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.

中文翻译：

---

SE(n)++：多姿态估计问题的有效解决方案

在机器人应用中，许多位姿问题涉及求解基于特殊欧几里得群的齐次变换 ${\mathrm{ SE}}(n)$ . 但由于非凸 ${\mathrm{ SE}}(n)$ ，其中许多求解器将旋转和平移分开处理，计算效率仍然不能令人满意。一种新技术称为 ${\mathrm{ SE}}(n)++$在这篇文章中提出了一个新的映射 ${\mathrm{ SE}}(n)$到 ${\mathrm{ SO}}(n + 1)$ . 该映射将旋转和平移之间的耦合转换为李群上的统一公式，并提供更好的分析结果和计算性能。具体来说，本文考虑了三个主要的位姿问题，即点云配准、手眼标定和 ${\mathrm{ SE}}(n)$同步。实验验证证实了所提出的方案的有效性 ${\mathrm{ SE}}(n)++$开放数据集中的方法。