joint-helical-unaligned.hpp

//
// Copyright (c) 2022-2023 INRIA
//

#ifndef __pinocchio_multibody_joint_helical_unaligned_hpp__
#define __pinocchio_multibody_joint_helical_unaligned_hpp__

#include "pinocchio/fwd.hpp"
#include "pinocchio/multibody/joint/joint-base.hpp"
#include "pinocchio/multibody/joint-motion-subspace.hpp"
#include "pinocchio/spatial/inertia.hpp"

#include "pinocchio/math/matrix.hpp"
#include "pinocchio/math/rotation.hpp"

namespace pinocchio
{

 template<typename Scalar, int Options>
 struct MotionHelicalUnalignedTpl;

 template<typename Scalar, int Options>
 struct SE3GroupAction<MotionHelicalUnalignedTpl<Scalar, Options>>
 {
 typedef MotionTpl<Scalar, Options> ReturnType;
 };

 template<typename Scalar, int Options, typename MotionDerived>
 struct MotionAlgebraAction<MotionHelicalUnalignedTpl<Scalar, Options>, MotionDerived>
 {
 typedef MotionTpl<Scalar, Options> ReturnType;
 };

 template<typename _Scalar, int _Options>
 struct traits<MotionHelicalUnalignedTpl<_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 MotionTpl<Scalar, Options> MotionPlain;
 typedef MotionPlain PlainReturnType;
 typedef Matrix4 HomogeneousMatrixType;
 enum
 {
 LINEAR = 0,
 ANGULAR = 3
 };
 }; // traits MotionHelicalUnalignedTpl

 template<typename _Scalar, int _Options>
 struct MotionHelicalUnalignedTpl : MotionBase<MotionHelicalUnalignedTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW

 MOTION_TYPEDEF_TPL(MotionHelicalUnalignedTpl);

 MotionHelicalUnalignedTpl()
 {
 }

 template<typename Vector3Like, typename OtherScalar>
 MotionHelicalUnalignedTpl(
 const Eigen::MatrixBase<Vector3Like> & axis, const OtherScalar & w, const OtherScalar & v)
 : m_axis(axis)
 , m_w(w)
 , m_v(v)
 {
 }

 inline PlainReturnType plain() const
 {
 return PlainReturnType(m_axis * m_v, m_axis * m_w);
 }

 template<typename OtherScalar>
 MotionHelicalUnalignedTpl __mult__(const OtherScalar & alpha) const
 {
 return MotionHelicalUnalignedTpl(m_axis, alpha * m_w, alpha * m_v);
 }

 template<typename MotionDerived>
 void setTo(MotionDense<MotionDerived> & m) const
 {
 for (Eigen::DenseIndex k = 0; k < 3; ++k)
 {
 m.angular().noalias() = m_axis * m_w;
 m.linear().noalias() = m_axis * m_v;
 }
 }

 template<typename MotionDerived>
 inline void addTo(MotionDense<MotionDerived> & v) const
 {
 v.angular() += m_axis * m_w;
 v.linear() += m_axis * m_v;
 }

 template<typename S2, int O2, typename D2>
 inline void se3Action_impl(const SE3Tpl<S2, O2> & m, MotionDense<D2> & v) const
 {
 v.angular().noalias() = m_w * m.rotation() * m_axis;
 v.linear().noalias() = m.translation().cross(v.angular()) + m_v * m.rotation() * m_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.angular().noalias() = m_axis.cross(m.translation());
 v.angular() *= m_w;
 v.linear().noalias() =
 m.rotation().transpose() * v.angular() + m_v * (m.rotation().transpose() * m_axis);

 // Angular
 v.angular().noalias() = m.rotation().transpose() * m_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>
 void motionAction(const MotionDense<M1> & v, MotionDense<M2> & mout) const
 {
 // Linear
 mout.linear().noalias() = v.linear().cross(m_axis);
 mout.linear() *= m_w;
 mout.angular().noalias() = v.angular().cross(m_axis);
 mout.angular() *= m_v;
 mout.linear() += mout.angular();

