This paper is dedicated to achieving scalable relative state estimation using inter-robot Euclidean distance measurements. We consider equipping robots with distance sensors and focus on the optimization problem underlying relative state estimation in this setup. We reveal the commonality between this problem and the coordinates realization problem of a sensor network. Based on this insight, we propose an effective unconstrained optimization model to infer the relative states among robots. To work on this model in a distributed manner, we propose an efficient and scalable optimization algorithm with the classical block coordinate descent method as its backbone. This algorithm exactly solves each block update subproblem with a closed-form solution while ensuring convergence. Our results pave the way for distance measurements-based relative state estimation in large-scale multi-robot systems.

翻译：本文致力于利用机器人间的欧氏距离测量实现可扩展的相对状态估计。我们考虑为机器人配备距离传感器，并聚焦于该场景下相对状态估计的底层优化问题。我们揭示了该问题与传感器网络坐标实现问题之间的共通性。基于这一洞见，我们提出了一种有效的无约束优化模型来推断机器人间的相对状态。为分布式求解该模型，我们提出了一种高效且可扩展的优化算法，其核心框架采用经典的块坐标下降法。该算法通过闭式解精确求解每个块更新子问题，同时保证收敛性。我们的研究为基于距离测量的大规模多机器人系统相对状态估计铺平了道路。