joint-prismatic-unaligned.hpp

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//
// Copyright (c) 2015-2020 CNRS INRIA
// Copyright (c) 2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
//
 
#ifndef __pinocchio_multibody_joint_prismatic_unaligned_hpp__
#define __pinocchio_multibody_joint_prismatic_unaligned_hpp__
 
#include "pinocchio/macros.hpp"
#include "pinocchio/multibody/joint/joint-base.hpp"
#include "pinocchio/multibody/joint/joint-translation.hpp"
#include "pinocchio/multibody/joint-motion-subspace.hpp"
#include "pinocchio/spatial/inertia.hpp"
#include "pinocchio/math/matrix.hpp"
 
namespace pinocchio
{
 
  template<typename Scalar, int Options = context::Options>
  struct MotionPrismaticUnalignedTpl;
  typedef MotionPrismaticUnalignedTpl<context::Scalar> MotionPrismaticUnaligned;
 
  template<typename Scalar, int Options>
  struct SE3GroupAction<MotionPrismaticUnalignedTpl<Scalar, Options>>
  {
    typedef MotionTpl<Scalar, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, typename MotionDerived>
  struct MotionAlgebraAction<MotionPrismaticUnalignedTpl<Scalar, Options>, MotionDerived>
  {
    typedef MotionTpl<Scalar, Options> ReturnType;
  };
 
  template<typename _Scalar, int _Options>
  struct traits<MotionPrismaticUnalignedTpl<_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 MotionPrismaticUnalignedTpl
 
  template<typename _Scalar, int _Options>
  struct MotionPrismaticUnalignedTpl : MotionBase<MotionPrismaticUnalignedTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    MOTION_TYPEDEF_TPL(MotionPrismaticUnalignedTpl);
 
    MotionPrismaticUnalignedTpl()
    {
    }
 
    template<typename Vector3Like, typename S2>
    MotionPrismaticUnalignedTpl(const Eigen::MatrixBase<Vector3Like> & axis, const S2 & v)
    : m_axis(axis)
    , m_v(v)
    {
      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3Like, 3);
    }
 
    inline PlainReturnType plain() const
    {
      return PlainReturnType(m_axis * m_v, PlainReturnType::Vector3::Zero());
    }
 
    template<typename OtherScalar>
    MotionPrismaticUnalignedTpl __mult__(const OtherScalar & alpha) const
    {
      return MotionPrismaticUnalignedTpl(m_axis, alpha * m_v);
    }
 
    template<typename Derived>
    void addTo(MotionDense<Derived> & other) const
    {
      other.linear() += m_axis * m_v;
    }
 
    template<typename Derived>
    void setTo(MotionDense<Derived> & other) const
    {
      other.linear().noalias() = m_axis * 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.linear().noalias() = m_v * (m.rotation() * m_axis); // TODO: check efficiency
      v.angular().setZero();
    }
 
    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() * m_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
      mout.linear().noalias() = v.angular().cross(m_axis);
      mout.linear() *= m_v;
 
      // Angular
      mout.angular().setZero();
    }
 
    template<typename M1>
    MotionPlain motionAction(const MotionDense<M1> & v) const
    {
      MotionPlain res;
      motionAction(v, res);
      return res;
    }
 
    bool isEqual_impl(const MotionPrismaticUnalignedTpl & other) const
    {
      return internal::comparison_eq(m_axis, other.m_axis)
             && internal::comparison_eq(m_v, other.m_v);
    }
 
    const Scalar & linearRate() const
    {
      return m_v;
    }
    Scalar & linearRate()
    {
      return m_v;
    }
 
    const Vector3 & axis() const
    {
      return m_axis;
    }
    Vector3 & axis()
    {
      return m_axis;
    }
 
  protected:
    Vector3 m_axis;
    Scalar m_v;
  }; // struct MotionPrismaticUnalignedTpl
 
  template<typename Scalar, int Options, typename MotionDerived>
  inline typename MotionDerived::MotionPlain operator+(
    const MotionPrismaticUnalignedTpl<Scalar, Options> & m1, const MotionDense<MotionDerived> & m2)
  {
    typedef typename MotionDerived::MotionPlain ReturnType;
    return ReturnType(m1.linearRate() * m1.axis() + m2.linear(), m2.angular());
  }
 
