Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally intractable, since the decision space grows exponentially with the number of robots. In this paper, we present a novel approach for multi-robot planning on topological graphs using mixed-integer programming. Central to our approach is the notion of a dynamic topological graph, where edge weights vary dynamically based on the locations of the robots in the graph. We construct this graph using the critical features of the planning problem and the relationships between robots; we then leverage mixed-integer programming to minimize a shared cost that depends on the paths of all robots through the graph. To improve computational tractability, we formulated our optimization problem with a fully convex relaxation and designed our decision space around eliminating the exponential dependence on the number of robots. We test our approach on a multi-robot reconnaissance scenario, where robots must coordinate to minimize detectability and maximize safety while gathering information. We demonstrate that our approach is able to scale to a series of representative scenarios and is capable of computing optimal coordinated strategic behaviors for autonomous multi-robot teams in seconds.

翻译：针对复杂环境下的多机器人团队规划问题，特别是当团队需协同完成共同目标时，最优解在决策空间随机器人数量指数增长的情况下通常难以计算。本文提出一种基于混合整数规划的拓扑图多机器人规划新方法。该方法的核心是动态拓扑图的概念，其中边的权重根据图上机器人的位置动态变化。我们利用规划问题的关键特征及机器人间的关系构建该图，进而通过混合整数规划最小化所有机器人路径相关的共享成本。为提高计算可解性，我们通过完全凸松弛优化问题，并设计决策空间以消除对机器人数量的指数依赖。在多机器人侦察场景中（需协调降低可探测性、最大化安全性并收集信息）验证了该方法：其可扩展至一系列代表性场景，并能于数秒内为自主多机器人团队计算出最优协调策略行为。