joint-prismatic.hpp

//
// Copyright (c) 2015-2020 CNRS INRIA
// Copyright (c) 2015-2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
//
 
#ifndef __pinocchio_multibody_joint_prismatic_hpp__
#define __pinocchio_multibody_joint_prismatic_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/spatial-axis.hpp"
#include "pinocchio/utils/axis-label.hpp"
 
namespace pinocchio
{
 
  template<typename Scalar, int Options, int _axis>
  struct MotionPrismaticTpl;
 
  template<typename Scalar, int Options, int axis>
  struct SE3GroupAction<MotionPrismaticTpl<Scalar, Options, axis>>
  {
    typedef MotionTpl<Scalar, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, int axis, typename MotionDerived>
  struct MotionAlgebraAction<MotionPrismaticTpl<Scalar, Options, axis>, MotionDerived>
  {
    typedef MotionTpl<Scalar, Options> ReturnType;
  };
 
  template<typename _Scalar, int _Options, int _axis>
  struct traits<MotionPrismaticTpl<_Scalar, _Options, _axis>>
  {
    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
    };
  }; // struct traits MotionPrismaticTpl
 
  template<typename _Scalar, int _Options, int _axis>
  struct MotionPrismaticTpl : MotionBase<MotionPrismaticTpl<_Scalar, _Options, _axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    MOTION_TYPEDEF_TPL(MotionPrismaticTpl);
 
    enum
    {
      axis = _axis
    };
 
    typedef SpatialAxis<_axis + LINEAR> Axis;
    typedef typename Axis::CartesianAxis3 CartesianAxis3;
 
    MotionPrismaticTpl()
    {
    }
    MotionPrismaticTpl(const Scalar & v)
    : m_v(v)
    {
    }
 
    inline PlainReturnType plain() const
    {
      return Axis() * m_v;
    }
 
    template<typename OtherScalar>
    MotionPrismaticTpl __mult__(const OtherScalar & alpha) const
    {
      return MotionPrismaticTpl(alpha * m_v);
    }
 
    template<typename Derived>
    void addTo(MotionDense<Derived> & other) const
    {
      typedef typename MotionDense<Derived>::Scalar OtherScalar;
      other.linear()[_axis] += (OtherScalar)m_v;
    }
 
    template<typename MotionDerived>
    void setTo(MotionDense<MotionDerived> & other) const
    {
      for (Eigen::DenseIndex k = 0; k < 3; ++k)
      {
        other.linear()[k] = k == axis ? m_v : Scalar(0);
      }
      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_v * (m.rotation().col(axis));
    }
 
    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_v * (m.rotation().transpose().col(axis));
 
      // 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
      CartesianAxis3::alphaCross(-m_v, v.angular(), mout.linear());
 
      // Angular
      mout.angular().setZero();
    }
 
    template<typename M1>
    MotionPlain motionAction(const MotionDense<M1> & v) const
    {
      MotionPlain res;
      motionAction(v, res);
      return res;
    }
 
    Scalar & linearRate()
    {
      return m_v;
    }
    const Scalar & linearRate() const
    {
      return m_v;
    }
 
    bool isEqual_impl(const MotionPrismaticTpl & other) const
    {
      return internal::comparison_eq(m_v, other.m_v);
    }
 
  protected:
    Scalar m_v;
  }; // struct MotionPrismaticTpl
 
  template<typename Scalar, int Options, int axis, typename MotionDerived>
  typename MotionDerived::MotionPlain operator+(
    const MotionPrismaticTpl<Scalar, Options, axis> & m1, const MotionDense<MotionDerived> & m2)
  {
    typename MotionDerived::MotionPlain res(m2);
    res += m1;
    return res;
  }
 
  template<typename MotionDerived, typename S2, int O2, int axis>
  EIGEN_STRONG_INLINE typename MotionDerived::MotionPlain
  operator^(const MotionDense<MotionDerived> & m1, const MotionPrismaticTpl<S2, O2, axis> & m2)
  {
    return m2.motionAction(m1);
  }
 
  template<typename Scalar, int Options, int axis>
  struct TransformPrismaticTpl;
 
  template<typename _Scalar, int _Options, int _axis>
  struct traits<TransformPrismaticTpl<_Scalar, _Options, _axis>>
  {
    enum
    {
      axis = _axis,
      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 const Vector3 LinearRef;
    typedef const Vector3 ConstLinearRef;
    typedef typename traits<PlainType>::ActionMatrixType ActionMatrixType;
    typedef typename traits<PlainType>::HomogeneousMatrixType HomogeneousMatrixType;
  }; // traits TransformPrismaticTpl
 
  template<typename Scalar, int Options, int axis>
  struct SE3GroupAction<TransformPrismaticTpl<Scalar, Options, axis>>
  {
    typedef typename traits<TransformPrismaticTpl<Scalar, Options, axis>>::PlainType ReturnType;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct TransformPrismaticTpl : SE3Base<TransformPrismaticTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    PINOCCHIO_SE3_TYPEDEF_TPL(TransformPrismaticTpl);
 
    typedef SpatialAxis<axis + LINEAR> Axis;
    typedef typename Axis::CartesianAxis3 CartesianAxis3;
 
