SE(n)++: An Efficient Solution to Multiple Pose Estimation Problems

In robotic applications, many pose problems involve solving the homogeneous transformation based on the special Euclidean group {\mathrm{ SE}}(n). However, due to the nonconvexity of {\mathrm{ SE}}(n) , many of these solvers treat rotation and translation separately, and the computational efficiency is still unsatisfactory. A new technique called the {\mathrm{ SE}}(n)++ is proposed in this article that exploits a novel mapping from {\mathrm{ SE}}(n) to {\mathrm{ SO}}(n + 1). The mapping transforms the coupling between rotation and translation into a unified formulation on the Lie group and gives better analytical results and computational performances. Specifically, three major pose problems are considered in this article, that is, the point-cloud registration, the hand-eye calibration, and the {\mathrm{ SE}}(n) synchronization. Experimental validations have confirmed the effectiveness of the proposed {\mathrm{ SE}}(n)++ method in open datasets.