 // Angular
 mout.angular().noalias() = v.angular().cross(m_axis);
 mout.angular() *= m_w;
 }

 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;
 }

 Scalar & linearRate()
 {
 return m_v;
 }
 const Scalar & linearRate() const
 {
 return m_v;
 }

 Vector3 & axis()
 {
 return m_axis;
 }
 const Vector3 & axis() const
 {
 return m_axis;
 }

 bool isEqual_impl(const MotionHelicalUnalignedTpl & other) const
 {
 return internal::comparison_eq(m_axis, other.m_axis)
 && internal::comparison_eq(m_w, other.m_w) && internal::comparison_eq(m_v, other.m_v);
 }

 protected:
 Vector3 m_axis;
 Scalar m_w, m_v;

 }; // struct MotionHelicalUnalignedTpl

 template<typename S1, int O1, typename MotionDerived>
 typename MotionDerived::MotionPlain
 operator+(const MotionHelicalUnalignedTpl<S1, O1> & m1, const MotionDense<MotionDerived> & m2)
 {
 typename MotionDerived::MotionPlain res(m2);
 res += m1;
 return res;
 }

 template<typename MotionDerived, typename S2, int O2>
 EIGEN_STRONG_INLINE typename MotionDerived::MotionPlain
 operator^(const MotionDense<MotionDerived> & m1, const MotionHelicalUnalignedTpl<S2, O2> & m2)
 {
 return m2.motionAction(m1);
 }

 template<typename Scalar, int Options>
 struct JointMotionSubspaceHelicalUnalignedTpl;

 template<typename Scalar, int Options>
 struct SE3GroupAction<JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options>>
 {
 typedef Eigen::Matrix<Scalar, 6, 1, Options> ReturnType;
 };

 template<typename Scalar, int Options, typename MotionDerived>
 struct MotionAlgebraAction<JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options>, MotionDerived>
 {
 typedef Eigen::Matrix<Scalar, 6, 1, Options> ReturnType;
 };

 template<typename Scalar, int Options, typename ForceDerived>
 struct ConstraintForceOp<JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options>, ForceDerived>
 {
 typedef typename Eigen::Matrix<Scalar, 1, 1> ReturnType;
 };

 template<typename Scalar, int Options, typename ForceSet>
 struct ConstraintForceSetOp<JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options>, ForceSet>
 {
 typedef typename Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> ReturnType;
 };

 template<typename _Scalar, int _Options>
 struct traits<JointMotionSubspaceHelicalUnalignedTpl<_Scalar, _Options>>
 {
 typedef _Scalar Scalar;
 enum
 {
 Options = _Options
 };
 enum
 {
 LINEAR = 0,
 ANGULAR = 3
 };

 typedef MotionHelicalUnalignedTpl<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 DenseBase MatrixReturnType;
 typedef const DenseBase ConstMatrixReturnType;

 typedef Eigen::Matrix<Scalar, 3, 1, Options> Vector3;

 typedef typename ReducedSquaredMatrix::IdentityReturnType StDiagonalMatrixSOperationReturnType;
 }; // traits JointMotionSubspaceHelicalUnalignedTpl

 template<typename _Scalar, int _Options>
 struct JointMotionSubspaceHelicalUnalignedTpl
 : JointMotionSubspaceBase<JointMotionSubspaceHelicalUnalignedTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW

 PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(JointMotionSubspaceHelicalUnalignedTpl)
 enum
 {
 NV = 1
 };

 JointMotionSubspaceHelicalUnalignedTpl()
 {
 }

 typedef typename traits<JointMotionSubspaceHelicalUnalignedTpl>::Vector3 Vector3;

 template<typename Vector3Like>
 JointMotionSubspaceHelicalUnalignedTpl(
 const Eigen::MatrixBase<Vector3Like> & axis, const Scalar & h)
 : m_axis(axis)
 , m_pitch(h)
 {
 }