  template<typename MotionDerived, typename S2, int O2>
  inline typename MotionDerived::MotionPlain
  operator^(const MotionDense<MotionDerived> & m1, const MotionPrismaticUnalignedTpl<S2, O2> & m2)
  {
    return m2.motionAction(m1);
  }
 
  template<typename Scalar, int Options>
  struct JointMotionSubspacePrismaticUnalignedTpl;
 
  template<typename _Scalar, int _Options>
  struct traits<JointMotionSubspacePrismaticUnalignedTpl<_Scalar, _Options>>
  {
    typedef _Scalar Scalar;
    enum
    {
      Options = _Options
    };
    enum
    {
      LINEAR = 0,
      ANGULAR = 3
    };
 
    typedef MotionPrismaticUnalignedTpl<Scalar, Options> 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 Eigen::Matrix<Scalar, 3, 1, Options> Vector3;
 
    typedef DenseBase MatrixReturnType;
    typedef const DenseBase ConstMatrixReturnType;
 
    typedef typename ReducedSquaredMatrix::IdentityReturnType StDiagonalMatrixSOperationReturnType;
  }; // traits JointMotionSubspacePrismaticUnalignedTpl
 
  template<typename Scalar, int Options>
  struct SE3GroupAction<JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options>>
  {
    typedef Eigen::Matrix<Scalar, 6, 1, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, typename MotionDerived>
  struct MotionAlgebraAction<
    JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options>,
    MotionDerived>
  {
    typedef Eigen::Matrix<Scalar, 6, 1, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, typename ForceDerived>
  struct ConstraintForceOp<JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options>, ForceDerived>
  {
    typedef
      typename traits<JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options>>::Vector3 Vector3;
    typedef Eigen::Matrix<
      typename PINOCCHIO_EIGEN_DOT_PRODUCT_RETURN_TYPE(
        Vector3, typename ForceDense<ForceDerived>::ConstAngularType),
      1,
      1,
      Options>
      ReturnType;
  };
 
  template<typename Scalar, int Options, typename ForceSet>
  struct ConstraintForceSetOp<JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options>, ForceSet>
  {
    typedef
      typename traits<JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options>>::Vector3 Vector3;
    typedef typename MatrixMatrixProduct<
      Eigen::Transpose<const Vector3>,
      typename Eigen::MatrixBase<const ForceSet>::template NRowsBlockXpr<3>::Type>::type ReturnType;
  };
 
  template<typename _Scalar, int _Options>
  struct JointMotionSubspacePrismaticUnalignedTpl
  : JointMotionSubspaceBase<JointMotionSubspacePrismaticUnalignedTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(JointMotionSubspacePrismaticUnalignedTpl)
 
    enum
    {
      NV = 1
    };
 
    typedef typename traits<JointMotionSubspacePrismaticUnalignedTpl>::Vector3 Vector3;
 
    JointMotionSubspacePrismaticUnalignedTpl()
    {
    }
 
    template<typename Vector3Like>
    JointMotionSubspacePrismaticUnalignedTpl(const Eigen::MatrixBase<Vector3Like> & axis)
    : m_axis(axis)
    {
      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3Like, 3);
    }
 
    template<typename Vector1Like>
    JointMotion __mult__(const Eigen::MatrixBase<Vector1Like> & v) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector1Like, 1);
      return JointMotion(m_axis, v[0]);
    }
 
    template<typename S1, int O1>
    typename SE3GroupAction<JointMotionSubspacePrismaticUnalignedTpl>::ReturnType
    se3Action(const SE3Tpl<S1, O1> & m) const
    {
      typename SE3GroupAction<JointMotionSubspacePrismaticUnalignedTpl>::ReturnType res;
      MotionRef<DenseBase> v(res);
      v.linear().noalias() = m.rotation() * m_axis;
      v.angular().setZero();
      return res;
    }
 
