Isolation in Synchronized Drone Formations

This paper expands on a theoretical model that is used for aerial robots that are working cooperatively to complete a task. In certain situations, such as when multiple robots have catastrophic failures, the surviving robots could become isolated so that they never again communicate with another robot. We prove some properties about isolated robots flying in a grid formation, and we present an algorithm that determines how many robots need to fail to isolate at least one robot. Finally, we propose a strategy that eliminates the possibility of isolation altogether.