 1) * 0.1;
  }

  MatrixNd H (MatrixNd::Zero (model->qdot_size, model->qdot_size));

  CompositeRigidBodyAlgorithm (*model, Q, H);

  MatrixNd L (H);
  SparseFactorizeLTL (*model, L);
  VectorNd x = L.transpose() * Q;

  SparseSolveLTx (*model, L, x);

  CHECK_ARRAY_CLOSE (Q.data(), x.data(), model->qdot_size, TEST_PREC);
}

TEST_FIXTURE (FixedBase6DoF12DoFFloatingBase, ForwardDynamicsContactsSparse) {
  ConstraintSet constraint_set_var1;

  constraint_set.AddContactConstraint (contact_body_id, contact_point, Vector3d (1., 0., 0.));
  constraint_set.AddContactConstraint (contact_body_id, contact_point, Vector3d (0., 1., 0.));
  constraint_set.AddContactConstraint (child_2_id, contact_point, Vector3d (0., 1., 0.));

  constraint_set_var1 = constraint_set.Copy();
  constraint_set_var1.Bind (*model);
  constraint_set.Bind (*model);

  VectorNd QDDot_var1 = VectorNd::Constant (model->dof_count, 0.);

  Q[0] = 0.1;
  Q[1] = -0.3;
  Q[2] = 0.15;
  Q[3] = -0.21;
  Q[4] = -0.81;
  Q[5] = 0.11;
  Q[6] = 0.31;
  Q[7] = -0.91;
  Q[8] = 0.61;

  QDot[0] =  1.3;
  QDot[1] = -1.7;
  QDot[2] =  3;
  QDot[3] = -2.5;
  QDot[4] =  1.5;
  QDot[5] = -5.5;
  QDot[6] =  2.5;
  QDot[7] = -1.5;
  QDot[8] = -3.5;

  ClearLogOutput();
  ForwardDynamicsContactsKokkevis (*model, Q, QDot, Tau, constraint_set, QDDot);

  ClearLogOutput();
  ForwardDynamicsConstraintsRangeSpaceSparse (*model, Q, QDot, Tau, constraint_set_var1, QDDot_var1);

  CHECK_ARRAY_CLOSE (QDDot.data(), QDDot_var1.data(), QDDot.size(), TEST_PREC);
}

TEST ( TestSparseFactorizationMultiDof) {
  Model model_emulated;
  Model model_3dof;

  Body body (1., Vector3d (1., 2., 1.), Matrix3d (1., 0., 0, 0., 1., 0., 0., 0., 1.));
  Joint joint_emulated (
      SpatialVector (0., 1., 0., 0., 0., 0.),
      SpatialVector (1., 0., 0., 0., 0., 0.),
      SpatialVector (0., 0., 1., 0., 0., 0.)
      );
  Joint joint_3dof (JointTypeEulerYXZ);

  Joint joint_rot_y (
      SpatialVector (0., 1., 0., 0., 0., 0.)
      );

  model_emulated.AppendBody (SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_rot_y, body);
  unsigned int multdof_body_id_emulated = model_emulated.AppendBody (SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_emulated, body);
  model_emulated.AppendBody (SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_emulated, body);
  model_emulated.AddBody (multdof_body_id_emulated, SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_rot_y, body);
  model_emulated.AppendBody (SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_emulated, body);

  model_3dof.AppendBody (SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_rot_y, body);
  unsigned int multdof_body_id_3dof = model_3dof.AppendBody (SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_3dof, body);
  model_3dof.AppendBody (SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_3dof, body);
  model_3dof.AddBody (multdof_body_id_3dof, SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_rot_y, body);
  model_3dof.AppendBody (SpatialTransform (Matrix3d::Identity(), Vector3d::Zero()), joint_3dof, body);

  VectorNd q (VectorNd::Zero (model_emulated.q_size));
  VectorNd qdot (VectorNd::Zero (model_emulated.qdot_size));
  VectorNd qddot_emulated (VectorNd::Zero (model_emulated.qdot_size));
  VectorNd qddot_3dof (VectorNd::Zero (model_emulated.qdot_size));
  VectorNd tau (VectorNd::Zero (model_emulated.qdot_size));

  for (unsigned int i = 0; i < q.size(); i++) {
    q[i] = 1.1 * (static_cast<double>(i + 1));
    qdot[i] = 0.55* (static_cast<double>(i + 1));
    qddot_emulated[i] = 0.23 * (static_cast<double>(i + 1));
    qddot_3dof[i] = 0.22 * (static_cast<double>(i + 1));
    tau[i] = 2.1 * (static_cast<double>(i + 1));
  }

  MatrixNd H_emulated (MatrixNd::Zero (q.size(), q.size()));
  MatrixNd H_3dof (MatrixNd::Zero (q.size(), q.size()));

  CompositeRigidBodyAlgorithm (model_emulated, q, H_emulated);
  CompositeRigidBodyAlgorithm (model_3dof, q, H_3dof);

  VectorNd b (VectorNd::Zero (q.size()));
  VectorNd x_emulated (VectorNd::Zero (q.size()));
  VectorNd x_3dof (VectorNd::Zero (q.size()));

  for (unsigned int i = 0; i < b.size(); i++) {
    b[i] = static_cast<double> (i + 1) * 2.152;
  }
  b = H_emulated * b;

