joint-translation.hpp

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//
// Copyright (c) 2015-2020 CNRS INRIA
// Copyright (c) 2015-2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
//
 
#ifndef __pinocchio_multibody_joint_translation_hpp__
#define __pinocchio_multibody_joint_translation_hpp__
 
#include "pinocchio/macros.hpp"
#include "pinocchio/multibody/joint/joint-base.hpp"
#include "pinocchio/multibody/joint-motion-subspace.hpp"
#include "pinocchio/spatial/inertia.hpp"
#include "pinocchio/spatial/skew.hpp"
 
namespace pinocchio
{
 
  template<typename Scalar, int Options = context::Options>
  struct MotionTranslationTpl;
  typedef MotionTranslationTpl<context::Scalar> MotionTranslation;
 
  template<typename Scalar, int Options>
  struct SE3GroupAction<MotionTranslationTpl<Scalar, Options>>
  {
    typedef MotionTpl<Scalar, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, typename MotionDerived>
  struct MotionAlgebraAction<MotionTranslationTpl<Scalar, Options>, MotionDerived>
  {
    typedef MotionTpl<Scalar, Options> ReturnType;
  };
 
  template<typename _Scalar, int _Options>
  struct traits<MotionTranslationTpl<_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 MotionTranslationTpl
 
  template<typename _Scalar, int _Options>
  struct MotionTranslationTpl : MotionBase<MotionTranslationTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 
    MOTION_TYPEDEF_TPL(MotionTranslationTpl);
 
    MotionTranslationTpl()
    {
    }
 
    template<typename Vector3Like>
    MotionTranslationTpl(const Eigen::MatrixBase<Vector3Like> & v)
    : m_v(v)
    {
    }
 
    MotionTranslationTpl(const MotionTranslationTpl & other)
    : m_v(other.m_v)
    {
    }
 
    Vector3 & operator()()
    {
      return m_v;
    }
    const Vector3 & operator()() const
    {
      return m_v;
    }
 
    inline PlainReturnType plain() const
    {
      return PlainReturnType(m_v, PlainReturnType::Vector3::Zero());
    }
 
    bool isEqual_impl(const MotionTranslationTpl & other) const
    {
      return internal::comparison_eq(m_v, other.m_v);
    }
 
    MotionTranslationTpl & operator=(const MotionTranslationTpl & other)
    {
      m_v = other.m_v;
      return *this;
    }
 
    template<typename Derived>
    void addTo(MotionDense<Derived> & other) const
    {
      other.linear() += m_v;
    }
 
    template<typename Derived>
    void setTo(MotionDense<Derived> & other) const
    {
      other.linear() = m_v;
      other.angular().setZero();
    }
 
    template<typename S2, int O2, typename D2>
    void se3Action_impl(const SE3Tpl<S2, O2> & m, MotionDense<D2> & v) const
    {
      v.angular().setZero();
      v.linear().noalias() = m.rotation() * m_v; // TODO: check efficiency
    }
 
    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
      v.linear().noalias() = m.rotation().transpose() * m_v;
 
      // Angular
      v.angular().setZero();
    }
 
    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.angular().cross(m_v);
 
      // Angular
      mout.angular().setZero();
    }
 
    template<typename M1>
    MotionPlain motionAction(const MotionDense<M1> & v) const
    {
      MotionPlain res;
      motionAction(v, res);
      return res;
    }
 
    const Vector3 & linear() const
    {
      return m_v;
    }
    Vector3 & linear()
    {
      return m_v;
    }
 
  protected:
    Vector3 m_v;
 
