joint-spherical-ZYX.hpp

//
// Copyright (c) 2015-2020 CNRS INRIA
// Copyright (c) 2015-2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
//

#ifndef __pinocchio_multibody_joint_spherical_ZYX_hpp__
#define __pinocchio_multibody_joint_spherical_ZYX_hpp__

#include "pinocchio/macros.hpp"
#include "pinocchio/multibody/joint/joint-base.hpp"
#include "pinocchio/multibody/joint/joint-spherical.hpp"
#include "pinocchio/multibody/joint-motion-subspace.hpp"
#include "pinocchio/math/sincos.hpp"
#include "pinocchio/math/matrix.hpp"
#include "pinocchio/spatial/inertia.hpp"
#include "pinocchio/spatial/skew.hpp"

namespace pinocchio
{
 template<typename Scalar, int Options>
 struct JointMotionSubspaceSphericalZYXTpl;

 template<typename _Scalar, int _Options>
 struct traits<JointMotionSubspaceSphericalZYXTpl<_Scalar, _Options>>
 {
 typedef _Scalar Scalar;
 enum
 {
 Options = _Options
 };

 enum
 {
 LINEAR = 0,
 ANGULAR = 3
 };

 typedef MotionSphericalTpl<Scalar, Options> JointMotion;
 typedef Eigen::Matrix<Scalar, 3, 1, Options> JointForce;
 typedef Eigen::Matrix<Scalar, 6, 3, Options> DenseBase;
 typedef Eigen::Matrix<Scalar, 3, 3, Options> ReducedSquaredMatrix;

 typedef DenseBase MatrixReturnType;
 typedef const DenseBase ConstMatrixReturnType;

 typedef ReducedSquaredMatrix StDiagonalMatrixSOperationReturnType;
 }; // struct traits struct ConstraintRotationalSubspace

 template<typename _Scalar, int _Options>
 struct JointMotionSubspaceSphericalZYXTpl
 : public JointMotionSubspaceBase<JointMotionSubspaceSphericalZYXTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW

 PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(JointMotionSubspaceSphericalZYXTpl)

 enum
 {
 NV = 3
 };
 typedef Eigen::Matrix<Scalar, 3, 3, Options> Matrix3;

 JointMotionSubspaceSphericalZYXTpl()
 {
 }

 template<typename Matrix3Like>
 JointMotionSubspaceSphericalZYXTpl(const Eigen::MatrixBase<Matrix3Like> & subspace)
 : m_S(subspace)
 {
 EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3Like, 3, 3);
 }

 template<typename Vector3Like>
 JointMotion __mult__(const Eigen::MatrixBase<Vector3Like> & v) const
 {
 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3Like, 3);
 return JointMotion(m_S * v);
 }

 Matrix3 & operator()()
 {
 return m_S;
 }
 const Matrix3 & operator()() const
 {
 return m_S;
 }

 int nv_impl() const
 {
 return NV;
 }

 struct ConstraintTranspose
 : JointMotionSubspaceTransposeBase<JointMotionSubspaceSphericalZYXTpl>
 {
 const JointMotionSubspaceSphericalZYXTpl & ref;
 ConstraintTranspose(const JointMotionSubspaceSphericalZYXTpl & ref)
 : ref(ref)
 {
 }

 template<typename Derived>
 const typename MatrixMatrixProduct<
 Eigen::Transpose<const Matrix3>,
 Eigen::Block<const typename ForceDense<Derived>::Vector6, 3, 1>>::type
 operator*(const ForceDense<Derived> & phi) const
 {
 return ref.m_S.transpose() * phi.angular();
 }

 /* [CRBA] MatrixBase operator* (Constraint::Transpose S, ForceSet::Block) */
 template<typename D>
 const typename MatrixMatrixProduct<
 typename Eigen::Transpose<const Matrix3>,
 typename Eigen::MatrixBase<const D>::template NRowsBlockXpr<3>::Type>::type
 operator*(const Eigen::MatrixBase<D> & F) const
 {
 EIGEN_STATIC_ASSERT(
 D::RowsAtCompileTime == 6, THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE)
 return ref.m_S.transpose() * F.template middleRows<3>(ANGULAR);
 }
 }; // struct ConstraintTranspose

