joint-revolute.hpp

//
// Copyright (c) 2015-2020 CNRS INRIA
// Copyright (c) 2015-2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
//
 
#ifndef __pinocchio_multibody_joint_revolute_hpp__
#define __pinocchio_multibody_joint_revolute_hpp__
 
#include "pinocchio/math/sincos.hpp"
#include "pinocchio/spatial/inertia.hpp"
#include "pinocchio/multibody/joint-motion-subspace.hpp"
#include "pinocchio/multibody/joint/joint-base.hpp"
#include "pinocchio/spatial/spatial-axis.hpp"
#include "pinocchio/utils/axis-label.hpp"
 
namespace pinocchio
{
 
  template<typename Scalar, int Options, int axis>
  struct MotionRevoluteTpl;
 
  template<typename Scalar, int Options, int axis>
  struct SE3GroupAction<MotionRevoluteTpl<Scalar, Options, axis>>
  {
    typedef MotionTpl<Scalar, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, int axis, typename MotionDerived>
  struct MotionAlgebraAction<MotionRevoluteTpl<Scalar, Options, axis>, MotionDerived>
  {
    typedef MotionTpl<Scalar, Options> ReturnType;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct traits<MotionRevoluteTpl<_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
    };
  }; // traits MotionRevoluteTpl
 
  template<typename Scalar, int Options, int axis>
  struct TransformRevoluteTpl;
 
  template<typename _Scalar, int _Options, int _axis>
  struct traits<TransformRevoluteTpl<_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 Matrix3 AngularType;
    typedef Matrix3 AngularRef;
    typedef Matrix3 ConstAngularRef;
    typedef typename Vector3::ConstantReturnType LinearType;
    typedef typename Vector3::ConstantReturnType LinearRef;
    typedef const typename Vector3::ConstantReturnType ConstLinearRef;
    typedef typename traits<PlainType>::ActionMatrixType ActionMatrixType;
    typedef typename traits<PlainType>::HomogeneousMatrixType HomogeneousMatrixType;
  }; // traits TransformRevoluteTpl
 
  template<typename Scalar, int Options, int axis>
  struct SE3GroupAction<TransformRevoluteTpl<Scalar, Options, axis>>
  {
    typedef typename traits<TransformRevoluteTpl<Scalar, Options, axis>>::PlainType ReturnType;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct TransformRevoluteTpl : SE3Base<TransformRevoluteTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    PINOCCHIO_SE3_TYPEDEF_TPL(TransformRevoluteTpl);
 
    TransformRevoluteTpl()
    {
    }
    TransformRevoluteTpl(const Scalar & sin, const Scalar & cos)
    : m_sin(sin)
    , m_cos(cos)
    {
    }
 
    PlainType plain() const
    {
      PlainType res(PlainType::Identity());
      _setRotation(res.rotation());
      return res;
    }
 
    operator PlainType() const
    {
      return plain();
    }
 
    template<typename S2, int O2>
    typename SE3GroupAction<TransformRevoluteTpl>::ReturnType
    se3action(const SE3Tpl<S2, O2> & m) const
    {
      typedef typename SE3GroupAction<TransformRevoluteTpl>::ReturnType ReturnType;
      ReturnType res;
      switch (axis)
      {
      case 0: {
        res.rotation().col(0) = m.rotation().col(0);
        res.rotation().col(1).noalias() = m_cos * m.rotation().col(1) + m_sin * m.rotation().col(2);
        res.rotation().col(2).noalias() = res.rotation().col(0).cross(res.rotation().col(1));
        break;
      }
      case 1: {
        res.rotation().col(2).noalias() = m_cos * m.rotation().col(2) + m_sin * m.rotation().col(0);
        res.rotation().col(1) = m.rotation().col(1);
        res.rotation().col(0).noalias() = res.rotation().col(1).cross(res.rotation().col(2));
        break;
      }
      case 2: {
        res.rotation().col(0).noalias() = m_cos * m.rotation().col(0) + m_sin * m.rotation().col(1);
        res.rotation().col(1).noalias() = res.rotation().col(2).cross(res.rotation().col(0));
        res.rotation().col(2) = m.rotation().col(2);
        break;
      }
      default: {
        assert(false && "must never happened");
        break;
      }
      }
      res.translation() = m.translation();
      return res;
    }
 
