joint-spherical.hpp

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

#ifndef __pinocchio_multibody_joint_spherical_hpp__
#define __pinocchio_multibody_joint_spherical_hpp__

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

namespace pinocchio
{

 template<typename Scalar, int Options = context::Options>
 struct MotionSphericalTpl;
 typedef MotionSphericalTpl<context::Scalar> MotionSpherical;

 template<typename Scalar, int Options>
 struct SE3GroupAction<MotionSphericalTpl<Scalar, Options>>
 {
 typedef MotionTpl<Scalar, Options> ReturnType;
 };

 template<typename Scalar, int Options, typename MotionDerived>
 struct MotionAlgebraAction<MotionSphericalTpl<Scalar, Options>, MotionDerived>
 {
 typedef MotionTpl<Scalar, Options> ReturnType;
 };

 template<typename _Scalar, int _Options>
 struct traits<MotionSphericalTpl<_Scalar, _Options>>
 {
 typedef _Scalar Scalar;
 enum
 {
 Options = _Options
 };
 typedef Eigen::Matrix<Scalar, 3, 1, Options> Vector3;
 typedef Eigen::Matrix<Scalar, 6, 1, Options> Vector6;
 typedef Eigen::Matrix<Scalar, 4, 4, Options> Matrix4;
 typedef Eigen::Matrix<Scalar, 6, 6, Options> Matrix6;
 typedef typename PINOCCHIO_EIGEN_REF_CONST_TYPE(Vector6) ToVectorConstReturnType;
 typedef typename PINOCCHIO_EIGEN_REF_TYPE(Vector6) ToVectorReturnType;
 typedef Vector3 AngularType;
 typedef Vector3 LinearType;
 typedef const Vector3 ConstAngularType;
 typedef const Vector3 ConstLinearType;
 typedef Matrix6 ActionMatrixType;
 typedef Matrix4 HomogeneousMatrixType;
 typedef MotionTpl<Scalar, Options> MotionPlain;
 typedef MotionPlain PlainReturnType;
 enum
 {
 LINEAR = 0,
 ANGULAR = 3
 };
 }; // traits MotionSphericalTpl

 template<typename _Scalar, int _Options>
 struct MotionSphericalTpl : MotionBase<MotionSphericalTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW

 MOTION_TYPEDEF_TPL(MotionSphericalTpl);

 MotionSphericalTpl()
 {
 }

 template<typename Vector3Like>
 MotionSphericalTpl(const Eigen::MatrixBase<Vector3Like> & w)
 : m_w(w)
 {
 }

 Vector3 & operator()()
 {
 return m_w;
 }
 const Vector3 & operator()() const
 {
 return m_w;
 }

 inline PlainReturnType plain() const
 {
 return PlainReturnType(PlainReturnType::Vector3::Zero(), m_w);
 }

 template<typename MotionDerived>
 void addTo(MotionDense<MotionDerived> & other) const
 {
 other.angular() += m_w;
 }

 template<typename Derived>
 void setTo(MotionDense<Derived> & other) const
 {
 other.linear().setZero();
 other.angular() = m_w;
 }

 MotionSphericalTpl __plus__(const MotionSphericalTpl & other) const
 {
 return MotionSphericalTpl(m_w + other.m_w);
 }

 bool isEqual_impl(const MotionSphericalTpl & other) const
 {
 return internal::comparison_eq(m_w, other.m_w);
 }

 template<typename MotionDerived>
 bool isEqual_impl(const MotionDense<MotionDerived> & other) const
 {
 return internal::comparison_eq(other.angular(), m_w) && other.linear().isZero(0);
 }

 template<typename S2, int O2, typename D2>
 void se3Action_impl(const SE3Tpl<S2, O2> & m, MotionDense<D2> & v) const
 {
 // Angular
 v.angular().noalias() = m.rotation() * m_w;

