joint-free-flyer.hpp

//
// Copyright (c) 2015-2018 CNRS
// Copyright (c) 2015-2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
//
// This file is part of Pinocchio
// Pinocchio is free software: you can redistribute it
// and/or modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation, either version
// 3 of the License, or (at your option) any later version.
//
// Pinocchio is distributed in the hope that it will be
// useful, but WITHOUT ANY WARRANTY; without even the implied warranty
// of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// General Lesser Public License for more details. You should have
// received a copy of the GNU Lesser General Public License along with
// Pinocchio If not, see
// <http://www.gnu.org/licenses/>.

#ifndef __se3_joint_free_flyer_hpp__
#define __se3_joint_free_flyer_hpp__

#include "pinocchio/macros.hpp"
#include "pinocchio/spatial/inertia.hpp"
#include "pinocchio/spatial/explog.hpp"
#include "pinocchio/multibody/joint/joint-base.hpp"
#include "pinocchio/multibody/constraint.hpp"
#include "pinocchio/math/fwd.hpp"
#include "pinocchio/math/quaternion.hpp"

namespace se3
{

  template<typename Scalar, int Options> struct ConstraintIdentityTpl;

  template<typename _Scalar, int _Options>
  struct traits< ConstraintIdentityTpl<_Scalar,_Options> >
  {
    typedef _Scalar Scalar;
    enum { Options = _Options };
    typedef Eigen::Matrix<Scalar,3,1,Options> Vector3;
    typedef Eigen::Matrix<Scalar,4,1,Options> Vector4;
    typedef Eigen::Matrix<Scalar,6,1,Options> Vector6;
    typedef Eigen::Matrix<Scalar,3,3,Options> Matrix3;
    typedef Eigen::Matrix<Scalar,4,4,Options> Matrix4;
    typedef Eigen::Matrix<Scalar,6,6,Options> Matrix6;
    typedef Matrix3 Angular_t;
    typedef Vector3 Linear_t;
    typedef const Matrix3 ConstAngular_t;
    typedef const Vector3 ConstLinear_t;
    typedef Matrix6 ActionMatrix_t;
    typedef Eigen::Quaternion<Scalar,Options> Quaternion_t;
    typedef SE3Tpl<Scalar,Options> SE3;
    typedef ForceTpl<Scalar,Options> Force;
    typedef MotionTpl<Scalar,Options> Motion;
    typedef Symmetric3Tpl<Scalar,Options> Symmetric3;
    enum {
      LINEAR = 0,
      ANGULAR = 3
    };
    typedef Eigen::Matrix<Scalar,6,1,Options> JointMotion;
    typedef Eigen::Matrix<Scalar,6,1,Options> JointForce;
    typedef Eigen::Matrix<Scalar,6,6,Options> DenseBase;
    typedef const DenseBase ConstMatrixReturnType;
    typedef DenseBase MatrixReturnType;
  }; // traits ConstraintRevolute


  template<typename _Scalar, int _Options>
  struct ConstraintIdentityTpl : ConstraintBase< ConstraintIdentityTpl<_Scalar,_Options> >
  {
    SPATIAL_TYPEDEF_TEMPLATE(ConstraintIdentityTpl);
    enum { NV = 6, Options = 0 };
    typedef typename traits<ConstraintIdentityTpl>::JointMotion JointMotion;
    typedef typename traits<ConstraintIdentityTpl>::JointForce JointForce;
    typedef typename traits<ConstraintIdentityTpl>::DenseBase DenseBase;
    
    template<typename S1, int O1>
    typename SE3::Matrix6 se3Action(const SE3Tpl<S1,O1> & m) const
    { return m.toActionMatrix(); }
    
    int nv_impl() const { return NV; }
    
    struct TransposeConst
    {
      template<typename Derived>
      typename ForceDense<Derived>::ToVectorConstReturnType
      operator*(const ForceDense<Derived> & phi)
      {  return phi.toVector();  }
      
