Mutual localization stands as a foundational component within various domains of multi-robot systems. Nevertheless, in relative pose estimation, time synchronization is usually underappreciated and rarely addressed, although it significantly influences estimation accuracy. In this paper, we introduce time synchronization into mutual localization to recover the time offset and relative poses between robots simultaneously. Under a constant velocity assumption in a short time, we fuse time offset estimation with our previous bearing-based mutual localization by a novel error representation. Based on the error model, we formulate a joint optimization problem and utilize semi-definite relaxation (SDR) to furnish a lossless relaxation. By solving the relaxed problem, time synchronization and relative pose estimation can be achieved when time drift between robots is limited. To enhance the application range of time offset estimation, we further propose an iterative method to recover the time offset from coarse to fine. Comparisons between the proposed method and the existing ones through extensive simulation tests present prominent benefits of time synchronization on mutual localization. Moreover, real-world experiments are conducted to show the practicality and robustness.

翻译：互定位是多机器人系统各领域中的基础组成部分。然而，在相对位姿估计中，时间同步通常未得到充分重视且鲜有解决，尽管它显著影响估计精度。本文提出将时间同步引入互定位，以同时恢复机器人之间的时间偏移和相对位姿。在短时间内基于恒定速度假设，我们通过一种新颖的误差表示，将时间偏移估计与我们先前基于方位角的互定位方法相融合。基于该误差模型，我们构建了一个联合优化问题，并利用半定松弛（SDR）提供无损松弛。通过求解松弛后的问题，当机器人之间的时间漂移有限时，可实现时间同步与相对位姿估计。为了扩展时间偏移估计的应用范围，我们进一步提出一种迭代方法，从粗到细地恢复时间偏移。通过大量仿真测试将所提方法与现有方法进行比较，结果突显了时间同步对互定位的显著优势。此外，还进行了真实世界实验以展示其实用性和鲁棒性。