    const Scalar & sin() const
    {
      return m_sin;
    }
    Scalar & sin()
    {
      return m_sin;
    }
 
    const Scalar & cos() const
    {
      return m_cos;
    }
    Scalar & cos()
    {
      return m_cos;
    }
 
    template<typename OtherScalar>
    void setValues(const OtherScalar & sin, const OtherScalar & cos)
    {
      m_sin = sin;
      m_cos = cos;
    }
 
    LinearType translation() const
    {
      return LinearType::PlainObject::Zero(3);
    }
    AngularType rotation() const
    {
      AngularType m(AngularType::Identity());
      _setRotation(m);
      return m;
    }
 
    bool isEqual(const TransformRevoluteTpl & other) const
    {
      return internal::comparison_eq(m_cos, other.m_cos)
             && internal::comparison_eq(m_sin, other.m_sin);
    }
 
  protected:
    Scalar m_sin, m_cos;
    inline void _setRotation(typename PlainType::AngularRef & rot) const
    {
      switch (axis)
      {
      case 0: {
        rot.coeffRef(1, 1) = m_cos;
        rot.coeffRef(1, 2) = -m_sin;
        rot.coeffRef(2, 1) = m_sin;
        rot.coeffRef(2, 2) = m_cos;
        break;
      }
      case 1: {
        rot.coeffRef(0, 0) = m_cos;
        rot.coeffRef(0, 2) = m_sin;
        rot.coeffRef(2, 0) = -m_sin;
        rot.coeffRef(2, 2) = m_cos;
        break;
      }
      case 2: {
        rot.coeffRef(0, 0) = m_cos;
        rot.coeffRef(0, 1) = -m_sin;
        rot.coeffRef(1, 0) = m_sin;
        rot.coeffRef(1, 1) = m_cos;
        break;
      }
      default: {
        assert(false && "must never happened");
        break;
      }
      }
    }
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct MotionRevoluteTpl : MotionBase<MotionRevoluteTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 
    MOTION_TYPEDEF_TPL(MotionRevoluteTpl);
    typedef SpatialAxis<axis + ANGULAR> Axis;
    typedef typename Axis::CartesianAxis3 CartesianAxis3;
 
    MotionRevoluteTpl()
    {
    }
 
    MotionRevoluteTpl(const Scalar & w)
    : m_w(w)
    {
    }
 
    template<typename Vector1Like>
    MotionRevoluteTpl(const Eigen::MatrixBase<Vector1Like> & v)
    : m_w(v[0])
    {
      using namespace Eigen;
      EIGEN_STATIC_ASSERT_SIZE_1x1(Vector1Like);
    }
 
    inline PlainReturnType plain() const
    {
      return Axis() * m_w;
    }
 
    template<typename OtherScalar>
    MotionRevoluteTpl __mult__(const OtherScalar & alpha) const
    {
      return MotionRevoluteTpl(alpha * m_w);
    }
 
    template<typename MotionDerived>
    void setTo(MotionDense<MotionDerived> & m) const
    {
      m.linear().setZero();
      for (Eigen::DenseIndex k = 0; k < 3; ++k)
      {
        m.angular()[k] = k == axis ? m_w : Scalar(0);
      }
    }
 
    template<typename MotionDerived>
    inline void addTo(MotionDense<MotionDerived> & v) const
    {
      typedef typename MotionDense<MotionDerived>::Scalar OtherScalar;
      v.angular()[axis] += (OtherScalar)m_w;
    }
 
    template<typename S2, int O2, typename D2>
    inline void se3Action_impl(const SE3Tpl<S2, O2> & m, MotionDense<D2> & v) const
    {
      v.angular().noalias() = m.rotation().col(axis) * m_w;
      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
      CartesianAxis3::alphaCross(m_w, m.translation(), v.angular());
      v.linear().noalias() = m.rotation().transpose() * v.angular();
 
