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__