  SparseFactorizeLTL (model_emulated, H_emulated);
  SparseFactorizeLTL (model_3dof, H_3dof);

  CHECK_ARRAY_CLOSE (H_emulated.data(), H_3dof.data(), q.size() * q.size(), TEST_PREC);

  x_emulated = b;
  SparseSolveLx (model_emulated, H_emulated, x_emulated);
  x_3dof = b;
  SparseSolveLx (model_3dof, H_3dof, x_3dof);

  CHECK_ARRAY_CLOSE (x_emulated.data(), x_3dof.data(), x_emulated.size(), 1.0e-9);

  x_emulated = b;
  SparseSolveLTx (model_emulated, H_emulated, x_emulated);
  x_3dof = b;
  SparseSolveLTx (model_3dof, H_3dof, x_3dof);

  CHECK_ARRAY_CLOSE (x_emulated.data(), x_3dof.data(), x_emulated.size(), 1.0e-9);
}

TEST ( TestSparseFactorizationMultiDofAndFixed) {
  Model model_emulated;
  Model model_3dof;

  Body body (1., Vector3d (1., 2., 1.), Matrix3d (1., 0., 0, 0., 1., 0., 0., 0., 1.));
  Joint joint_emulated (
      SpatialVector (0., 1., 0., 0., 0., 0.),
      SpatialVector (1., 0., 0., 0., 0., 0.),
      SpatialVector (0., 0., 1., 0., 0., 0.)
      );
  Joint joint_3dof (JointTypeEulerYXZ);

  Joint joint_rot_y (
      SpatialVector (0., 1., 0., 0., 0., 0.)
      );

  SpatialTransform translate_x (Matrix3d::Identity(), Vector3d (1., 0., 0.));

  model_emulated.AppendBody (SpatialTransform(Matrix3d::Identity(), Vector3d::Zero()), joint_rot_y, body);
  unsigned int multdof_body_id_emulated = model_emulated.AppendBody (translate_x, joint_emulated, body);
  model_emulated.AppendBody (translate_x, joint_emulated, body);
  model_emulated.AddBody(multdof_body_id_emulated, translate_x, Joint(JointTypeFixed), body);
  model_emulated.AppendBody (translate_x, joint_emulated, body);

  model_3dof.AppendBody (SpatialTransform(Matrix3d::Identity(), Vector3d::Zero()), joint_rot_y, body);
  unsigned int multdof_body_id_3dof = model_3dof.AppendBody (translate_x, joint_3dof, body);
  model_3dof.AppendBody (translate_x, joint_3dof, body);
  model_3dof.AddBody (multdof_body_id_3dof, translate_x, Joint(JointTypeFixed), body);
  model_3dof.AppendBody (translate_x, joint_3dof, body);

  VectorNd q (VectorNd::Zero (model_emulated.q_size));
  VectorNd qdot (VectorNd::Zero (model_emulated.qdot_size));
  VectorNd qddot_emulated (VectorNd::Zero (model_emulated.qdot_size));
  VectorNd qddot_3dof (VectorNd::Zero (model_emulated.qdot_size));
  VectorNd tau (VectorNd::Zero (model_emulated.qdot_size));

  for (unsigned int i = 0; i < q.size(); i++) {
    q[i] = 1.1 * (static_cast<double>(i + 1));
    qdot[i] = 0.55* (static_cast<double>(i + 1));
    qddot_emulated[i] = 0.23 * (static_cast<double>(i + 1));
    qddot_3dof[i] = 0.22 * (static_cast<double>(i + 1));
    tau[i] = 2.1 * (static_cast<double>(i + 1));
  }

  MatrixNd H_emulated (MatrixNd::Zero (q.size(), q.size()));
  MatrixNd H_3dof (MatrixNd::Zero (q.size(), q.size()));

  CompositeRigidBodyAlgorithm (model_emulated, q, H_emulated);
  CompositeRigidBodyAlgorithm (model_3dof, q, H_3dof);

  VectorNd b (VectorNd::Zero (q.size()));
  VectorNd x_emulated (VectorNd::Zero (q.size()));
  VectorNd x_3dof (VectorNd::Zero (q.size()));

  for (unsigned int i = 0; i < b.size(); i++) {
    b[i] = static_cast<double> (i + 1) * 2.152;
  }
  b = H_emulated * b;

  SparseFactorizeLTL (model_emulated, H_emulated);
  SparseFactorizeLTL (model_3dof, H_3dof);

  CHECK_ARRAY_CLOSE (H_emulated.data(), H_3dof.data(), q.size() * q.size(), TEST_PREC);

  x_emulated = b;
  SparseSolveLx (model_emulated, H_emulated, x_emulated);
  x_3dof = b;
  SparseSolveLx (model_3dof, H_3dof, x_3dof);

  CHECK_ARRAY_CLOSE (x_emulated.data(), x_3dof.data(), x_emulated.size(), 1.0e-9);

  x_emulated = b;
  SparseSolveLTx (model_emulated, H_emulated, x_emulated);
  x_3dof = b;
  SparseSolveLTx (model_3dof, H_3dof, x_3dof);

  CHECK_ARRAY_CLOSE (x_emulated.data(), x_3dof.data(), x_emulated.size(), 1.0e-9);
}