      // Angular
      v.angular().noalias() = m.rotation().transpose().col(axis) * 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>
    EIGEN_STRONG_INLINE void motionAction(const MotionDense<M1> & v, MotionDense<M2> & mout) const
    {
      // Linear
      CartesianAxis3::alphaCross(-m_w, v.linear(), mout.linear());
 
      // Angular
      CartesianAxis3::alphaCross(-m_w, v.angular(), mout.angular());
    }
 
    template<typename M1>
    MotionPlain motionAction(const MotionDense<M1> & v) const
    {
      MotionPlain res;
      motionAction(v, res);
      return res;
    }
 
    Scalar & angularRate()
    {
      return m_w;
    }
    const Scalar & angularRate() const
    {
      return m_w;
    }
 
    bool isEqual_impl(const MotionRevoluteTpl & other) const
    {
      return internal::comparison_eq(m_w, other.m_w);
    }
 
  protected:
    Scalar m_w;
  }; // struct MotionRevoluteTpl
 
  template<typename S1, int O1, int axis, typename MotionDerived>
  typename MotionDerived::MotionPlain
  operator+(const MotionRevoluteTpl<S1, O1, 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 MotionRevoluteTpl<S2, O2, axis> & m2)
  {
    return m2.motionAction(m1);
  }
 
  template<typename Scalar, int Options, int axis>
  struct JointMotionSubspaceRevoluteTpl;
 
  template<typename Scalar, int Options, int axis>
  struct SE3GroupAction<JointMotionSubspaceRevoluteTpl<Scalar, Options, axis>>
  {
    typedef Eigen::Matrix<Scalar, 6, 1, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, int axis, typename MotionDerived>
  struct MotionAlgebraAction<JointMotionSubspaceRevoluteTpl<Scalar, Options, axis>, MotionDerived>
  {
    typedef Eigen::Matrix<Scalar, 6, 1, Options> ReturnType;
  };
 
  template<typename Scalar, int Options, int axis, typename ForceDerived>
  struct ConstraintForceOp<JointMotionSubspaceRevoluteTpl<Scalar, Options, axis>, ForceDerived>
  {
    typedef typename ForceDense<
      ForceDerived>::ConstAngularType::template ConstFixedSegmentReturnType<1>::Type ReturnType;
  };
 
  template<typename Scalar, int Options, int axis, typename ForceSet>
  struct ConstraintForceSetOp<JointMotionSubspaceRevoluteTpl<Scalar, Options, axis>, ForceSet>
  {
    typedef typename Eigen::MatrixBase<ForceSet>::ConstRowXpr ReturnType;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct traits<JointMotionSubspaceRevoluteTpl<_Scalar, _Options, axis>>
  {
    typedef _Scalar Scalar;
    enum
    {
      Options = _Options
    };
    enum
    {
      LINEAR = 0,
      ANGULAR = 3
    };
 
    typedef MotionRevoluteTpl<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 JointMotionSubspaceRevoluteTpl
 
  template<typename _Scalar, int _Options, int axis>
  struct JointMotionSubspaceRevoluteTpl
  : JointMotionSubspaceBase<JointMotionSubspaceRevoluteTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 
    PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(JointMotionSubspaceRevoluteTpl)
    enum
    {
      NV = 1
    };
 
    typedef SpatialAxis<ANGULAR + axis> Axis;
 