 // Linear
 v.linear().noalias() = m.translation().cross(v.angular());
 }

 template<typename S2, int O2>
 MotionPlain se3Action_impl(const SE3Tpl<S2, O2> & m) const
 {
 MotionPlain res;
 se3Action_impl(m, res);
 return res;
 }

 template<typename S2, int O2, typename D2>
 void se3ActionInverse_impl(const SE3Tpl<S2, O2> & m, MotionDense<D2> & v) const
 {
 // Linear
 // TODO: use v.angular() as temporary variable
 Vector3 v3_tmp;
 v3_tmp.noalias() = m_w.cross(m.translation());
 v.linear().noalias() = m.rotation().transpose() * v3_tmp;

 // Angular
 v.angular().noalias() = m.rotation().transpose() * m_w;
 }

 template<typename S2, int O2>
 MotionPlain se3ActionInverse_impl(const SE3Tpl<S2, O2> & m) const
 {
 MotionPlain res;
 se3ActionInverse_impl(m, res);
 return res;
 }

 template<typename M1, typename M2>
 void motionAction(const MotionDense<M1> & v, MotionDense<M2> & mout) const
 {
 // Linear
 mout.linear().noalias() = v.linear().cross(m_w);

 // Angular
 mout.angular().noalias() = v.angular().cross(m_w);
 }

 template<typename M1>
 MotionPlain motionAction(const MotionDense<M1> & v) const
 {
 MotionPlain res;
 motionAction(v, res);
 return res;
 }

 const Vector3 & angular() const
 {
 return m_w;
 }
 Vector3 & angular()
 {
 return m_w;
 }

 protected:
 Vector3 m_w;
 }; // struct MotionSphericalTpl

 template<typename S1, int O1, typename MotionDerived>
 inline typename MotionDerived::MotionPlain
 operator+(const MotionSphericalTpl<S1, O1> & m1, const MotionDense<MotionDerived> & m2)
 {
 return typename MotionDerived::MotionPlain(m2.linear(), m2.angular() + m1.angular());
 }

 template<typename Scalar, int Options>
 struct JointMotionSubspaceSphericalTpl;

 template<typename _Scalar, int _Options>
 struct traits<JointMotionSubspaceSphericalTpl<_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 typename ReducedSquaredMatrix::IdentityReturnType StDiagonalMatrixSOperationReturnType;
 }; // struct traits struct JointMotionSubspaceSphericalTpl

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

 PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(JointMotionSubspaceSphericalTpl)

 JointMotionSubspaceSphericalTpl()
 {
 }

 enum
 {
 NV = 3
 };

 int nv_impl() const
 {
 return NV;
 }

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

 struct TransposeConst : JointMotionSubspaceTransposeBase<JointMotionSubspaceSphericalTpl>
 {
 template<typename Derived>
 typename ForceDense<Derived>::ConstAngularType operator*(const ForceDense<Derived> & phi)
 {
 return phi.angular();
 }

 /* [CRBA] MatrixBase operator* (Constraint::Transpose S, ForceSet::Block) */
 template<typename MatrixDerived>
 const typename SizeDepType<3>::RowsReturn<MatrixDerived>::ConstType
 operator*(const Eigen::MatrixBase<MatrixDerived> & F) const
 {
 assert(F.rows() == 6);
 return F.derived().template middleRows<3>(Inertia::ANGULAR);
 }
 };

 TransposeConst transpose() const
 {
 return TransposeConst();
 }

 DenseBase matrix_impl() const
 {
 DenseBase S;
 S.template block<3, 3>(LINEAR, 0).setZero();
 S.template block<3, 3>(ANGULAR, 0).setIdentity();
 return S;
 }

 template<typename S1, int O1>
 Eigen::Matrix<S1, 6, 3, O1> se3Action(const SE3Tpl<S1, O1> & m) const
 {
 Eigen::Matrix<S1, 6, 3, O1> X_subspace;
 cross(m.translation(), m.rotation(), X_subspace.template middleRows<3>(LINEAR));
 X_subspace.template middleRows<3>(ANGULAR) = m.rotation();

 return X_subspace;
 }

 template<typename S1, int O1>
 Eigen::Matrix<S1, 6, 3, O1> se3ActionInverse(const SE3Tpl<S1, O1> & m) const
 {
 Eigen::Matrix<S1, 6, 3, O1> X_subspace;
 XAxis::cross(m.translation(), X_subspace.template middleRows<3>(ANGULAR).col(0));
 YAxis::cross(m.translation(), X_subspace.template middleRows<3>(ANGULAR).col(1));
 ZAxis::cross(m.translation(), X_subspace.template middleRows<3>(ANGULAR).col(2));