    TransformPrismaticTpl()
    {
    }
    TransformPrismaticTpl(const Scalar & displacement)
    : m_displacement(displacement)
    {
    }
 
    PlainType plain() const
    {
      PlainType res(PlainType::Identity());
      res.rotation().setIdentity();
      res.translation()[axis] = m_displacement;
 
      return res;
    }
 
    operator PlainType() const
    {
      return plain();
    }
 
    template<typename S2, int O2>
    typename SE3GroupAction<TransformPrismaticTpl>::ReturnType
    se3action(const SE3Tpl<S2, O2> & m) const
    {
      typedef typename SE3GroupAction<TransformPrismaticTpl>::ReturnType ReturnType;
      ReturnType res(m);
      res.translation()[axis] += m_displacement;
 
      return res;
    }
 
    const Scalar & displacement() const
    {
      return m_displacement;
    }
    Scalar & displacement()
    {
      return m_displacement;
    }
 
    ConstLinearRef translation() const
    {
      return CartesianAxis3() * displacement();
    };
    AngularType rotation() const
    {
      return AngularType(3, 3);
    }
 
    bool isEqual(const TransformPrismaticTpl & other) const
    {
      return internal::comparison_eq(m_displacement, other.m_displacement);
    }
 
  protected:
    Scalar m_displacement;
  };
 
  template<typename Scalar, int Options, int axis>
  struct JointMotionSubspacePrismaticTpl;
 
  template<typename _Scalar, int _Options, int axis>
  struct traits<JointMotionSubspacePrismaticTpl<_Scalar, _Options, axis>>
  {
    typedef _Scalar Scalar;
    enum
    {
      Options = _Options
    };
    enum
    {
      LINEAR = 0,
      ANGULAR = 3
    };
    typedef MotionPrismaticTpl<Scalar, Options, axis> JointMotion;
    typedef Eigen::Matrix<Scalar, 1, 1, Options> JointForce;
    typedef Eigen::Matrix<Scalar, 6, 1, Options> DenseBase;
    typedef Eigen::Matrix<Scalar, 1, 1, Options> ReducedSquaredMatrix;
 
    typedef DenseBase MatrixReturnType;
    typedef const DenseBase ConstMatrixReturnType;
 
    typedef typename ReducedSquaredMatrix::IdentityReturnType StDiagonalMatrixSOperationReturnType;
  }; // traits ConstraintRevolute
 
  template<typename Scalar, int Options, int axis>
  struct SE3GroupAction<JointMotionSubspacePrismaticTpl<Scalar, Options, axis>>
  {
    typedef Eigen::Matrix<Scalar, 6, 1, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, int axis, typename MotionDerived>
  struct MotionAlgebraAction<JointMotionSubspacePrismaticTpl<Scalar, Options, axis>, MotionDerived>
  {
    typedef Eigen::Matrix<Scalar, 6, 1, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, int axis, typename ForceDerived>
  struct ConstraintForceOp<JointMotionSubspacePrismaticTpl<Scalar, Options, axis>, ForceDerived>
  {
    typedef typename ForceDense<
      ForceDerived>::ConstLinearType::template ConstFixedSegmentReturnType<1>::Type ReturnType;
  };
 
  template<typename Scalar, int Options, int axis, typename ForceSet>
  struct ConstraintForceSetOp<JointMotionSubspacePrismaticTpl<Scalar, Options, axis>, ForceSet>
  {
    typedef typename Eigen::MatrixBase<ForceSet>::ConstRowXpr ReturnType;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct JointMotionSubspacePrismaticTpl
  : JointMotionSubspaceBase<JointMotionSubspacePrismaticTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(JointMotionSubspacePrismaticTpl)
    enum
    {
      NV = 1
    };
 
    typedef SpatialAxis<LINEAR + axis> Axis;
 