    template<typename S1, int O1>
    typename SE3GroupAction<JointMotionSubspacePrismaticUnalignedTpl>::ReturnType
    se3ActionInverse(const SE3Tpl<S1, O1> & m) const
    {
      typename SE3GroupAction<JointMotionSubspacePrismaticUnalignedTpl>::ReturnType res;
      MotionRef<DenseBase> v(res);
      v.linear().noalias() = m.rotation().transpose() * m_axis;
      v.angular().setZero();
      return res;
    }
 
    int nv_impl() const
    {
      return NV;
    }
 
    struct TransposeConst
    : JointMotionSubspaceTransposeBase<JointMotionSubspacePrismaticUnalignedTpl>
    {
      const JointMotionSubspacePrismaticUnalignedTpl & ref;
      TransposeConst(const JointMotionSubspacePrismaticUnalignedTpl & ref)
      : ref(ref)
      {
      }
 
      template<typename ForceDerived>
      typename ConstraintForceOp<JointMotionSubspacePrismaticUnalignedTpl, ForceDerived>::ReturnType
      operator*(const ForceDense<ForceDerived> & f) const
      {
        typedef typename ConstraintForceOp<
          JointMotionSubspacePrismaticUnalignedTpl, ForceDerived>::ReturnType ReturnType;
        ReturnType res;
        res[0] = ref.axis().dot(f.linear());
        return res;
      }
 
      /* [CRBA]  MatrixBase operator* (Constraint::Transpose S, ForceSet::Block) */
      template<typename ForceSet>
      typename ConstraintForceSetOp<JointMotionSubspacePrismaticUnalignedTpl, ForceSet>::ReturnType
      operator*(const Eigen::MatrixBase<ForceSet> & F)
      {
        EIGEN_STATIC_ASSERT(
          ForceSet::RowsAtCompileTime == 6, THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE)
        /* Return ax.T * F[1:3,:] */
        return ref.axis().transpose() * F.template middleRows<3>(LINEAR);
      }
    };
 
    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;
      S.template segment<3>(LINEAR) = m_axis;
      S.template segment<3>(ANGULAR).setZero();
      return S;
    }
 
    template<typename MotionDerived>
    DenseBase motionAction(const MotionDense<MotionDerived> & v) const
    {
      DenseBase res;
      res.template segment<3>(LINEAR).noalias() = v.angular().cross(m_axis);
      res.template segment<3>(ANGULAR).setZero();
 
      return res;
    }
 
    const Vector3 & axis() const
    {
      return m_axis;
    }
    Vector3 & axis()
    {
      return m_axis;
    }
 
    bool isEqual(const JointMotionSubspacePrismaticUnalignedTpl & other) const
    {
      return internal::comparison_eq(m_axis, other.m_axis);
    }
 
  protected:
    Vector3 m_axis;
 
  }; // struct JointMotionSubspacePrismaticUnalignedTpl
 
  template<typename S1, int O1, typename S2, int O2>
  struct MultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspacePrismaticUnalignedTpl<S2, O2>>
  {
    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>, JointMotionSubspacePrismaticUnalignedTpl<S2, O2>>
    {
      typedef InertiaTpl<S1, O1> Inertia;
      typedef JointMotionSubspacePrismaticUnalignedTpl<S2, O2> Constraint;
      typedef typename MultiplicationOp<Inertia, Constraint>::ReturnType ReturnType;
 
      static inline ReturnType run(const Inertia & Y, const Constraint & cpu)
      {
        ReturnType res;
        /* YS = [ m -mcx ; mcx I-mcxcx ] [ 0 ; w ] = [ mcxw ; Iw -mcxcxw ] */
        const S1 & m = Y.mass();
        const typename Inertia::Vector3 & c = Y.lever();
 
        res.template segment<3>(Constraint::LINEAR).noalias() = m * cpu.axis();
        res.template segment<3>(Constraint::ANGULAR).noalias() =
          c.cross(res.template segment<3>(Constraint::LINEAR));
 
        return res;
      }
    };
  } // namespace impl
 
  template<typename M6Like, typename Scalar, int Options>
  struct MultiplicationOp<
    Eigen::MatrixBase<M6Like>,
    JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options>>
  {
    typedef typename SizeDepType<3>::ColsReturn<M6Like>::ConstType M6LikeCols;
    typedef typename Eigen::internal::remove_const<M6LikeCols>::type M6LikeColsNonConst;
 
    typedef JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options> Constraint;
    typedef typename Constraint::Vector3 Vector3;
    typedef const typename MatrixMatrixProduct<M6LikeColsNonConst, Vector3>::type ReturnType;
  };
 