 ConstraintTranspose transpose() const
 {
 return ConstraintTranspose(*this);
 }

 DenseBase matrix_impl() const
 {
 DenseBase S;
 S.template middleRows<3>(LINEAR).setZero();
 S.template middleRows<3>(ANGULAR) = m_S;
 return S;
 }

 // const typename Eigen::ProductReturnType<
 // const ConstraintDense,
 // const Matrix3
 // >::Type
 template<typename S1, int O1>
 Eigen::Matrix<Scalar, 6, 3, Options> se3Action(const SE3Tpl<S1, O1> & m) const
 {
 // Eigen::Matrix <Scalar,6,3,Options> X_subspace;
 // X_subspace.template block <3,3> (Motion::LINEAR, 0) = skew (m.translation ()) *
 // m.rotation (); X_subspace.template block <3,3> (Motion::ANGULAR, 0) = m.rotation ();
 //
 // return (X_subspace * m_S).eval();

 Eigen::Matrix<Scalar, 6, 3, Options> result;

 // ANGULAR
 result.template middleRows<3>(ANGULAR).noalias() = m.rotation() * m_S;

 // LINEAR
 cross(
 m.translation(), result.template middleRows<3>(Motion::ANGULAR),
 result.template middleRows<3>(LINEAR));

 return result;
 }

 template<typename S1, int O1>
 Eigen::Matrix<Scalar, 6, 3, Options> se3ActionInverse(const SE3Tpl<S1, O1> & m) const
 {
 Eigen::Matrix<Scalar, 6, 3, Options> result;

 // LINEAR
 cross(m.translation(), m_S, result.template middleRows<3>(ANGULAR));
 result.template middleRows<3>(LINEAR).noalias() =
 -m.rotation().transpose() * result.template middleRows<3>(ANGULAR);

 // ANGULAR
 result.template middleRows<3>(ANGULAR).noalias() = m.rotation().transpose() * m_S;

 return result;
 }

 template<typename MotionDerived>
 DenseBase motionAction(const MotionDense<MotionDerived> & m) const
 {
 const typename MotionDerived::ConstLinearType v = m.linear();
 const typename MotionDerived::ConstAngularType w = m.angular();

 DenseBase res;
 cross(v, m_S, res.template middleRows<3>(LINEAR));
 cross(w, m_S, res.template middleRows<3>(ANGULAR));

 return res;
 }

 Matrix3 & angularSubspace()
 {
 return m_S;
 }
 const Matrix3 & angularSubspace() const
 {
 return m_S;
 }

 bool isEqual(const JointMotionSubspaceSphericalZYXTpl & other) const
 {
 return internal::comparison_eq(m_S, other.m_S);
 }

 protected:
 Matrix3 m_S;

 }; // struct JointMotionSubspaceSphericalZYXTpl

 namespace details
 {
 template<typename Scalar, int Options>
 struct StDiagonalMatrixSOperation<JointMotionSubspaceSphericalZYXTpl<Scalar, Options>>
 {
 typedef JointMotionSubspaceSphericalZYXTpl<Scalar, Options> Constraint;
 typedef typename traits<Constraint>::StDiagonalMatrixSOperationReturnType ReturnType;

 static ReturnType run(const JointMotionSubspaceBase<Constraint> & constraint)
 {
 return constraint.matrix().transpose() * constraint.matrix();
 }
 };
 } // namespace details

 /* [CRBA] ForceSet operator* (Inertia Y,Constraint S) */
 template<typename S1, int O1, typename S2, int O2>
 Eigen::Matrix<S1, 6, 3, O1>
 operator*(const InertiaTpl<S1, O1> & Y, const JointMotionSubspaceSphericalZYXTpl<S2, O2> & S)
 {
 typedef typename InertiaTpl<S1, O1>::Symmetric3 Symmetric3;
 typedef JointMotionSubspaceSphericalZYXTpl<S2, O2> Constraint;
 Eigen::Matrix<S1, 6, 3, O1> M;
 alphaSkew(-Y.mass(), Y.lever(), M.template middleRows<3>(Constraint::LINEAR));
 M.template middleRows<3>(Constraint::ANGULAR) =
 (Y.inertia() - typename Symmetric3::AlphaSkewSquare(Y.mass(), Y.lever())).matrix();