    JointMotionSubspacePrismaticTpl() {};
 
    template<typename Vector1Like>
    JointMotion __mult__(const Eigen::MatrixBase<Vector1Like> & v) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector1Like, 1);
      assert(v.size() == 1);
      return JointMotion(v[0]);
    }
 
    template<typename S2, int O2>
    typename SE3GroupAction<JointMotionSubspacePrismaticTpl>::ReturnType
    se3Action(const SE3Tpl<S2, O2> & m) const
    {
      typename SE3GroupAction<JointMotionSubspacePrismaticTpl>::ReturnType res;
      MotionRef<DenseBase> v(res);
      v.linear() = m.rotation().col(axis);
      v.angular().setZero();
      return res;
    }
 
    template<typename S2, int O2>
    typename SE3GroupAction<JointMotionSubspacePrismaticTpl>::ReturnType
    se3ActionInverse(const SE3Tpl<S2, O2> & m) const
    {
      typename SE3GroupAction<JointMotionSubspacePrismaticTpl>::ReturnType res;
      MotionRef<DenseBase> v(res);
      v.linear() = m.rotation().transpose().col(axis);
      v.angular().setZero();
      return res;
    }
 
    int nv_impl() const
    {
      return NV;
    }
 
    struct TransposeConst : JointMotionSubspaceTransposeBase<JointMotionSubspacePrismaticTpl>
    {
      const JointMotionSubspacePrismaticTpl & ref;
      TransposeConst(const JointMotionSubspacePrismaticTpl & ref)
      : ref(ref)
      {
      }
 
      template<typename ForceDerived>
      typename ConstraintForceOp<JointMotionSubspacePrismaticTpl, ForceDerived>::ReturnType
      operator*(const ForceDense<ForceDerived> & f) const
      {
        return f.linear().template segment<1>(axis);
      }
 
      /* [CRBA]  MatrixBase operator* (Constraint::Transpose S, ForceSet::Block) */
      template<typename Derived>
      typename ConstraintForceSetOp<JointMotionSubspacePrismaticTpl, Derived>::ReturnType
      operator*(const Eigen::MatrixBase<Derived> & F)
      {
        assert(F.rows() == 6);
        return F.row(LINEAR + axis);
      }
 
    }; // struct TransposeConst
    TransposeConst transpose() const
    {
      return TransposeConst(*this);
    }
 
    /* CRBA joint operators
     *   - ForceSet::Block = ForceSet
     *   - ForceSet operator* (Inertia Y,Constraint S)
     *   - MatrixBase operator* (Constraint::Transpose S, ForceSet::Block)
     *   - SE3::act(ForceSet::Block)
     */
    DenseBase matrix_impl() const
    {
      DenseBase S;
      MotionRef<DenseBase> v(S);
      v << Axis();
      return S;
    }
 
    template<typename MotionDerived>
    typename MotionAlgebraAction<JointMotionSubspacePrismaticTpl, MotionDerived>::ReturnType
    motionAction(const MotionDense<MotionDerived> & m) const
    {
      typename MotionAlgebraAction<JointMotionSubspacePrismaticTpl, MotionDerived>::ReturnType res;
      MotionRef<DenseBase> v(res);
      v = m.cross(Axis());
      return res;
    }
 
    bool isEqual(const JointMotionSubspacePrismaticTpl &) const
    {
      return true;
    }
 
  }; // struct JointMotionSubspacePrismaticTpl
 
  template<typename S1, int O1, typename S2, int O2, int axis>
  struct MultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspacePrismaticTpl<S2, O2, axis>>
  {
    typedef Eigen::Matrix<S2, 6, 1, O2> ReturnType;
  };
 
  /* [CRBA] ForceSet operator* (Inertia Y,Constraint S) */
  namespace impl
  {
    template<typename S1, int O1, typename S2, int O2>
    struct LhsMultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspacePrismaticTpl<S2, O2, 0>>
    {
      typedef InertiaTpl<S1, O1> Inertia;
      typedef JointMotionSubspacePrismaticTpl<S2, O2, 0> Constraint;
      typedef typename MultiplicationOp<Inertia, Constraint>::ReturnType ReturnType;
      static inline ReturnType run(const Inertia & Y, const Constraint & /*constraint*/)
      {
        ReturnType res;
 
        /* Y(:,0) = ( 1,0, 0, 0 , z , -y ) */
        const S1 &m = Y.mass(), &y = Y.lever()[1], &z = Y.lever()[2];
        res << m, S1(0), S1(0), S1(0), m * z, -m * y;
 
        return res;
      }
    };
 
    template<typename S1, int O1, typename S2, int O2>
    struct LhsMultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspacePrismaticTpl<S2, O2, 1>>
    {
      typedef InertiaTpl<S1, O1> Inertia;
      typedef JointMotionSubspacePrismaticTpl<S2, O2, 1> Constraint;
      typedef typename MultiplicationOp<Inertia, Constraint>::ReturnType ReturnType;
      static inline ReturnType run(const Inertia & Y, const Constraint & /*constraint*/)
      {
        ReturnType res;
 
