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
    };
    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;
 
    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::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>
    EIGEN_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>
    EIGEN_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());
      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__