 X_subspace.template middleRows<3>(LINEAR).noalias() =
 m.rotation().transpose() * X_subspace.template middleRows<3>(ANGULAR);
 X_subspace.template middleRows<3>(ANGULAR) = m.rotation().transpose();

 return X_subspace;
 }

 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;
 skew(v, res.template middleRows<3>(LINEAR));
 skew(w, res.template middleRows<3>(ANGULAR));

 return res;
 }

 bool isEqual(const JointMotionSubspaceSphericalTpl &) const
 {
 return true;
 }

 }; // struct JointMotionSubspaceSphericalTpl

 template<typename MotionDerived, typename S2, int O2>
 inline typename MotionDerived::MotionPlain
 operator^(const MotionDense<MotionDerived> & m1, const MotionSphericalTpl<S2, O2> & m2)
 {
 return m2.motionAction(m1);
 }

 /* [CRBA] ForceSet operator* (Inertia Y,Constraint S) */
 template<typename S1, int O1, typename S2, int O2>
 inline Eigen::Matrix<S2, 6, 3, O2>
 operator*(const InertiaTpl<S1, O1> & Y, const JointMotionSubspaceSphericalTpl<S2, O2> &)
 {
 typedef InertiaTpl<S1, O1> Inertia;
 typedef typename Inertia::Symmetric3 Symmetric3;
 Eigen::Matrix<S2, 6, 3, O2> M;
 // M.block <3,3> (Inertia::LINEAR, 0) = - Y.mass () * skew(Y.lever ());
 M.template block<3, 3>(Inertia::LINEAR, 0) = alphaSkew(-Y.mass(), Y.lever());
 M.template block<3, 3>(Inertia::ANGULAR, 0) =
 (Y.inertia() - typename Symmetric3::AlphaSkewSquare(Y.mass(), Y.lever())).matrix();
 return M;
 }

 /* [ABA] Y*S operator*/
 template<typename M6Like, typename S2, int O2>
 inline typename SizeDepType<3>::ColsReturn<M6Like>::ConstType
 operator*(const Eigen::MatrixBase<M6Like> & Y, const JointMotionSubspaceSphericalTpl<S2, O2> &)
 {
 typedef JointMotionSubspaceSphericalTpl<S2, O2> Constraint;
 return Y.derived().template middleCols<3>(Constraint::ANGULAR);
 }

 template<typename S1, int O1>
 struct SE3GroupAction<JointMotionSubspaceSphericalTpl<S1, O1>>
 {
 typedef Eigen::Matrix<S1, 6, 3, O1> ReturnType;
 };

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

 template<typename Scalar, int Options>
 struct JointSphericalTpl;

 template<typename _Scalar, int _Options>
 struct traits<JointSphericalTpl<_Scalar, _Options>>
 {
 enum
 {
 NQ = 4,
 NV = 3,
 NVExtended = 3
 };
 typedef _Scalar Scalar;
 enum
 {
 Options = _Options
 };
 typedef JointDataSphericalTpl<Scalar, Options> JointDataDerived;
 typedef JointModelSphericalTpl<Scalar, Options> JointModelDerived;
 typedef JointMotionSubspaceSphericalTpl<Scalar, Options> Constraint_t;
 typedef SE3Tpl<Scalar, Options> Transformation_t;
 typedef MotionSphericalTpl<Scalar, Options> Motion_t;
 typedef MotionZeroTpl<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<JointDataSphericalTpl<_Scalar, _Options>>
 {
 typedef JointSphericalTpl<_Scalar, _Options> JointDerived;
 typedef _Scalar Scalar;
 };

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

 template<typename _Scalar, int _Options>
 struct JointDataSphericalTpl : public JointDataBase<JointDataSphericalTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW

 typedef JointSphericalTpl<_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;