 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(m_axis, v[0], Scalar(v[0] * m_pitch));
 }

 template<typename S1, int O1>
 typename SE3GroupAction<JointMotionSubspaceHelicalUnalignedTpl>::ReturnType
 se3Action(const SE3Tpl<S1, O1> & m) const
 {
 typedef
 typename SE3GroupAction<JointMotionSubspaceHelicalUnalignedTpl>::ReturnType ReturnType;
 ReturnType res;
 res.template segment<3>(ANGULAR).noalias() = m.rotation() * m_axis;
 res.template segment<3>(LINEAR).noalias() =
 m.translation().cross(res.template segment<3>(ANGULAR)) + m_pitch * (m.rotation() * m_axis);
 return res;
 }

 template<typename S1, int O1>
 typename SE3GroupAction<JointMotionSubspaceHelicalUnalignedTpl>::ReturnType
 se3ActionInverse(const SE3Tpl<S1, O1> & m) const
 {
 typedef
 typename SE3GroupAction<JointMotionSubspaceHelicalUnalignedTpl>::ReturnType ReturnType;

 ReturnType res;
 res.template segment<3>(ANGULAR).noalias() = m.rotation().transpose() * m_axis;
 res.template segment<3>(LINEAR).noalias() =
 -m.rotation().transpose() * m.translation().cross(m_axis)
 + m.rotation().transpose() * m_axis * m_pitch;

 return res;
 }

 int nv_impl() const
 {
 return NV;
 }

 struct TransposeConst : JointMotionSubspaceTransposeBase<JointMotionSubspaceHelicalUnalignedTpl>
 {
 const JointMotionSubspaceHelicalUnalignedTpl & ref;
 TransposeConst(const JointMotionSubspaceHelicalUnalignedTpl & ref)
 : ref(ref)
 {
 }

 template<typename ForceDerived>
 typename ConstraintForceOp<JointMotionSubspaceHelicalUnalignedTpl, ForceDerived>::ReturnType
 operator*(const ForceDense<ForceDerived> & f) const
 {
 typedef typename ConstraintForceOp<
 JointMotionSubspaceHelicalUnalignedTpl, ForceDerived>::ReturnType ReturnType;
 ReturnType res;
 res[0] = ref.axis().dot(f.angular()) + ref.axis().dot(f.linear()) * ref.m_pitch;
 return res;
 }

 template<typename Derived>
 typename ConstraintForceSetOp<JointMotionSubspaceHelicalUnalignedTpl, Derived>::ReturnType
 operator*(const Eigen::MatrixBase<Derived> & F) const
 {
 assert(F.rows() == 6);
 return (
 ref.axis().transpose() * F.template middleRows<3>(ANGULAR)
 + (ref.axis().transpose() * F.template middleRows<3>(LINEAR) * ref.m_pitch));
 }
 }; // 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;
 S.template segment<3>(LINEAR) = m_axis * m_pitch;
 S.template segment<3>(ANGULAR) = m_axis;
 return S;
 }

 template<typename MotionDerived>
 typename MotionAlgebraAction<JointMotionSubspaceHelicalUnalignedTpl, MotionDerived>::ReturnType
 motionAction(const MotionDense<MotionDerived> & m) const
 {
 const typename MotionDerived::ConstLinearType v = m.linear();
 const typename MotionDerived::ConstAngularType w = m.angular();

 DenseBase res;
 res.template segment<3>(LINEAR).noalias() = v.cross(m_axis);
 res.template segment<3>(ANGULAR).noalias() = w.cross(m_axis * m_pitch);
 res.template segment<3>(LINEAR).noalias() += res.template segment<3>(ANGULAR);
 res.template segment<3>(ANGULAR).noalias() = w.cross(m_axis);

 return res;
 }

 bool isEqual(const JointMotionSubspaceHelicalUnalignedTpl & other) const
 {
 return internal::comparison_eq(m_axis, other.m_axis)
 && internal::comparison_eq(m_pitch, other.m_pitch);
 }