 return (M * S.angularSubspace()).eval();
 }

 /* [ABA] Y*S operator (Inertia Y,Constraint S) */
 // inline Eigen::Matrix<context::Scalar,6,3>
 template<typename Matrix6Like, typename S2, int O2>
 const typename MatrixMatrixProduct<
 typename Eigen::internal::remove_const<
 typename SizeDepType<3>::ColsReturn<Matrix6Like>::ConstType>::type,
 typename JointMotionSubspaceSphericalZYXTpl<S2, O2>::Matrix3>::type
 operator*(
 const Eigen::MatrixBase<Matrix6Like> & Y, const JointMotionSubspaceSphericalZYXTpl<S2, O2> & S)
 {
 EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix6Like, 6, 6);
 return Y.derived().template middleCols<3>(Inertia::ANGULAR) * S.angularSubspace();
 }

 template<typename S1, int O1>
 struct SE3GroupAction<JointMotionSubspaceSphericalZYXTpl<S1, O1>>
 {
 // typedef const typename Eigen::ProductReturnType<
 // Eigen::Matrix <context::Scalar,6,3,0>,
 // Eigen::Matrix <context::Scalar,3,3,0>
 // >::Type Type;
 typedef Eigen::Matrix<S1, 6, 3, O1> ReturnType;
 };

 template<typename S1, int O1, typename MotionDerived>
 struct MotionAlgebraAction<JointMotionSubspaceSphericalZYXTpl<S1, O1>, MotionDerived>
 {
 typedef Eigen::Matrix<S1, 6, 3, O1> ReturnType;
 };

 template<typename Scalar, int Options>
 struct JointSphericalZYXTpl;

 template<typename _Scalar, int _Options>
 struct traits<JointSphericalZYXTpl<_Scalar, _Options>>
 {
 enum
 {
 NQ = 3,
 NV = 3,
 NVExtended = 3
 };
 typedef _Scalar Scalar;
 enum
 {
 Options = _Options
 };
 typedef JointDataSphericalZYXTpl<Scalar, Options> JointDataDerived;
 typedef JointModelSphericalZYXTpl<Scalar, Options> JointModelDerived;
 typedef JointMotionSubspaceSphericalZYXTpl<Scalar, Options> Constraint_t;
 typedef SE3Tpl<Scalar, Options> Transformation_t;
 typedef MotionSphericalTpl<Scalar, Options> Motion_t;
 typedef MotionSphericalTpl<Scalar, Options> Bias_t;

 // [ABA]
 typedef Eigen::Matrix<Scalar, 6, NV, Options> U_t;
 typedef Eigen::Matrix<Scalar, NV, NV, Options> D_t;
 typedef Eigen::Matrix<Scalar, 6, NV, Options> UD_t;

 typedef Eigen::Matrix<Scalar, NQ, 1, Options> ConfigVector_t;
 typedef Eigen::Matrix<Scalar, NV, 1, Options> TangentVector_t;

 typedef boost::mpl::false_ is_mimicable_t;

 PINOCCHIO_JOINT_DATA_BASE_ACCESSOR_DEFAULT_RETURN_TYPE
 };

 template<typename _Scalar, int _Options>
 struct traits<JointDataSphericalZYXTpl<_Scalar, _Options>>
 {
 typedef JointSphericalZYXTpl<_Scalar, _Options> JointDerived;
 typedef _Scalar Scalar;
 };

 template<typename _Scalar, int _Options>
 struct traits<JointModelSphericalZYXTpl<_Scalar, _Options>>
 {
 typedef JointSphericalZYXTpl<_Scalar, _Options> JointDerived;
 typedef _Scalar Scalar;
 };

 template<typename _Scalar, int _Options>
 struct JointDataSphericalZYXTpl
 : public JointDataBase<JointDataSphericalZYXTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 typedef JointSphericalZYXTpl<_Scalar, _Options> JointDerived;
 PINOCCHIO_JOINT_DATA_TYPEDEF_TEMPLATE(JointDerived);
 PINOCCHIO_JOINT_DATA_BASE_DEFAULT_ACCESSOR

