Bearing measurements,as the most common modality in nature, have recently gained traction in multi-robot systems to enhance mutual localization and swarm collaboration. Despite their advantages, challenges such as sensory noise, obstacle occlusion, and uncoordinated swarm motion persist in real-world scenarios, potentially leading to erroneous state estimation and undermining the system's flexibility, practicality, and robustness.In response to these challenges, in this paper we address theoretical and practical problem related to both mutual localization and swarm planning.Firstly, we propose a certifiable mutual localization algorithm.It features a concise problem formulation coupled with lossless convex relaxation, enabling independence from initial values and globally optimal relative pose recovery.Then, to explore how detection noise and swarm motion influence estimation optimality, we conduct a comprehensive analysis on the interplay between robots' mutual spatial relationship and mutual localization. We develop a differentiable metric correlated with swarm trajectories to explicitly evaluate the noise resistance of optimal estimation.By establishing a finite and pre-computable threshold for this metric and accordingly generating swarm trajectories, the estimation optimality can be strictly guaranteed under arbitrary noise. Based on these findings, an optimization-based swarm planner is proposed to generate safe and smooth trajectories, with consideration of both inter-robot visibility and estimation optimality.Through numerical simulations, we evaluate the optimality and certifiablity of our estimator, and underscore the significance of our planner in enhancing estimation performance.The results exhibit considerable potential of our methods to pave the way for advanced closed-loop intelligence in swarm systems.

翻译：轴承测量作为自然界中最常见的感知模态，近年来在多机器人系统中受到广泛关注，以增强互定位与集群协作。尽管具有诸多优势，但在实际场景中仍面临传感器噪声、障碍物遮挡以及集群运动不协调等挑战，这些因素可能导致状态估计错误，削弱系统的灵活性、实用性和鲁棒性。针对这些挑战，本文研究了与互定位和集群规划相关的理论与实际问题。首先，我们提出了一种可认证的互定位算法，该算法具有简洁的问题表述与无损凸松弛特性，无需初始值即可实现全局最优的相对位姿恢复。随后，为探究检测噪声与集群运动对估计最优性的影响，我们对机器人间空间关系与互定位的相互作用机制进行了全面分析，并开发了一种与集群轨迹相关的可微度量指标，以显式评估最优估计的抗噪性能。通过为该度量指标建立有限且可预计算的阈值，并据此生成集群轨迹，可在任意噪声条件下严格保证估计最优性。基于这些发现，我们提出了一种基于优化的集群规划器，在考虑机器人间可视性与估计最优性的同时生成安全平滑的轨迹。通过数值仿真，我们评估了所提估计器的最优性与可认证性，并强调了规划器在提升估计性能中的重要作用。结果表明，该方法具有极大潜力，可为集群系统的高级闭环智能奠定基础。