 Vector3 & axis()
 {
 return m_axis;
 }
 const Vector3 & axis() const
 {
 return m_axis;
 }

 Scalar & h()
 {
 return m_pitch;
 }
 const Scalar & h() const
 {
 return m_pitch;
 }

 Vector3 m_axis;
 Scalar m_pitch;

 }; // struct JointMotionSubspaceHelicalUnalignedTpl

 template<typename _Scalar, int _Options>
 Eigen::Matrix<_Scalar, 1, 1, _Options> operator*(
 const typename JointMotionSubspaceHelicalUnalignedTpl<_Scalar, _Options>::TransposeConst &
 S_transpose,
 const JointMotionSubspaceHelicalUnalignedTpl<_Scalar, _Options> & S)
 {
 Eigen::Matrix<_Scalar, 1, 1, _Options> res;
 res(0) = (S_transpose.ref.axis() * S_transpose.ref.h()).dot(S.axis() * S.h())
 + (S_transpose.ref.axis().dot(S.axis()));
 return res;
 }

 template<typename S1, int O1, typename S2, int O2>
 struct MultiplicationOp<InertiaTpl<S1, O1>, JointMotionSubspaceHelicalUnalignedTpl<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>, JointMotionSubspaceHelicalUnalignedTpl<S2, O2>>
 {
 typedef InertiaTpl<S1, O1> Inertia;
 typedef JointMotionSubspaceHelicalUnalignedTpl<S2, O2> Constraint;
 typedef typename JointMotionSubspaceHelicalUnalignedTpl<S2, O2>::Vector3 Vector3;
 typedef typename MultiplicationOp<Inertia, Constraint>::ReturnType ReturnType;
 static inline ReturnType run(const Inertia & Y, const Constraint & cru)
 {
 ReturnType res;
 /* YS = [ m -mcx ; mcx I-mcxcx ] [ h ; w ] = [mh-mcxw ; mcxh+Iw-mcxcxw ] */

 const S2 & m_pitch = cru.h();
 const typename Inertia::Scalar & m = Y.mass();
 const typename Inertia::Vector3 & c = Y.lever();
 const typename Inertia::Symmetric3 & I = Y.inertia();

 res.template segment<3>(Inertia::LINEAR) = -m * c.cross(cru.axis());
 res.template segment<3>(Inertia::ANGULAR).noalias() = I * cru.axis();
 res.template segment<3>(Inertia::ANGULAR) += c.cross(cru.axis()) * m * m_pitch;
 res.template segment<3>(Inertia::ANGULAR) +=
 c.cross(res.template segment<3>(Inertia::LINEAR));
 res.template segment<3>(Inertia::LINEAR) += m * m_pitch * cru.axis();
 return res;
 }
 };
 } // namespace impl

 template<typename M6Like, typename Scalar, int Options>
 struct MultiplicationOp<
 Eigen::MatrixBase<M6Like>,
 JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options>>
 {
 typedef const Eigen::Matrix<Scalar, 6, 1> ReturnType;
 };

 /* [ABA] operator* (Inertia Y,Constraint S) */
 namespace impl
 {
 template<typename M6Like, typename Scalar, int Options>
 struct LhsMultiplicationOp<
 Eigen::MatrixBase<M6Like>,
 JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options>>
 {
 typedef JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options> Constraint;
 typedef Eigen::Matrix<Scalar, 6, 1> 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::ANGULAR) * cru.axis()
 + Y.derived().template middleCols<3>(Constraint::LINEAR) * cru.axis() * cru.h();
 }
 };
 } // namespace impl

 template<typename Scalar, int Options>
 struct JointHelicalUnalignedTpl;

 template<typename _Scalar, int _Options>
 struct traits<JointHelicalUnalignedTpl<_Scalar, _Options>>
 {
 enum
 {
 NQ = 1,
 NV = 1,
 NVExtended = 1
 };
 typedef _Scalar Scalar;
 enum
 {
 Options = _Options
 };
 typedef JointDataHelicalUnalignedTpl<Scalar, Options> JointDataDerived;
 typedef JointModelHelicalUnalignedTpl<Scalar, Options> JointModelDerived;
 typedef JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options> Constraint_t;
 typedef SE3Tpl<Scalar, Options> Transformation_t;
 typedef MotionHelicalUnalignedTpl<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;

 typedef boost::mpl::true_ is_mimicable_t;