  }; // struct MotionTranslationTpl
 
  template<typename S1, int O1, typename MotionDerived>
  inline typename MotionDerived::MotionPlain
  operator+(const MotionTranslationTpl<S1, O1> & m1, const MotionDense<MotionDerived> & m2)
  {
    return typename MotionDerived::MotionPlain(m2.linear() + m1.linear(), m2.angular());
  }
 
  template<typename Scalar, int Options>
  struct TransformTranslationTpl;
 
  template<typename _Scalar, int _Options>
  struct traits<TransformTranslationTpl<_Scalar, _Options>>
  {
    enum
    {
      Options = _Options,
      LINEAR = 0,
      ANGULAR = 3
    };
    typedef _Scalar Scalar;
    typedef SE3Tpl<Scalar, Options> PlainType;
    typedef Eigen::Matrix<Scalar, 3, 1, Options> Vector3;
    typedef Eigen::Matrix<Scalar, 3, 3, Options> Matrix3;
    typedef typename Matrix3::IdentityReturnType AngularType;
    typedef AngularType AngularRef;
    typedef AngularType ConstAngularRef;
    typedef Vector3 LinearType;
    typedef LinearType & LinearRef;
    typedef const LinearType & ConstLinearRef;
    typedef typename traits<PlainType>::ActionMatrixType ActionMatrixType;
    typedef typename traits<PlainType>::HomogeneousMatrixType HomogeneousMatrixType;
  }; // traits TransformTranslationTpl
 
  template<typename Scalar, int Options>
  struct SE3GroupAction<TransformTranslationTpl<Scalar, Options>>
  {
    typedef typename traits<TransformTranslationTpl<Scalar, Options>>::PlainType ReturnType;
  };
 
  template<typename _Scalar, int _Options>
  struct TransformTranslationTpl : SE3Base<TransformTranslationTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    PINOCCHIO_SE3_TYPEDEF_TPL(TransformTranslationTpl);
    typedef typename traits<TransformTranslationTpl>::Vector3 Vector3;
 
    TransformTranslationTpl()
    {
    }
 
    template<typename Vector3Like>
    TransformTranslationTpl(const Eigen::MatrixBase<Vector3Like> & translation)
    : m_translation(translation)
    {
    }
 
    PlainType plain() const
    {
      PlainType res(PlainType::Identity());
      res.rotation().setIdentity();
      res.translation() = translation();
 
      return res;
    }
 
    operator PlainType() const
    {
      return plain();
    }
 
    template<typename S2, int O2>
    typename SE3GroupAction<TransformTranslationTpl>::ReturnType
    se3action(const SE3Tpl<S2, O2> & m) const
    {
      typedef typename SE3GroupAction<TransformTranslationTpl>::ReturnType ReturnType;
      ReturnType res(m);
      res.translation() += translation();
 
      return res;
    }
 
    ConstLinearRef translation() const
    {
      return m_translation;
    }
    LinearRef translation()
    {
      return m_translation;
    }
 
    AngularType rotation() const
    {
      return AngularType(3, 3);
    }
 
    bool isEqual(const TransformTranslationTpl & other) const
    {
      return internal::comparison_eq(m_translation, other.m_translation);
    }
 
  protected:
    LinearType m_translation;
  };
 
  template<typename Scalar, int Options>
  struct JointMotionSubspaceTranslationTpl;
 
  template<typename _Scalar, int _Options>
  struct traits<JointMotionSubspaceTranslationTpl<_Scalar, _Options>>
  {
    typedef _Scalar Scalar;
 
    enum
    {
      Options = _Options
    };
    enum
    {
      LINEAR = 0,
      ANGULAR = 3
    };
 
    typedef MotionTranslationTpl<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;
  }; // traits JointMotionSubspaceTranslationTpl
 
  template<typename _Scalar, int _Options>
  struct JointMotionSubspaceTranslationTpl
  : JointMotionSubspaceBase<JointMotionSubspaceTranslationTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 
    PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(JointMotionSubspaceTranslationTpl)
 
    enum
    {
      NV = 3
    };
 