  /* [ABA] operator* (Inertia Y,Constraint S) */
  namespace impl
  {
    template<typename M6Like, typename Scalar, int Options>
    struct LhsMultiplicationOp<
      Eigen::MatrixBase<M6Like>,
      JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options>>
    {
      typedef JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options> Constraint;
      typedef
        typename MultiplicationOp<Eigen::MatrixBase<M6Like>, Constraint>::ReturnType ReturnType;
      static inline ReturnType run(const Eigen::MatrixBase<M6Like> & Y, const Constraint & cru)
      {
        EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(M6Like, 6, 6);
        return Y.derived().template middleCols<3>(Constraint::LINEAR) * cru.axis();
      }
    };
  } // namespace impl
 
  template<typename Scalar, int Options>
  struct JointPrismaticUnalignedTpl;
 
  template<typename _Scalar, int _Options>
  struct traits<JointPrismaticUnalignedTpl<_Scalar, _Options>>
  {
    enum
    {
      NQ = 1,
      NV = 1
    };
    typedef _Scalar Scalar;
    enum
    {
      Options = _Options
    };
    typedef JointDataPrismaticUnalignedTpl<Scalar, Options> JointDataDerived;
    typedef JointModelPrismaticUnalignedTpl<Scalar, Options> JointModelDerived;
    typedef JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options> Constraint_t;
    typedef TransformTranslationTpl<Scalar, Options> Transformation_t;
    typedef MotionPrismaticUnalignedTpl<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<JointDataPrismaticUnalignedTpl<_Scalar, _Options>>
  {
    typedef JointPrismaticUnalignedTpl<_Scalar, _Options> JointDerived;
    typedef _Scalar Scalar;
  };
 
  template<typename _Scalar, int _Options>
  struct JointDataPrismaticUnalignedTpl
  : public JointDataBase<JointDataPrismaticUnalignedTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    typedef JointPrismaticUnalignedTpl<_Scalar, _Options> JointDerived;
    PINOCCHIO_JOINT_DATA_TYPEDEF_TEMPLATE(JointDerived);
    PINOCCHIO_JOINT_DATA_BASE_DEFAULT_ACCESSOR
 
    ConfigVector_t joint_q;
    TangentVector_t joint_v;
 
    Transformation_t M;
    Constraint_t S;
    Motion_t v;
    Bias_t c;
 
    // [ABA] specific data
    U_t U;
    D_t Dinv;
    UD_t UDinv;
    D_t StU;
 
    JointDataPrismaticUnalignedTpl()
    : joint_q(ConfigVector_t::Zero())
    , joint_v(TangentVector_t::Zero())
    , M(Transformation_t::Vector3::Zero())
    , S(Constraint_t::Vector3::Zero())
    , v(Constraint_t::Vector3::Zero(), (Scalar)0)
    , U(U_t::Zero())
    , Dinv(D_t::Zero())
    , UDinv(UD_t::Zero())
    , StU(D_t::Zero())
    {
    }
 
    template<typename Vector3Like>
    JointDataPrismaticUnalignedTpl(const Eigen::MatrixBase<Vector3Like> & axis)
    : joint_q(ConfigVector_t::Zero())
    , joint_v(TangentVector_t::Zero())
    , M(Transformation_t::Vector3::Zero())
    , S(axis)
    , v(axis, (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("JointDataPrismaticUnaligned");
    }
    std::string shortname() const
    {
      return classname();
    }
 
