euler_converter.h

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#ifndef TOWR_VARIABLES_ANGULAR_STATE_CONVERTER_H_
#define TOWR_VARIABLES_ANGULAR_STATE_CONVERTER_H_

#include <array>

#include <Eigen/Dense>
#include <Eigen/Sparse>

#include "cartesian_dimensions.h"
#include "node_spline.h"

namespace towr {

class EulerConverter {
public:
  using Vector3d    = Eigen::Vector3d;
  using EulerAngles = Vector3d; 
  using EulerRates  = Vector3d; 

  using JacobianRow = Eigen::SparseVector<double, Eigen::RowMajor>;
  using MatrixSXd   = Eigen::SparseMatrix<double, Eigen::RowMajor>;
  using Jacobian    = MatrixSXd;
  using JacRowMatrix = std::array<std::array<JacobianRow, k3D>, k3D>;

  EulerConverter () = default;

  EulerConverter (const NodeSpline::Ptr& euler_angles);
  virtual ~EulerConverter () = default;

  Eigen::Quaterniond GetQuaternionBaseToWorld (double t) const;

  MatrixSXd GetRotationMatrixBaseToWorld(double t) const;

  Vector3d GetAngularVelocityInWorld(double t) const;

  Vector3d GetAngularAccelerationInWorld(double t) const;

  Jacobian GetDerivOfAngVelWrtEulerNodes(double t) const;

  Jacobian GetDerivOfAngAccWrtEulerNodes(double t) const;

  Jacobian DerivOfRotVecMult(double t, const Vector3d& v, bool inverse) const;
private:
  NodeSpline::Ptr euler_;

  // Internal calculations for the conversion from euler rates to angular
  // velocities and accelerations. These are done using the matrix M defined
  // here: http://docs.leggedrobotics.com/kindr/cheatsheet_latest.pdf
  static MatrixSXd GetM(const EulerAngles& xyz);

  static MatrixSXd GetMdot(const EulerAngles& xyz, const EulerRates& xyz_d);

  Jacobian GetDerivMwrtNodes(double t, Dim3D dim) const;

  Jacobian GetDerivMdotwrtNodes(double t, Dim3D dim) const;

  JacRowMatrix GetDerivativeOfRotationMatrixWrtNodes(double t) const;

  static MatrixSXd GetRotationMatrixBaseToWorld(const EulerAngles& xyz);

  static Eigen::Quaterniond GetQuaternionBaseToWorld(const EulerAngles& pos);

  static Vector3d GetAngularAccelerationInWorld(State euler);

  static Vector3d GetAngularVelocityInWorld(const EulerAngles& pos,
                                            const EulerRates& vel);

  JacobianRow GetJac(double t, Dx deriv, Dim3D dim) const;
  Jacobian jac_wrt_nodes_structure_;
};

} /* namespace towr */

#endif /* TOWR_VARIABLES_ANGULAR_STATE_CONVERTER_H_ */