    JointMotionSubspaceRevoluteTpl()
    {
    }
 
    template<typename Vector1Like>
    JointMotion __mult__(const Eigen::MatrixBase<Vector1Like> & v) const
    {
      return JointMotion(v[0]);
    }
 
    template<typename S1, int O1>
    typename SE3GroupAction<JointMotionSubspaceRevoluteTpl>::ReturnType
    se3Action(const SE3Tpl<S1, O1> & m) const
    {
      typedef typename SE3GroupAction<JointMotionSubspaceRevoluteTpl>::ReturnType ReturnType;
      ReturnType res;
      res.template segment<3>(LINEAR) = m.translation().cross(m.rotation().col(axis));
      res.template segment<3>(ANGULAR) = m.rotation().col(axis);
      return res;
    }
 
    template<typename S1, int O1>
    typename SE3GroupAction<JointMotionSubspaceRevoluteTpl>::ReturnType
    se3ActionInverse(const SE3Tpl<S1, O1> & m) const
    {
      typedef typename SE3GroupAction<JointMotionSubspaceRevoluteTpl>::ReturnType ReturnType;
      typedef typename Axis::CartesianAxis3 CartesianAxis3;
      ReturnType res;
      res.template segment<3>(LINEAR).noalias() =
        m.rotation().transpose() * CartesianAxis3::cross(m.translation());
      res.template segment<3>(ANGULAR) = m.rotation().transpose().col(axis);
      return res;
    }
 
    int nv_impl() const
    {
      return NV;
    }
 
    struct TransposeConst : JointMotionSubspaceTransposeBase<JointMotionSubspaceRevoluteTpl>
    {
      const JointMotionSubspaceRevoluteTpl & ref;
      TransposeConst(const JointMotionSubspaceRevoluteTpl & ref)
      : ref(ref)
      {
      }
 
      template<typename ForceDerived>
      typename ConstraintForceOp<JointMotionSubspaceRevoluteTpl, ForceDerived>::ReturnType
      operator*(const ForceDense<ForceDerived> & f) const
      {
        return f.angular().template segment<1>(axis);
      }
 
      template<typename Derived>
      typename ConstraintForceSetOp<JointMotionSubspaceRevoluteTpl, Derived>::ReturnType
      operator*(const Eigen::MatrixBase<Derived> & F) const
      {
        assert(F.rows() == 6);
        return F.row(ANGULAR + 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<JointMotionSubspaceRevoluteTpl, MotionDerived>::ReturnType
    motionAction(const MotionDense<MotionDerived> & m) const
    {
      typedef
        typename MotionAlgebraAction<JointMotionSubspaceRevoluteTpl, MotionDerived>::ReturnType
          ReturnType;
      ReturnType res;
      MotionRef<ReturnType> v(res);
      v = m.cross(Axis());
      return res;
    }
 
    bool isEqual(const JointMotionSubspaceRevoluteTpl &) const
    {
      return true;
    }
 
  }; // struct JointMotionSubspaceRevoluteTpl
 
  template<typename _Scalar, int _Options, int _axis>
  struct JointRevoluteTpl
  {
    typedef _Scalar Scalar;
 
    enum
    {
      Options = _Options,
      axis = _axis
    };
  };
 
  template<typename S1, int O1, typename S2, int O2, int axis>
  struct MultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspaceRevoluteTpl<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>, JointMotionSubspaceRevoluteTpl<S2, O2, 0>>
    {
      typedef InertiaTpl<S1, O1> Inertia;
      typedef JointMotionSubspaceRevoluteTpl<S2, O2, 0> Constraint;
      typedef typename MultiplicationOp<Inertia, Constraint>::ReturnType ReturnType;
      static inline ReturnType run(const Inertia & Y, const Constraint & /*constraint*/)
      {
        ReturnType res;
 
        /* Y(:,3) = ( 0,-z, y,  I00+yy+zz,  I01-xy   ,  I02-xz   ) */
        const S1 &m = Y.mass(), &x = Y.lever()[0], &y = Y.lever()[1], &z = Y.lever()[2];
        const typename Inertia::Symmetric3 & I = Y.inertia();
 
        res << (S2)0, -m * z, m * y, I(0, 0) + m * (y * y + z * z), I(0, 1) - m * x * y,
          I(0, 2) - m * x * z;
 
        return res;
      }
    };
 
    template<typename S1, int O1, typename S2, int O2>
    struct LhsMultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspaceRevoluteTpl<S2, O2, 1>>
    {
      typedef InertiaTpl<S1, O1> Inertia;
      typedef JointMotionSubspaceRevoluteTpl<S2, O2, 1> Constraint;
      typedef typename MultiplicationOp<Inertia, Constraint>::ReturnType ReturnType;
      static inline ReturnType run(const Inertia & Y, const Constraint & /*constraint*/)
      {
        ReturnType res;
 