 PINOCCHIO_JOINT_DATA_BASE_ACCESSOR_DEFAULT_RETURN_TYPE
 };

 template<typename _Scalar, int _Options>
 struct traits<JointDataHelicalUnalignedTpl<_Scalar, _Options>>
 {
 typedef JointHelicalUnalignedTpl<_Scalar, _Options> JointDerived;
 typedef _Scalar Scalar;
 };

 template<typename _Scalar, int _Options>
 struct traits<JointModelHelicalUnalignedTpl<_Scalar, _Options>>
 {
 typedef JointHelicalUnalignedTpl<_Scalar, _Options> JointDerived;
 typedef _Scalar Scalar;
 };

 template<typename _Scalar, int _Options>
 struct JointDataHelicalUnalignedTpl
 : public JointDataBase<JointDataHelicalUnalignedTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 typedef JointHelicalUnalignedTpl<_Scalar, _Options> 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;

 JointDataHelicalUnalignedTpl()
 : joint_q(ConfigVector_t::Zero())
 , joint_v(TangentVector_t::Zero())
 , S(Constraint_t::Vector3::Zero(), (Scalar)0)
 , M(Transformation_t::Identity())
 , v(Constraint_t::Vector3::Zero(), (Scalar)0, (Scalar)0)
 , U(U_t::Zero())
 , Dinv(D_t::Zero())
 , UDinv(UD_t::Zero())
 , StU(D_t::Zero())
 {
 }

 template<typename Vector3Like>
 JointDataHelicalUnalignedTpl(const Eigen::MatrixBase<Vector3Like> & axis)
 : joint_q(ConfigVector_t::Zero())
 , joint_v(TangentVector_t::Zero())
 , S(axis, (Scalar)0)
 , M(Transformation_t::Identity())
 , v(axis, (Scalar)0, (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("JointDataHelicalUnaligned");
 }
 std::string shortname() const
 {
 return classname();
 }

 }; // struct JointDataHelicalUnalignedTpl

 PINOCCHIO_JOINT_CAST_TYPE_SPECIALIZATION(JointModelHelicalUnalignedTpl);
 template<typename _Scalar, int _Options>
 struct JointModelHelicalUnalignedTpl
 : public JointModelBase<JointModelHelicalUnalignedTpl<_Scalar, _Options>>
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 typedef JointHelicalUnalignedTpl<_Scalar, _Options> JointDerived;
 PINOCCHIO_JOINT_TYPEDEF_TEMPLATE(JointDerived);
 typedef Eigen::Matrix<Scalar, 3, 1, _Options> Vector3;

 typedef JointModelBase<JointModelHelicalUnalignedTpl> Base;
 using Base::id;
 using Base::idx_q;
 using Base::idx_v;
 using Base::idx_vExtended;
 using Base::setIndexes;

 JointModelHelicalUnalignedTpl()
 {
 }

 template<typename Vector3Like>
 JointModelHelicalUnalignedTpl(const Eigen::MatrixBase<Vector3Like> & axis)
 : axis(axis)
 , m_pitch((Scalar)0)
 {
 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Vector3Like);
 assert(isUnitary(axis) && "Rotation axis is not unitary");
 }