      /* [CRBA]  MatrixBase operator* (Constraint::Transpose S, ForceSet::Block) */
      template<typename MatrixDerived>
      typename EIGEN_REF_CONSTTYPE(MatrixDerived)
      operator*(const Eigen::MatrixBase<MatrixDerived> & F)
      {
        return F.derived();
      }
    };
    
    TransposeConst transpose() const { return TransposeConst(); }
    DenseBase matrix_impl() const { return DenseBase::Identity(); }
    
    template<typename MotionDerived>
    typename MotionDerived::ActionMatrixType
    motionAction(const MotionBase<MotionDerived> & v) const
    { return v.toActionMatrix(); }
    
  }; // struct ConstraintIdentityTpl
  
  template<typename Scalar, int Options, typename Vector6Like>
  typename ConstraintIdentityTpl<Scalar,Options>::Motion
  operator*(const ConstraintIdentityTpl<Scalar,Options> &, const Eigen::MatrixBase<Vector6Like>& v)
  {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector6Like,6);
    typedef typename ConstraintIdentityTpl<Scalar,Options>::Motion Motion;
    return Motion(v);
  }

  /* [CRBA] ForceSet operator* (Inertia Y,Constraint S) */
  template<typename S1, int O1, typename S2, int O2>
  inline typename InertiaTpl<S1,O1>::Matrix6
  operator*(const InertiaTpl<S1,O1> & Y, const ConstraintIdentityTpl<S2,O2> &)
  {
    return Y.matrix();
  }
  
  /* [ABA] Y*S operator*/
  template<typename Matrix6Like, typename S2, int O2>
  inline typename EIGEN_REF_CONSTTYPE(Matrix6Like)
  operator*(const Eigen::MatrixBase<Matrix6Like> & Y, const ConstraintIdentityTpl<S2,O2> &)
  {
    return Y.derived();
  }
  
  namespace internal
  {
    template<typename S1, int O1>
    struct SE3GroupAction< ConstraintIdentityTpl<S1,O1> >
    { typedef typename SE3Tpl<S1,O1>::Matrix6 ReturnType; };
    
    template<typename S1, int O1, typename MotionDerived>
    struct MotionAlgebraAction< ConstraintIdentityTpl<S1,O1>,MotionDerived >
    { typedef typename SE3Tpl<S1,O1>::Matrix6 ReturnType; };
  }

  template<typename Scalar, int Options> struct JointFreeFlyerTpl;

  template<typename _Scalar, int _Options>
  struct traits< JointFreeFlyerTpl<_Scalar,_Options> >
  {
    enum {
      NQ = 7,
      NV = 6
    };
    typedef double Scalar;
    enum { Options = _Options };
    typedef JointDataFreeFlyerTpl<Scalar,Options> JointDataDerived;
    typedef JointModelFreeFlyerTpl<Scalar,Options> JointModelDerived;
    typedef ConstraintIdentityTpl<Scalar,Options> Constraint_t;
    typedef SE3Tpl<Scalar,Options> Transformation_t;
    typedef MotionTpl<Scalar,Options> Motion_t;
    typedef BiasZero Bias_t;
    typedef Eigen::Matrix<Scalar,6,NV,Options> F_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;
  };
  
  template<typename Scalar, int Options>
  struct traits< JointDataFreeFlyerTpl<Scalar,Options> >
  { typedef JointFreeFlyerTpl<Scalar,Options> JointDerived; };
  
  template<typename Scalar, int Options>
  struct traits< JointModelFreeFlyerTpl<Scalar,Options> >
  { typedef JointFreeFlyerTpl<Scalar,Options> JointDerived; };

  template<typename _Scalar, int _Options>
  struct JointDataFreeFlyerTpl : public JointDataBase< JointDataFreeFlyerTpl<_Scalar,_Options> >
  {
    typedef JointFreeFlyerTpl<_Scalar,_Options> JointDerived;
    SE3_JOINT_TYPEDEF_TEMPLATE;
    