  }; // struct JointDataPrismaticUnalignedTpl
 
  template<typename _Scalar, int _Options>
  struct traits<JointModelPrismaticUnalignedTpl<_Scalar, _Options>>
  {
    typedef JointPrismaticUnalignedTpl<_Scalar, _Options> JointDerived;
    typedef _Scalar Scalar;
  };
 
  PINOCCHIO_JOINT_CAST_TYPE_SPECIALIZATION(JointModelPrismaticUnalignedTpl);
  template<typename _Scalar, int _Options>
  struct JointModelPrismaticUnalignedTpl
  : public JointModelBase<JointModelPrismaticUnalignedTpl<_Scalar, _Options>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    typedef JointPrismaticUnalignedTpl<_Scalar, _Options> JointDerived;
    PINOCCHIO_JOINT_TYPEDEF_TEMPLATE(JointDerived);
 
    typedef JointModelBase<JointModelPrismaticUnalignedTpl> Base;
    using Base::id;
    using Base::idx_q;
    using Base::idx_v;
    using Base::setIndexes;
 
    typedef Eigen::Matrix<Scalar, 3, 1, _Options> Vector3;
 
    JointModelPrismaticUnalignedTpl()
    : axis(Vector3::UnitX())
    {
    }
    JointModelPrismaticUnalignedTpl(const Scalar & x, const Scalar & y, const Scalar & z)
    : axis(x, y, z)
    {
      normalize(axis);
      assert(isUnitary(axis) && "Translation axis is not unitary");
    }
 
    template<typename Vector3Like>
    JointModelPrismaticUnalignedTpl(const Eigen::MatrixBase<Vector3Like> & axis)
    : axis(axis)
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Vector3Like);
      assert(isUnitary(axis) && "Translation axis is not unitary");
    }
 
    JointDataDerived createData() const
    {
      return JointDataDerived(axis);
    }
 
    const std::vector<bool> hasConfigurationLimit() const
    {
      return {true};
    }
 
    const std::vector<bool> hasConfigurationLimitInTangent() const
    {
      return {true};
    }
 
    using Base::isEqual;
    bool isEqual(const JointModelPrismaticUnalignedTpl & other) const
    {
      return Base::isEqual(other) && internal::comparison_eq(axis, other.axis);
    }
 
    template<typename ConfigVector>
    void calc(JointDataDerived & data, const typename Eigen::MatrixBase<ConfigVector> & qs) const
    {
      data.joint_q[0] = qs[idx_q()];
      data.M.translation().noalias() = axis * 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.noalias() = I.template block<6, 3>(0, Inertia::LINEAR) * axis;
      data.Dinv[0] =
        Scalar(1) / (axis.dot(data.U.template segment<3>(Inertia::LINEAR)) + armature[0]);
      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("JointModelPrismaticUnaligned");
    }
    std::string shortname() const
    {
      return classname();
    }
 
    template<typename NewScalar>
    JointModelPrismaticUnalignedTpl<NewScalar, Options> cast() const
    {
      typedef JointModelPrismaticUnalignedTpl<NewScalar, Options> ReturnType;
      ReturnType res(axis.template cast<NewScalar>());
      res.setIndexes(id(), idx_q(), idx_v());
      return res;
    }
 
    // data
 
    Vector3 axis;
  }; // struct JointModelPrismaticUnalignedTpl
 
} // namespace pinocchio
 
#include <boost/type_traits.hpp>
 
namespace boost
{
  template<typename Scalar, int Options>
  struct has_nothrow_constructor<::pinocchio::JointModelPrismaticUnalignedTpl<Scalar, Options>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options>
  struct has_nothrow_copy<::pinocchio::JointModelPrismaticUnalignedTpl<Scalar, Options>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options>
  struct has_nothrow_constructor<::pinocchio::JointDataPrismaticUnalignedTpl<Scalar, Options>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options>
  struct has_nothrow_copy<::pinocchio::JointDataPrismaticUnalignedTpl<Scalar, Options>>
  : public integral_constant<bool, true>
  {
  };
} // namespace boost
 
#endif // ifndef __pinocchio_multibody_joint_prismatic_unaligned_hpp__