A Discrete and Continuous Study of the Max-Chain-Formation Problem: Slow Down to Speed up

摘要: Robot coordination problems deal with systems consisting of many autonomous, but simple, mobile agents that try to achieve a common, complex task. The agents' capabilities depend on the exact model and task are typically very restricted. For example, there is usually no common coordinate system or sense direction, often have limited sensing capabilities. Among most basic well-studied type tasks GATHERING problems, in which initially scattered must gather at single point. CHAINFORMATION represent another important formation primitive. Here, take role communication relays that, initially, form winding chain connecting two base stations. move such becomes straight, allowing for more energy-efficient along relay chain. Both can be described as contracting: starting from an formation, they seek reach smaller, efficient structure. A natural complement extension where start dense extended covers much area possible. While some results about if grids rings, standard discrete continuous models Euclidean plane scarce. Our work introduces MAXFORM problem provides first analytical both case.