    JointMotionSubspaceTranslationTpl()
    {
    }
 
    //    template<typename S1, int O1>
    //    Motion operator*(const MotionTranslationTpl<S1,O1> & vj) const
    //    { return Motion(vj(), Motion::Vector3::Zero()); }
 
    template<typename Vector3Like>
    JointMotion __mult__(const Eigen::MatrixBase<Vector3Like> & v) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3Like, 3);
      return JointMotion(v);
    }
 
    int nv_impl() const
    {
      return NV;
    }
 
    struct ConstraintTranspose : JointMotionSubspaceTransposeBase<JointMotionSubspaceTranslationTpl>
    {
      const JointMotionSubspaceTranslationTpl & ref;
      ConstraintTranspose(const JointMotionSubspaceTranslationTpl & ref)
      : ref(ref)
      {
      }
 
      template<typename Derived>
      typename ForceDense<Derived>::ConstLinearType operator*(const ForceDense<Derived> & phi)
      {
        return phi.linear();
      }
 
      /* [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>(LINEAR);
      }
 
    }; // struct ConstraintTranspose
 
    ConstraintTranspose transpose() const
    {
      return ConstraintTranspose(*this);
    }
 
    DenseBase matrix_impl() const
    {
      DenseBase S;
      S.template middleRows<3>(LINEAR).setIdentity();
      S.template middleRows<3>(ANGULAR).setZero();
      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> M;
      M.template middleRows<3>(LINEAR) = m.rotation();
      M.template middleRows<3>(ANGULAR).setZero();
 
      return M;
    }
 
    template<typename S1, int O1>
    Eigen::Matrix<S1, 6, 3, O1> se3ActionInverse(const SE3Tpl<S1, O1> & m) const
    {
      Eigen::Matrix<S1, 6, 3, O1> M;
      M.template middleRows<3>(LINEAR) = m.rotation().transpose();
      M.template middleRows<3>(ANGULAR).setZero();
 
      return M;
    }
 
    template<typename MotionDerived>
    DenseBase motionAction(const MotionDense<MotionDerived> & m) const
    {
      const typename MotionDerived::ConstAngularType w = m.angular();
 
      DenseBase res;
      skew(w, res.template middleRows<3>(LINEAR));
      res.template middleRows<3>(ANGULAR).setZero();
 
      return res;
    }
 
    bool isEqual(const JointMotionSubspaceTranslationTpl &) const
    {
      return true;
    }
 
  }; // struct JointMotionSubspaceTranslationTpl
 
  template<typename MotionDerived, typename S2, int O2>
  inline typename MotionDerived::MotionPlain
  operator^(const MotionDense<MotionDerived> & m1, const MotionTranslationTpl<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 JointMotionSubspaceTranslationTpl<S2, O2> &)
  {
    typedef JointMotionSubspaceTranslationTpl<S2, O2> Constraint;
    Eigen::Matrix<S2, 6, 3, O2> M;
    alphaSkew(Y.mass(), Y.lever(), M.template middleRows<3>(Constraint::ANGULAR));
    M.template middleRows<3>(Constraint::LINEAR).setZero();
    M.template middleRows<3>(Constraint::LINEAR).diagonal().fill(Y.mass());
 
    return M;
  }
 
  /* [ABA] Y*S operator*/
  template<typename M6Like, typename S2, int O2>
  inline const typename SizeDepType<3>::ColsReturn<M6Like>::ConstType
  operator*(const Eigen::MatrixBase<M6Like> & Y, const JointMotionSubspaceTranslationTpl<S2, O2> &)
  {
    typedef JointMotionSubspaceTranslationTpl<S2, O2> Constraint;
    return Y.derived().template middleCols<3>(Constraint::LINEAR);
  }
 
  template<typename S1, int O1>
  struct SE3GroupAction<JointMotionSubspaceTranslationTpl<S1, O1>>
  {
    typedef Eigen::Matrix<S1, 6, 3, O1> ReturnType;
  };
 
  template<typename S1, int O1, typename MotionDerived>
  struct MotionAlgebraAction<JointMotionSubspaceTranslationTpl<S1, O1>, MotionDerived>
  {
    typedef Eigen::Matrix<S1, 6, 3, O1> ReturnType;
  };
 
  template<typename Scalar, int Options>
  struct JointTranslationTpl;
 
