Generalized n-Dimensional Rigid Registration: Theory and Applications
研究了高维欧氏空间中的广义刚体配准问题，推导出闭式线性最小二乘解，可生成配准协方差（旋转和平移的不确定性信息），在计算效率上优于传统SVD和LMI方法，并应用于机器人导航中的激光雷达建图。
The generalized rigid registration problem in high-dimensional Euclidean spaces is studied. The loss function is minimized with an equivalent error formulation by the Cayley formula. The closed-form linear least-square solution to such a problem is derived which generates the registration covariances, i.e., uncertainty information of rotation and translation, providing quite accurate probabilistic descriptions. Simulation results indicate the correctness of the proposed method and also present its efficiency on computation-time consumption, compared with previous algorithms using singular value decomposition (SVD) and linear matrix inequality (LMI). The proposed scheme is then applied to an interpolation problem on the special Euclidean group SE(n) with covariance-preserving functionality. Finally, experiments on covariance-aided Lidar mapping show practical superiority in robotic navigation.