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：我们研究在已知二维环境中为执行预定义的扫描计划而分配大量移动机器人的问题，其应用涵盖搜索与救援、覆盖、监视、监控、追捕-规避等领域。移动机器人（或智能体）被假定为具有一维感知能力，且该能力具有概率保证，随着感知距离的增加而下降。在解决此类任务时，必须计算沿扫描前沿的机器人时间参数化分布，其目标是最小化用于实现所需覆盖质量保证的机器人数量，或最大化给定数量机器人的概率保证。我们提出一种基于最大流的算法来解决此分配任务，该算法构建于工作空间分解技术之上，作为众所周知的牛耕式分解的推广。我们提出的算法具有极低的多项式运行时间，对于具有超过 $10^5$ 个顶点的多边形环境，可在两秒内完成。在三个基于现实的用例上进行了仿真实验，其中包含随机生成的形状、大小和空间分布各异的障碍物，这证明了我们提出方法的适用性和可扩展性。