examples/slam/pose_graph_2d/pose_graph_2d_error_term.h

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: vitus@google.com (Michael Vitus)
//
// Cost function for a 2D pose graph formulation.

#ifndef CERES_EXAMPLES_POSE_GRAPH_2D_POSE_GRAPH_2D_ERROR_TERM_H_
#define CERES_EXAMPLES_POSE_GRAPH_2D_POSE_GRAPH_2D_ERROR_TERM_H_

#include "Eigen/Core"

namespace ceres {
namespace examples {

template <typename T>
Eigen::Matrix<T, 2, 2> RotationMatrix2D(T yaw_radians) {
  const T cos_yaw = ceres::cos(yaw_radians);
  const T sin_yaw = ceres::sin(yaw_radians);

  Eigen::Matrix<T, 2, 2> rotation;
  rotation << cos_yaw, -sin_yaw, sin_yaw, cos_yaw;
  return rotation;
}

// Computes the error term for two poses that have a relative pose measurement
// between them. Let the hat variables be the measurement.
//
// residual =  information^{1/2} * [  r_a^T * (p_b - p_a) - \hat{p_ab}   ]
//                                 [ Normalize(yaw_b - yaw_a - \hat{yaw_ab}) ]
//
// where r_a is the rotation matrix that rotates a vector represented in frame A
// into the global frame, and Normalize(*) ensures the angles are in the range
// [-pi, pi).
class PoseGraph2dErrorTerm {
 public:
  PoseGraph2dErrorTerm(double x_ab,
                       double y_ab,
                       double yaw_ab_radians,
                       const Eigen::Matrix3d& sqrt_information)
      : p_ab_(x_ab, y_ab),
        yaw_ab_radians_(yaw_ab_radians),
        sqrt_information_(sqrt_information) {}

  template <typename T>
  bool operator()(const T* const x_a,
                  const T* const y_a,
                  const T* const yaw_a,
                  const T* const x_b,
                  const T* const y_b,
                  const T* const yaw_b,
                  T* residuals_ptr) const {
    const Eigen::Matrix<T, 2, 1> p_a(*x_a, *y_a);
    const Eigen::Matrix<T, 2, 1> p_b(*x_b, *y_b);

    Eigen::Map<Eigen::Matrix<T, 3, 1>> residuals_map(residuals_ptr);

    residuals_map.template head<2>() =
        RotationMatrix2D(*yaw_a).transpose() * (p_b - p_a) - p_ab_.cast<T>();
    residuals_map(2) = ceres::examples::NormalizeAngle(
        (*yaw_b - *yaw_a) - static_cast<T>(yaw_ab_radians_));

    // Scale the residuals by the square root information matrix to account for
    // the measurement uncertainty.
    residuals_map = sqrt_information_.template cast<T>() * residuals_map;

    return true;
  }

  static ceres::CostFunction* Create(double x_ab,
                                     double y_ab,
                                     double yaw_ab_radians,
                                     const Eigen::Matrix3d& sqrt_information) {
    return (new ceres::
                AutoDiffCostFunction<PoseGraph2dErrorTerm, 3, 1, 1, 1, 1, 1, 1>(
                    new PoseGraph2dErrorTerm(
                        x_ab, y_ab, yaw_ab_radians, sqrt_information)));
  }

  EIGEN_MAKE_ALIGNED_OPERATOR_NEW

 private:
  // The position of B relative to A in the A frame.
  const Eigen::Vector2d p_ab_;
  // The orientation of frame B relative to frame A.
  const double yaw_ab_radians_;
  // The inverse square root of the measurement covariance matrix.
  const Eigen::Matrix3d sqrt_information_;
};

}  // namespace examples
}  // namespace ceres

#endif  // CERES_EXAMPLES_POSE_GRAPH_2D_POSE_GRAPH_2D_ERROR_TERM_H_