        /* Y(:,4) = ( z, 0,-x,  I10-xy   ,  I11+xx+zz,  I12-yz   ) */
        const S1 &m = Y.mass(), &x = Y.lever()[0], &y = Y.lever()[1], &z = Y.lever()[2];
        const typename Inertia::Symmetric3 & I = Y.inertia();
 
        res << m * z, (S2)0, -m * x, I(1, 0) - m * x * y, I(1, 1) + m * (x * x + z * z),
          I(1, 2) - m * y * z;
 
        return res;
      }
    };
 
    template<typename S1, int O1, typename S2, int O2>
    struct LhsMultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspaceRevoluteTpl<S2, O2, 2>>
    {
      typedef InertiaTpl<S1, O1> Inertia;
      typedef JointMotionSubspaceRevoluteTpl<S2, O2, 2> Constraint;
      typedef typename MultiplicationOp<Inertia, Constraint>::ReturnType ReturnType;
      static inline ReturnType run(const Inertia & Y, const Constraint & /*constraint*/)
      {
        ReturnType res;
 
        /* Y(:,5) = (-y, x, 0,  I20-xz   ,  I21-yz   ,  I22+xx+yy) */
        const S1 &m = Y.mass(), &x = Y.lever()[0], &y = Y.lever()[1], &z = Y.lever()[2];
        const typename Inertia::Symmetric3 & I = Y.inertia();
 
        res << -m * y, m * x, (S2)0, I(2, 0) - m * x * z, I(2, 1) - m * y * z,
          I(2, 2) + m * (x * x + y * y);
 
        return res;
      }
    };
  } // namespace impl
 
  template<typename M6Like, typename S2, int O2, int axis>
  struct MultiplicationOp<Eigen::MatrixBase<M6Like>, JointMotionSubspaceRevoluteTpl<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>,
      JointMotionSubspaceRevoluteTpl<Scalar, Options, axis>>
    {
      typedef JointMotionSubspaceRevoluteTpl<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.col(Inertia::ANGULAR + axis);
      }
    };
  } // namespace impl
 
  template<typename _Scalar, int _Options, int axis>
  struct traits<JointRevoluteTpl<_Scalar, _Options, axis>>
  {
    enum
    {
      NQ = 1,
      NV = 1,
      NVExtended = 1
    };
    typedef _Scalar Scalar;
    enum
    {
      Options = _Options
    };
    typedef JointDataRevoluteTpl<Scalar, Options, axis> JointDataDerived;
    typedef JointModelRevoluteTpl<Scalar, Options, axis> JointModelDerived;
    typedef JointMotionSubspaceRevoluteTpl<Scalar, Options, axis> Constraint_t;
    typedef TransformRevoluteTpl<Scalar, Options, axis> Transformation_t;
    typedef MotionRevoluteTpl<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<JointDataRevoluteTpl<_Scalar, _Options, axis>>
  {
    typedef JointRevoluteTpl<_Scalar, _Options, axis> JointDerived;
    typedef _Scalar Scalar;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct traits<JointModelRevoluteTpl<_Scalar, _Options, axis>>
  {
    typedef JointRevoluteTpl<_Scalar, _Options, axis> JointDerived;
    typedef _Scalar Scalar;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct JointDataRevoluteTpl : public JointDataBase<JointDataRevoluteTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    typedef JointRevoluteTpl<_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;
 
    JointDataRevoluteTpl()
    : joint_q(ConfigVector_t::Zero())
    , joint_v(TangentVector_t::Zero())
    , M((Scalar)0, (Scalar)1)
    , 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("JointDataR") + axisLabel<axis>();
    }
    std::string shortname() const
    {
      return classname();
    }
 