        /* Y(:,1) = ( 0,1, 0, -z , 0 , x) */
        const S1 &m = Y.mass(), &x = Y.lever()[0], &z = Y.lever()[2];
 
        res << S1(0), m, S1(0), -m * z, S1(0), m * x;
 
        return res;
      }
    };
 
    template<typename S1, int O1, typename S2, int O2>
    struct LhsMultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspacePrismaticTpl<S2, O2, 2>>
    {
      typedef InertiaTpl<S1, O1> Inertia;
      typedef JointMotionSubspacePrismaticTpl<S2, O2, 2> Constraint;
      typedef typename MultiplicationOp<Inertia, Constraint>::ReturnType ReturnType;
      static inline ReturnType run(const Inertia & Y, const Constraint & /*constraint*/)
      {
        ReturnType res;
 
        /* Y(:,2) = ( 0,0, 1, y , -x , 0) */
        const S1 &m = Y.mass(), &x = Y.lever()[0], &y = Y.lever()[1];
 
        res << S1(0), S1(0), m, m * y, -m * x, S1(0);
 
        return res;
      }
    };
  } // namespace impl
 
  template<typename M6Like, typename S2, int O2, int axis>
  struct MultiplicationOp<Eigen::MatrixBase<M6Like>, JointMotionSubspacePrismaticTpl<S2, O2, axis>>
  {
    typedef typename M6Like::ConstColXpr ReturnType;
  };
 
  /* [ABA] operator* (Inertia Y,Constraint S) */
  namespace impl
  {
    template<typename M6Like, typename Scalar, int Options, int axis>
    struct LhsMultiplicationOp<
      Eigen::MatrixBase<M6Like>,
      JointMotionSubspacePrismaticTpl<Scalar, Options, axis>>
    {
      typedef JointMotionSubspacePrismaticTpl<Scalar, Options, axis> Constraint;
      typedef
        typename MultiplicationOp<Eigen::MatrixBase<M6Like>, Constraint>::ReturnType ReturnType;
      static inline ReturnType
      run(const Eigen::MatrixBase<M6Like> & Y, const Constraint & /*constraint*/)
      {
        EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(M6Like, 6, 6);
        return Y.derived().col(Inertia::LINEAR + axis);
      }
    };
  } // namespace impl
 
  template<typename _Scalar, int _Options, int _axis>
  struct JointPrismaticTpl
  {
    typedef _Scalar Scalar;
 
    enum
    {
      Options = _Options,
      axis = _axis
    };
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct traits<JointPrismaticTpl<_Scalar, _Options, axis>>
  {
    enum
    {
      NQ = 1,
      NV = 1
    };
    typedef _Scalar Scalar;
    enum
    {
      Options = _Options
    };
    typedef JointDataPrismaticTpl<Scalar, Options, axis> JointDataDerived;
    typedef JointModelPrismaticTpl<Scalar, Options, axis> JointModelDerived;
    typedef JointMotionSubspacePrismaticTpl<Scalar, Options, axis> Constraint_t;
    typedef TransformPrismaticTpl<Scalar, Options, axis> Transformation_t;
    typedef MotionPrismaticTpl<Scalar, Options, axis> 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, int axis>
  struct traits<JointDataPrismaticTpl<_Scalar, _Options, axis>>
  {
    typedef JointPrismaticTpl<_Scalar, _Options, axis> JointDerived;
    typedef _Scalar Scalar;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct traits<JointModelPrismaticTpl<_Scalar, _Options, axis>>
  {
    typedef JointPrismaticTpl<_Scalar, _Options, axis> JointDerived;
    typedef _Scalar Scalar;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct JointDataPrismaticTpl
  : public JointDataBase<JointDataPrismaticTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    typedef JointPrismaticTpl<_Scalar, _Options, axis> 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;
 
    JointDataPrismaticTpl()
    : joint_q(ConfigVector_t::Zero())
    , joint_v(TangentVector_t::Zero())
    , M((Scalar)0)
    , v((Scalar)0)
    , U(U_t::Zero())
    , Dinv(D_t::Zero())
    , UDinv(UD_t::Zero())
    , StU(D_t::Zero())
    {
    }
 
    static std::string classname()
    {
      return std::string("JointDataP") + axisLabel<axis>();
    }
    std::string shortname() const
    {
      return classname();
    }
 
