Continuous surveillance of a spatial region using distributed robots and sensors is a well-studied application in the area of multi-agent systems. This paper investigates a practically-relevant scenario where robotic sensors are introduced asynchronously and inter-robot communication is discrete, event-driven, local and asynchronous. Furthermore, we work with lazy robots; i.e., the robots seek to minimize their area of responsibility by equipartitioning the domain to be covered. We adapt a well-known algorithm which is practicable and known to generally work well for coverage problems. For a specially chosen geometry of the spatial domain, we show that there exists a non-trivial sequence of inter-robot communication events which leads to an instantaneous loss of coverage when the number of robots exceeds a certain threshold. The same sequence of events preserves coverage and, further, leads to an equipartition of the domain when the number of robots is smaller than the threshold. This result demonstrates that coverage guarantees for a given algorithm might be sensitive to the number of robots and, therefore, may not scale in obvious ways. It also suggests that when such algorithms are to be verified and validated prior to field deployment, the number of robots or sensors used in test scenarios should match that deployed on the field.

翻译：使用分布式机器人和传感器对空间区域进行连续监视是多智能体系统领域中一个研究充分的应用。本文研究了一个实际相关场景：机器人传感器异步引入，机器人间通信具有离散、事件驱动、局部和异步特性。此外，我们使用懒惰机器人；即，机器人通过等分待覆盖区域来最小化其责任范围。我们改编了一个已知算法，该算法切实可行且通常能有效处理覆盖问题。针对特定空间域几何结构，我们证明存在一个非平凡的机器人间通信事件序列，当机器人数量超过一定阈值时，会导致覆盖瞬时损失。而当机器人数量小于该阈值时，相同的通信事件序列既能维持覆盖，又能实现区域的等分。这一结果表明，给定算法的覆盖保证可能对机器人数量敏感，因此可能无法以显而易见的方式扩展。这也表明，当此类算法在实际部署前需进行验证和确认时，测试场景中使用的机器人或传感器数量应与现场部署的数量相匹配。