 ConfigVector_t joint_q;
 TangentVector_t joint_v;

 Constraint_t S;
 Transformation_t M;
 Motion_t v;
 Bias_t c;

 // [ABA] specific data
 U_t U;
 D_t Dinv;
 UD_t UDinv;
 D_t StU;

 JointDataSphericalZYXTpl()
 : joint_q(ConfigVector_t::Zero())
 , joint_v(TangentVector_t::Zero())
 , S(Constraint_t::Matrix3::Zero())
 , M(Transformation_t::Identity())
 , v(Motion_t::Vector3::Zero())
 , c(Bias_t::Vector3::Zero())
 , U(U_t::Zero())
 , Dinv(D_t::Zero())
 , UDinv(UD_t::Zero())
 , StU(D_t::Zero())
 {
 }

 static std::string classname()
 {
 return std::string("JointDataSphericalZYX");
 }
 std::string shortname() const
 {
 return classname();
 }

 }; // strcut JointDataSphericalZYXTpl

 PINOCCHIO_JOINT_CAST_TYPE_SPECIALIZATION(JointModelSphericalZYXTpl);
 template<typename _Scalar, int _Options>
 struct JointModelSphericalZYXTpl
 : public JointModelBase<JointModelSphericalZYXTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 typedef JointSphericalZYXTpl<_Scalar, _Options> JointDerived;
 PINOCCHIO_JOINT_TYPEDEF_TEMPLATE(JointDerived);

 typedef JointModelBase<JointModelSphericalZYXTpl> Base;
 using Base::id;
 using Base::idx_q;
 using Base::idx_v;
 using Base::idx_vExtended;
 using Base::setIndexes;

 JointDataDerived createData() const
 {
 return JointDataDerived();
 }

 const std::vector<bool> hasConfigurationLimit() const
 {
 return {true, true, true};
 }

 const std::vector<bool> hasConfigurationLimitInTangent() const
 {
 return {true, true, true};
 }

 template<typename ConfigVector>
 void calc(JointDataDerived & data, const typename Eigen::MatrixBase<ConfigVector> & qs) const
 {
 data.joint_q = qs.template segment<NQ>(idx_q());

 Scalar c0, s0;
 SINCOS(data.joint_q(0), &s0, &c0);
 Scalar c1, s1;
 SINCOS(data.joint_q(1), &s1, &c1);
 Scalar c2, s2;
 SINCOS(data.joint_q(2), &s2, &c2);

 data.M.rotation() << c0 * c1, c0 * s1 * s2 - s0 * c2, c0 * s1 * c2 + s0 * s2, s0 * c1,
 s0 * s1 * s2 + c0 * c2, s0 * s1 * c2 - c0 * s2, -s1, c1 * s2, c1 * c2;

 data.S.angularSubspace() << -s1, Scalar(0), Scalar(1), c1 * s2, c2, Scalar(0), c1 * c2, -s2,
 Scalar(0);
 }

 template<typename TangentVector>
 void
 calc(JointDataDerived & data, const Blank, const typename Eigen::MatrixBase<TangentVector> & vs)
 const
 {
 data.joint_v = vs.template segment<NV>(idx_v());
 data.v().noalias() = data.S.angularSubspace() * data.joint_v;

 // TODO(jcarpent): to be done
 // #define q_dot data.joint_v
 // data.c()(0) = -c1 * q_dot(0) * q_dot(1);
 // data.c()(1) = -s1 * s2 * q_dot(0) * q_dot(1) + c1 * c2 * q_dot(0) * q_dot(2) - s2 *
 // q_dot(1) * q_dot(2); data.c()(2) = -s1 * c2 * q_dot(0) * q_dot(1) - c1 * s2 *
 // q_dot(0) * q_dot(2) - c2 * q_dot(1) * q_dot(2);
 // #undef q_dot
 }

 template<typename ConfigVector, typename TangentVector>
 void calc(
 JointDataDerived & data,
 const typename Eigen::MatrixBase<ConfigVector> & qs,
 const typename Eigen::MatrixBase<TangentVector> & vs) const
 {
 data.joint_q = qs.template segment<NQ>(idx_q());

