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 an objective function 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：在多机器人团队协作完成共同目标的复杂环境规划中，决策空间随机器人数量呈指数增长，导致此类规划问题的最优解在计算上具有难解性。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概念，其中边权重根据机器人在图中的位置动态变化。我们通过提取规划问题的关键特征及机器人间关系构建该图，进而利用混合整数规划最小化所有机器人路径相关的共享代价。为提升计算可解性，我们设计了具有完全凸松弛的目标函数，并通过消除决策空间对机器人数量的指数依赖进行优化。在多机器人侦察场景中测试该方法时，机器人需在信息采集过程中协调行动以最小化可探测性并最大化安全性。实验表明，该方法可扩展至一系列代表性场景，并在数秒内为自主多机器人团队计算出最优协调策略行为。