    Constraint_t S;
    Transformation_t M;
    Motion_t v;
    Bias_t c;

    F_t F; // TODO if not used anymore, clean F_t
    
    // [ABA] specific data
    U_t U;
    D_t Dinv;
    UD_t UDinv;
    
    JointDataFreeFlyerTpl() : M(1), U(), Dinv(), UDinv(UD_t::Identity()) {}

  }; // struct JointDataFreeFlyerTpl

  template<typename _Scalar, int _Options>
  struct JointModelFreeFlyerTpl : public JointModelBase< JointModelFreeFlyerTpl<_Scalar,_Options> >
  {
    typedef JointFreeFlyerTpl<_Scalar,_Options> JointDerived;
    SE3_JOINT_TYPEDEF_TEMPLATE;

    using JointModelBase<JointModelFreeFlyerTpl>::id;
    using JointModelBase<JointModelFreeFlyerTpl>::idx_q;
    using JointModelBase<JointModelFreeFlyerTpl>::idx_v;
    using JointModelBase<JointModelFreeFlyerTpl>::setIndexes;

    JointDataDerived createData() const { return JointDataDerived(); }
    
    template<typename ConfigVectorLike>
    inline void forwardKinematics(Transformation_t & M, const Eigen::MatrixBase<ConfigVectorLike> & q_joint) const
    {
      EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ConfigVector_t,ConfigVectorLike);
      typedef typename Eigen::Quaternion<typename ConfigVectorLike::Scalar,EIGEN_PLAIN_TYPE(ConfigVectorLike)::Options> Quaternion;
      typedef Eigen::Map<const Quaternion> ConstQuaternionMap;

      ConstQuaternionMap quat(q_joint.template tail<4>().data());
      //assert(std::fabs(quat.coeffs().squaredNorm()-1.) <= sqrt(Eigen::NumTraits<typename V::Scalar>::epsilon())); TODO: check validity of the rhs precision
      assert(std::fabs(quat.coeffs().squaredNorm()-1.) <= 1e-4);
      
      M.rotation(quat.matrix());
      M.translation(q_joint.template head<3>());
    }
    
    template<typename ConfigVector>
    void calc(JointDataDerived & data,
              const typename Eigen::MatrixBase<ConfigVector> & qs) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(ConfigVector);
      typedef typename Eigen::Quaternion<typename ConfigVector::Scalar,ConfigVector::Options> Quaternion;
      typedef Eigen::Map<const Quaternion> ConstQuaternionMap;
      
      typename ConfigVector::template ConstFixedSegmentReturnType<NQ>::Type q = qs.template segment<NQ>(idx_q());
      ConstQuaternionMap quat(q.template tail<4>().data());
      
      data.M.rotation(quat.matrix());
      data.M.translation(q.template head<3>());
    }
    
    template<typename ConfigVector, typename TangentVector>
    void calc(JointDataDerived & data,
              const typename Eigen::MatrixBase<ConfigVector> & qs,
              const typename Eigen::MatrixBase<TangentVector> & vs) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(TangentVector);
      calc(data,qs.derived());
      
      data.v = vs.template segment<NV>(idx_v());
    }
    
    template<typename S2, int O2>
    void calc_aba(JointDataDerived & data, Eigen::Matrix<S2,6,6,O2> & I, const bool update_I) const
    {
      data.U = I;
      data.Dinv = I.inverse();
      
      if (update_I)
        I.setZero();
    }

    Scalar finiteDifferenceIncrement() const
    {
      using std::sqrt;
      return 2.*sqrt(sqrt(Eigen::NumTraits<Scalar>::epsilon()));
    }

    static std::string classname() { return std::string("JointModelFreeFlyer"); }
    std::string shortname() const { return classname(); }

  }; // struct JointModelFreeFlyerTpl

} // namespace se3

#endif // ifndef __se3_joint_free_flyer_hpp__