 JointDataSphericalTpl()
 : joint_q(Scalar(0), Scalar(0), Scalar(0), Scalar(1))
 , joint_v(TangentVector_t::Zero())
 , M(Transformation_t::Identity())
 , v(Motion_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("JointDataSpherical");
 }
 std::string shortname() const
 {
 return classname();
 }

 }; // struct JointDataSphericalTpl

 PINOCCHIO_JOINT_CAST_TYPE_SPECIALIZATION(JointModelSphericalTpl);
 template<typename _Scalar, int _Options>
 struct JointModelSphericalTpl : public JointModelBase<JointModelSphericalTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW

 typedef JointSphericalTpl<_Scalar, _Options> JointDerived;
 PINOCCHIO_JOINT_TYPEDEF_TEMPLATE(JointDerived);

 typedef JointModelBase<JointModelSphericalTpl> 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 {false, false, false, false};
 }

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

 template<typename ConfigVectorLike>
 inline void forwardKinematics(
 Transformation_t & M, const Eigen::MatrixBase<ConfigVectorLike> & q_joint) const
 {
 typedef typename ConfigVectorLike::Scalar Scalar;
 EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ConfigVector_t, ConfigVectorLike);
 typedef
 typename Eigen::Quaternion<Scalar, PINOCCHIO_EIGEN_PLAIN_TYPE(ConfigVectorLike)::Options>
 Quaternion;
 typedef Eigen::Map<const Quaternion> ConstQuaternionMap;

 ConstQuaternionMap quat(q_joint.derived().data());
 // assert(math::fabs(quat.coeffs().squaredNorm()-1.) <= sqrt(Eigen::NumTraits<typename
 // V::Scalar>::epsilon())); TODO: check validity of the rhs precision
 assert(math::fabs(static_cast<Scalar>(quat.coeffs().squaredNorm() - 1)) <= 1e-4);

 M.rotation(quat.matrix());
 M.translation().setZero();
 }

 template<typename QuaternionDerived>
 void calc(
 JointDataDerived & data, const typename Eigen::QuaternionBase<QuaternionDerived> & quat) const
 {
 data.joint_q = quat.coeffs();
 data.M.rotation(quat.matrix());
 }

 template<typename ConfigVector>
 PINOCCHIO_DONT_INLINE void
 calc(JointDataDerived & data, const typename Eigen::PlainObjectBase<ConfigVector> & qs) const
 {
 typedef typename Eigen::Quaternion<typename ConfigVector::Scalar, ConfigVector::Options>
 Quaternion;
 typedef Eigen::Map<const Quaternion> ConstQuaternionMap;

 ConstQuaternionMap quat(qs.template segment<NQ>(idx_q()).data());
 calc(data, quat);
 }

 template<typename ConfigVector>
 PINOCCHIO_DONT_INLINE void
 calc(JointDataDerived & data, const typename Eigen::MatrixBase<ConfigVector> & qs) const
 {
 typedef typename Eigen::Quaternion<Scalar, Options> Quaternion;

 const Quaternion quat(qs.template segment<NQ>(idx_q()));
 calc(data, quat);
 }

 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.angular() = data.joint_v;
 }

 template<typename ConfigVector, typename TangentVector>
 void calc(
 JointDataDerived & data,
 const typename Eigen::MatrixBase<ConfigVector> & qs,
 const typename Eigen::MatrixBase<TangentVector> & vs) const
 {
 calc(data, qs.derived());
 data.joint_v = vs.template segment<NV>(idx_v());
 data.v.angular() = data.joint_v;
 }

 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 = I.template block<6, 3>(0, Inertia::ANGULAR);
 data.StU = data.U.template middleRows<3>(Inertia::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("JointModelSpherical");
 }
 std::string shortname() const
 {
 return classname();
 }

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

 }; // struct JointModelSphericalTpl

} // namespace pinocchio

#include <boost/type_traits.hpp>

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

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

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

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

#endif // ifndef __pinocchio_multibody_joint_spherical_hpp__