  template<typename _Scalar, int _Options>
  struct traits<JointTranslationTpl<_Scalar, _Options>>
  {
    enum
    {
      NQ = 3,
      NV = 3,
      NVExtended = 3
    };
    typedef _Scalar Scalar;
    enum
    {
      Options = _Options
    };
    typedef JointDataTranslationTpl<Scalar, Options> JointDataDerived;
    typedef JointModelTranslationTpl<Scalar, Options> JointModelDerived;
    typedef JointMotionSubspaceTranslationTpl<Scalar, Options> Constraint_t;
    typedef TransformTranslationTpl<Scalar, Options> Transformation_t;
    typedef MotionTranslationTpl<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
  }; // traits JointTranslationTpl
 
  template<typename _Scalar, int _Options>
  struct traits<JointDataTranslationTpl<_Scalar, _Options>>
  {
    typedef JointTranslationTpl<_Scalar, _Options> JointDerived;
    typedef _Scalar Scalar;
  };
 
  template<typename _Scalar, int _Options>
  struct traits<JointModelTranslationTpl<_Scalar, _Options>>
  {
    typedef JointTranslationTpl<_Scalar, _Options> JointDerived;
    typedef _Scalar Scalar;
  };
 
  template<typename _Scalar, int _Options>
  struct JointDataTranslationTpl : public JointDataBase<JointDataTranslationTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 
    typedef JointTranslationTpl<_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;
 
    JointDataTranslationTpl()
    : joint_q(ConfigVector_t::Zero())
    , joint_v(TangentVector_t::Zero())
    , M(Transformation_t::Vector3::Zero())
    , 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("JointDataTranslation");
    }
    std::string shortname() const
    {
      return classname();
    }
  }; // struct JointDataTranslationTpl
 
  PINOCCHIO_JOINT_CAST_TYPE_SPECIALIZATION(JointModelTranslationTpl);
  template<typename _Scalar, int _Options>
  struct JointModelTranslationTpl
  : public JointModelBase<JointModelTranslationTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 
    typedef JointTranslationTpl<_Scalar, _Options> JointDerived;
    PINOCCHIO_JOINT_TYPEDEF_TEMPLATE(JointDerived);
 
    typedef JointModelBase<JointModelTranslationTpl> 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 = this->jointConfigSelector(qs);
      data.M.translation() = data.joint_q;
    }
 
    template<typename TangentVector>
    void
    calc(JointDataDerived & data, const Blank, const typename Eigen::MatrixBase<TangentVector> & vs)
      const
    {
      data.joint_v = this->jointVelocitySelector(vs);
      data.v.linear() = 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 = this->jointVelocitySelector(vs);
      data.v.linear() = 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 middleCols<3>(Inertia::LINEAR);
 
      data.StU = data.U.template middleRows<3>(Inertia::LINEAR);
      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("JointModelTranslation");
    }
    std::string shortname() const
    {
      return classname();
    }
 
    template<typename NewScalar>
    JointModelTranslationTpl<NewScalar, Options> cast() const
    {
      typedef JointModelTranslationTpl<NewScalar, Options> ReturnType;
      ReturnType res;
      res.setIndexes(id(), idx_q(), idx_v(), idx_vExtended());
      return res;
    }
 
  }; // struct JointModelTranslationTpl
 
  template<typename Scalar, int Options>
  struct ConfigVectorAffineTransform<JointTranslationTpl<Scalar, Options>>
  {
    typedef LinearAffineTransform Type;
  };
} // namespace pinocchio
 
#include <boost/type_traits.hpp>
 
namespace boost
{
  template<typename Scalar, int Options>
  struct has_nothrow_constructor<::pinocchio::JointModelTranslationTpl<Scalar, Options>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options>
  struct has_nothrow_copy<::pinocchio::JointModelTranslationTpl<Scalar, Options>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options>
  struct has_nothrow_constructor<::pinocchio::JointDataTranslationTpl<Scalar, Options>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options>
  struct has_nothrow_copy<::pinocchio::JointDataTranslationTpl<Scalar, Options>>
  : public integral_constant<bool, true>
  {
  };
} // namespace boost
 
#endif // ifndef __pinocchio_multibody_joint_translation_hpp__