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

Jin Wu,Ming Liu,Yulong Huang,Chi Jin,Yuanxin Wu

Published 2020 in IEEE Transactions on Cybernetics

ABSTRACT

In robotic applications, many pose problems involve solving the homogeneous transformation based on the special Euclidean group <inline-formula> <tex-math notation="LaTeX">${\mathrm{ SE}}(n)$ </tex-math></inline-formula>. However, due to the nonconvexity of <inline-formula> <tex-math notation="LaTeX">${\mathrm{ SE}}(n)$ </tex-math></inline-formula>, many of these solvers treat rotation and translation separately, and the computational efficiency is still unsatisfactory. A new technique called the <inline-formula> <tex-math notation="LaTeX">${\mathrm{ SE}}(n)++$ </tex-math></inline-formula> is proposed in this article that exploits a novel mapping from <inline-formula> <tex-math notation="LaTeX">${\mathrm{ SE}}(n)$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">${\mathrm{ SO}}(n + 1)$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">${\mathrm{ SE}}(n)$ </tex-math></inline-formula> synchronization. Experimental validations have confirmed the effectiveness of the proposed <inline-formula> <tex-math notation="LaTeX">${\mathrm{ SE}}(n)++$ </tex-math></inline-formula> method in open datasets.

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