We study the problem of allocating many mobile robots for the execution of a pre-defined sweep schedule in a known two-dimensional environment, with applications toward search and rescue, coverage, surveillance, monitoring, pursuit-evasion, and so on. The mobile robots (or agents) are assumed to have one-dimensional sensing capability with probabilistic guarantees that deteriorate as the sensing distance increases. In solving such tasks, a time-parameterized distribution of robots along the sweep frontier must be computed, with the objective to minimize the number of robots used to achieve some desired coverage quality guarantee or to maximize the probabilistic guarantee for a given number of robots. We propose a max-flow based algorithm for solving the allocation task, which builds on a decomposition technique of the workspace as a generalization of the well-known boustrophedon decomposition. Our proposed algorithm has a very low polynomial running time and completes in under two seconds for polygonal environments with over $10^5$ vertices. Simulation experiments are carried out on three realistic use cases with randomly generated obstacles of varying shapes, sizes, and spatial distributions, which demonstrate the applicability and scalability our proposed method.

翻译：我们研究了在已知二维环境中，为执行预定义扫掠调度而分配大量移动机器人的问题，其应用涵盖搜索救援、覆盖、监控、监视、追捕-规避等场景。假设移动机器人（或智能体）具有一维感知能力，其概率保障随感知距离增加而降低。在解决此类任务时，必须计算沿扫掠前沿的时变机器人分布，目标是最小化实现所需覆盖质量保障所需的机器人数量，或最大化给定数量机器人的概率保障。我们提出了一种基于最大流算法的分配方法，该方法建立在对工作空间进行分解的技术之上，该技术是经典的牛耕式分解的推广。所提算法具有极低的多项式运行时间复杂度，对于具有超过10^5个顶点的多边形环境，计算时间不到两秒。我们在三个现实用例中进行了仿真实验，其中包含随机生成的形状、尺寸和空间分布各异的障碍物，实验结果证明了所提方法的适用性和可扩展性。