  }; // struct JointDataPrismaticTpl
 
  template<typename NewScalar, typename Scalar, int Options, int axis>
  struct CastType<NewScalar, JointModelPrismaticTpl<Scalar, Options, axis>>
  {
    typedef JointModelPrismaticTpl<NewScalar, Options, axis> type;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct JointModelPrismaticTpl
  : public JointModelBase<JointModelPrismaticTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    typedef JointPrismaticTpl<_Scalar, _Options, axis> JointDerived;
    PINOCCHIO_JOINT_TYPEDEF_TEMPLATE(JointDerived);
 
    typedef JointModelBase<JointModelPrismaticTpl> Base;
    using Base::id;
    using Base::idx_q;
    using Base::idx_v;
    using Base::setIndexes;
 
    typedef Eigen::Matrix<Scalar, 3, 1, _Options> Vector3;
 
    JointDataDerived createData() const
    {
      return JointDataDerived();
    }
 
    const std::vector<bool> hasConfigurationLimit() const
    {
      return {true};
    }
 
    const std::vector<bool> hasConfigurationLimitInTangent() const
    {
      return {true};
    }
 
    template<typename ConfigVector>
    void calc(JointDataDerived & data, const typename Eigen::MatrixBase<ConfigVector> & qs) const
    {
      data.joint_q[0] = qs[idx_q()];
      data.M.displacement() = data.joint_q[0];
    }
 
    template<typename TangentVector>
    void
    calc(JointDataDerived & data, const Blank, const typename Eigen::MatrixBase<TangentVector> & vs)
      const
    {
      data.joint_v[0] = vs[idx_v()];
      data.v.linearRate() = data.joint_v[0];
    }
 
    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[0] = vs[idx_v()];
      data.v.linearRate() = data.joint_v[0];
    }
 
    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.col(Inertia::LINEAR + axis);
      data.Dinv[0] = Scalar(1) / (I(Inertia::LINEAR + axis, Inertia::LINEAR + axis) + armature[0]);
      data.UDinv.noalias() = data.U * data.Dinv[0];
 
      if (update_I)
        PINOCCHIO_EIGEN_CONST_CAST(Matrix6Like, I).noalias() -= data.UDinv * data.U.transpose();
    }
 
    static std::string classname()
    {
      return std::string("JointModelP") + axisLabel<axis>();
    }
    std::string shortname() const
    {
      return classname();
    }
 
    Vector3 getMotionAxis() const
    {
      switch (axis)
      {
      case 0:
        return Vector3::UnitX();
      case 1:
        return Vector3::UnitY();
      case 2:
        return Vector3::UnitZ();
      default:
        assert(false && "must never happen");
        break;
      }
    }
 
    template<typename NewScalar>
    JointModelPrismaticTpl<NewScalar, Options, axis> cast() const
    {
      typedef JointModelPrismaticTpl<NewScalar, Options, axis> ReturnType;
      ReturnType res;
      res.setIndexes(id(), idx_q(), idx_v());
      return res;
    }
 
  }; // struct JointModelPrismaticTpl
 
  typedef JointPrismaticTpl<context::Scalar, context::Options, 0> JointPX;
  typedef JointDataPrismaticTpl<context::Scalar, context::Options, 0> JointDataPX;
  typedef JointModelPrismaticTpl<context::Scalar, context::Options, 0> JointModelPX;
 
  typedef JointPrismaticTpl<context::Scalar, context::Options, 1> JointPY;
  typedef JointDataPrismaticTpl<context::Scalar, context::Options, 1> JointDataPY;
  typedef JointModelPrismaticTpl<context::Scalar, context::Options, 1> JointModelPY;
 
  typedef JointPrismaticTpl<context::Scalar, context::Options, 2> JointPZ;
  typedef JointDataPrismaticTpl<context::Scalar, context::Options, 2> JointDataPZ;
  typedef JointModelPrismaticTpl<context::Scalar, context::Options, 2> JointModelPZ;
 
} // namespace pinocchio
 
#include <boost/type_traits.hpp>
 
namespace boost
{
  template<typename Scalar, int Options, int axis>
  struct has_nothrow_constructor<::pinocchio::JointModelPrismaticTpl<Scalar, Options, axis>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options, int axis>
  struct has_nothrow_copy<::pinocchio::JointModelPrismaticTpl<Scalar, Options, axis>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options, int axis>
  struct has_nothrow_constructor<::pinocchio::JointDataPrismaticTpl<Scalar, Options, axis>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options, int axis>
  struct has_nothrow_copy<::pinocchio::JointDataPrismaticTpl<Scalar, Options, axis>>
  : public integral_constant<bool, true>
  {
  };
} // namespace boost
 
#endif // ifndef __pinocchio_multibody_joint_prismatic_hpp__