 Scalar c0, s0;
 SINCOS(data.joint_q(0), &s0, &c0);
 Scalar c1, s1;
 SINCOS(data.joint_q(1), &s1, &c1);
 Scalar c2, s2;
 SINCOS(data.joint_q(2), &s2, &c2);

 data.M.rotation() << c0 * c1, c0 * s1 * s2 - s0 * c2, c0 * s1 * c2 + s0 * s2, s0 * c1,
 s0 * s1 * s2 + c0 * c2, s0 * s1 * c2 - c0 * s2, -s1, c1 * s2, c1 * c2;

 data.S.angularSubspace() << -s1, Scalar(0), Scalar(1), c1 * s2, c2, Scalar(0), c1 * c2, -s2,
 Scalar(0);

 data.joint_v = vs.template segment<NV>(idx_v());
 data.v().noalias() = data.S.angularSubspace() * data.joint_v;

#define q_dot data.joint_v
 data.c()(0) = -c1 * q_dot(0) * q_dot(1);
 data.c()(1) =
 -s1 * s2 * q_dot(0) * q_dot(1) + c1 * c2 * q_dot(0) * q_dot(2) - s2 * q_dot(1) * q_dot(2);
 data.c()(2) =
 -s1 * c2 * q_dot(0) * q_dot(1) - c1 * s2 * q_dot(0) * q_dot(2) - c2 * q_dot(1) * q_dot(2);
#undef q_dot
 }

 template<typename VectorLike, typename Matrix6Like>
 void calc_aba(
 JointDataDerived & data,
 const Eigen::MatrixBase<VectorLike> & armature,
 const Eigen::MatrixBase<Matrix6Like> & I,
 const bool update_I) const
 {
 data.U.noalias() = I.template middleCols<3>(Motion::ANGULAR) * data.S.angularSubspace();
 data.StU.noalias() =
 data.S.angularSubspace().transpose() * data.U.template middleRows<3>(Motion::ANGULAR);
 data.StU.diagonal() += armature;

 internal::PerformStYSInversion<Scalar>::run(data.StU, data.Dinv);

 data.UDinv.noalias() = data.U * data.Dinv;

 if (update_I)
 PINOCCHIO_EIGEN_CONST_CAST(Matrix6Like, I).noalias() -= data.UDinv * data.U.transpose();
 }

 static std::string classname()
 {
 return std::string("JointModelSphericalZYX");
 }
 std::string shortname() const
 {
 return classname();
 }

 template<typename NewScalar>
 JointModelSphericalZYXTpl<NewScalar, Options> cast() const
 {
 typedef JointModelSphericalZYXTpl<NewScalar, Options> ReturnType;
 ReturnType res;
 res.setIndexes(id(), idx_q(), idx_v(), idx_vExtended());
 return res;
 }

 }; // struct JointModelSphericalZYXTpl

} // namespace pinocchio

#include <boost/type_traits.hpp>

namespace boost
{
 template<typename Scalar, int Options>
 struct has_nothrow_constructor<::pinocchio::JointModelSphericalZYXTpl<Scalar, Options>>
 : public integral_constant<bool, true>
 {
 };

 template<typename Scalar, int Options>
 struct has_nothrow_copy<::pinocchio::JointModelSphericalZYXTpl<Scalar, Options>>
 : public integral_constant<bool, true>
 {
 };

 template<typename Scalar, int Options>
 struct has_nothrow_constructor<::pinocchio::JointDataSphericalZYXTpl<Scalar, Options>>
 : public integral_constant<bool, true>
 {
 };

 template<typename Scalar, int Options>
 struct has_nothrow_copy<::pinocchio::JointDataSphericalZYXTpl<Scalar, Options>>
 : public integral_constant<bool, true>
 {
 };
} // namespace boost

#endif // ifndef __pinocchio_multibody_joint_spherical_ZYX_hpp__