Maintaining a robust communication network plays an important role in the success of a multi-robot team jointly performing an optimization task. A key characteristic of a robust multi-robot system is the ability to repair the communication topology itself in the case of robot failure. In this paper, we focus on the Fast Biconnectivity Restoration (FBR) problem, which aims to repair a connected network to make it biconnected as fast as possible, where a biconnected network is a communication topology that cannot be disconnected by removing one node. We develop a Quadratically Constrained Program (QCP) formulation of the FBR problem, which provides a way to optimally solve the problem. We also propose an approximation algorithm for the FBR problem based on graph theory. By conducting empirical studies, we demonstrate that our proposed approximation algorithm performs close to the optimal while significantly outperforming the existing solutions.

翻译：维持鲁棒通信网络在多机器人团队协同执行优化任务中起着关键作用。多机器人系统鲁棒性的一个重要特征是在机器人发生故障时能够自主修复通信拓扑结构。本文聚焦于快速双连通性恢复（FBR）问题，旨在以最快速度将连通网络修复为双连通网络——即移除任意单个节点仍能保持连通的通信拓扑。我们提出了该问题的二次约束规划（QCP）模型，实现了问题的最优求解。同时，基于图论理论设计了FBR问题的近似算法。实验研究表明，我们提出的近似算法在性能上接近最优解，且显著优于现有方案。