 JointModelHelicalUnalignedTpl(
 const Scalar & x, const Scalar & y, const Scalar & z, const Scalar & h)
 : axis(x, y, z)
 , m_pitch(h)
 {
 normalize(axis);
 assert(isUnitary(axis) && "Rotation axis is not unitary");
 }

 template<typename Vector3Like>
 JointModelHelicalUnalignedTpl(const Eigen::MatrixBase<Vector3Like> & axis, const Scalar & h)
 : axis(axis)
 , m_pitch(h)
 {
 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Vector3Like);
 assert(isUnitary(axis) && "Rotation axis is not unitary");
 }

 const std::vector<bool> hasConfigurationLimit() const
 {
 return {true, true};
 }

 const std::vector<bool> hasConfigurationLimitInTangent() const
 {
 return {true, true};
 }

 JointDataDerived createData() const
 {
 return JointDataDerived();
 }

 using Base::isEqual;
 bool isEqual(const JointModelHelicalUnalignedTpl & other) const
 {
 return Base::isEqual(other) && internal::comparison_eq(axis, other.axis)
 && internal::comparison_eq(m_pitch, other.m_pitch);
 }

 template<typename ConfigVector>
 void calc(JointDataDerived & data, const typename Eigen::MatrixBase<ConfigVector> & qs) const
 {
 data.joint_q[0] = qs[idx_q()];

 toRotationMatrix(axis, data.joint_q[0], data.M.rotation());
 data.M.translation() = axis * data.joint_q[0] * m_pitch;
 data.S.h() = m_pitch;
 data.S.axis() = axis;
 }

 template<typename TangentVector>
 void
 calc(JointDataDerived & data, const Blank, const typename Eigen::MatrixBase<TangentVector> & vs)
 const
 {
 data.v.angularRate() = static_cast<Scalar>(vs[idx_v()]);
 data.v.axis() = axis;
 data.v.linearRate() = static_cast<Scalar>(vs[idx_v()] * m_pitch);
 }

 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.v.angularRate() = static_cast<Scalar>(vs[idx_v()]);
 data.v.axis() = axis;
 data.v.linearRate() = static_cast<Scalar>(vs[idx_v()] * m_pitch);
 }

 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 middleCols<3>(Motion::ANGULAR) * axis
 + m_pitch * I.template middleCols<3>(Motion::LINEAR) * axis;
 data.StU[0] = axis.dot(data.U.template segment<3>(Motion::ANGULAR))
 + m_pitch * axis.dot(data.U.template segment<3>(Motion::LINEAR)) + armature[0];
 data.Dinv[0] = Scalar(1) / data.StU[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("JointModelHelicalUnaligned");
 }
 std::string shortname() const
 {
 return classname();
 }

 template<typename NewScalar>
 JointModelHelicalUnalignedTpl<NewScalar, Options> cast() const
 {
 typedef JointModelHelicalUnalignedTpl<NewScalar, Options> ReturnType;
 ReturnType res(axis.template cast<NewScalar>(), ScalarCast<NewScalar, Scalar>::cast(m_pitch));
 res.setIndexes(id(), idx_q(), idx_v(), idx_vExtended());
 return res;
 }

 Vector3 axis;
 Scalar m_pitch;

 }; // struct JointModelHelicalUnalignedTpl

} // namespace pinocchio

#include <boost/type_traits.hpp>

namespace boost
{
 template<typename Scalar, int Options>
 struct has_nothrow_constructor<::pinocchio::JointModelHelicalUnalignedTpl<Scalar, Options>>
 : public integral_constant<bool, true>
 {
 };

 template<typename Scalar, int Options>
 struct has_nothrow_copy<::pinocchio::JointModelHelicalUnalignedTpl<Scalar, Options>>
 : public integral_constant<bool, true>
 {
 };

 template<typename Scalar, int Options>
 struct has_nothrow_constructor<::pinocchio::JointDataHelicalUnalignedTpl<Scalar, Options>>
 : public integral_constant<bool, true>
 {
 };

 template<typename Scalar, int Options>
 struct has_nothrow_copy<::pinocchio::JointDataHelicalUnalignedTpl<Scalar, Options>>
 : public integral_constant<bool, true>
 {
 };
} // namespace boost

#endif // ifndef __pinocchio_multibody_joint_helical_unaligned_hpp__