  }; // struct JointDataRevoluteTpl
 
  template<typename NewScalar, typename Scalar, int Options, int axis>
  struct CastType<NewScalar, JointModelRevoluteTpl<Scalar, Options, axis>>
  {
    typedef JointModelRevoluteTpl<NewScalar, Options, axis> type;
  };
 
  template<typename _Scalar, int _Options, int axis>
  struct JointModelRevoluteTpl
  : public JointModelBase<JointModelRevoluteTpl<_Scalar, _Options, axis>>
  {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    typedef JointRevoluteTpl<_Scalar, _Options, axis> JointDerived;
    PINOCCHIO_JOINT_TYPEDEF_TEMPLATE(JointDerived);
 
    typedef JointModelBase<JointModelRevoluteTpl> 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();
    }
 
    JointModelRevoluteTpl()
    {
    }
 
    const std::vector<bool> hasConfigurationLimit() const
    {
      return {true};
    }
 
    const std::vector<bool> hasConfigurationLimitInTangent() const
    {
      return {true};
    }
 
    template<typename ConfigVector>
    PINOCCHIO_DONT_INLINE void
    calc(JointDataDerived & data, const typename Eigen::MatrixBase<ConfigVector> & qs) const
    {
      data.joint_q[0] = qs[idx_q()];
      Scalar ca, sa;
      SINCOS(data.joint_q[0], &sa, &ca);
      data.M.setValues(sa, ca);
    }
 
    template<typename TangentVector>
    PINOCCHIO_DONT_INLINE void
    calc(JointDataDerived & data, const Blank, const typename Eigen::MatrixBase<TangentVector> & vs)
      const
    {
      data.joint_v[0] = vs[idx_v()];
      data.v.angularRate() = data.joint_v[0];
    }
 
    template<typename ConfigVector, typename TangentVector>
    PINOCCHIO_DONT_INLINE 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.angularRate() = 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::ANGULAR + axis);
      data.Dinv[0] =
        Scalar(1) / (I(Inertia::ANGULAR + axis, Inertia::ANGULAR + 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("JointModelR") + 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>
    JointModelRevoluteTpl<NewScalar, Options, axis> cast() const
    {
      typedef JointModelRevoluteTpl<NewScalar, Options, axis> ReturnType;
      ReturnType res;
      res.setIndexes(id(), idx_q(), idx_v(), idx_vExtended());
      return res;
    }
 
  }; // struct JointModelRevoluteTpl
 
  typedef JointRevoluteTpl<context::Scalar, context::Options, 0> JointRX;
  typedef JointDataRevoluteTpl<context::Scalar, context::Options, 0> JointDataRX;
  typedef JointModelRevoluteTpl<context::Scalar, context::Options, 0> JointModelRX;
 
  typedef JointRevoluteTpl<context::Scalar, context::Options, 1> JointRY;
  typedef JointDataRevoluteTpl<context::Scalar, context::Options, 1> JointDataRY;
  typedef JointModelRevoluteTpl<context::Scalar, context::Options, 1> JointModelRY;
 
  typedef JointRevoluteTpl<context::Scalar, context::Options, 2> JointRZ;
  typedef JointDataRevoluteTpl<context::Scalar, context::Options, 2> JointDataRZ;
  typedef JointModelRevoluteTpl<context::Scalar, context::Options, 2> JointModelRZ;
 
  template<typename Scalar, int Options, int axis>
  struct ConfigVectorAffineTransform<JointRevoluteTpl<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::JointModelRevoluteTpl<Scalar, Options, axis>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options, int axis>
  struct has_nothrow_copy<::pinocchio::JointModelRevoluteTpl<Scalar, Options, axis>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options, int axis>
  struct has_nothrow_constructor<::pinocchio::JointDataRevoluteTpl<Scalar, Options, axis>>
  : public integral_constant<bool, true>
  {
  };
 
  template<typename Scalar, int Options, int axis>
  struct has_nothrow_copy<::pinocchio::JointDataRevoluteTpl<Scalar, Options, axis>>
  : public integral_constant<bool, true>
  {
  };
} // namespace boost
 
#endif // ifndef __pinocchio_multibody_joint_revolute_hpp__