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,
 NVExtended = 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;

 typedef boost::mpl::true_ is_mimicable_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::idx_vExtended;
 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(), idx_vExtended());
 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;

 template<typename Scalar, int Options, int axis>
 struct ConfigVectorAffineTransform<JointPrismaticTpl<Scalar, Options, axis>>
 {
 typedef LinearAffineTransform Type;
 };
} // 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__