Adversarial Fragmentation of Robotic Teams Operating Under Reynolds' Rules with Bounded Communication Radius

Abstract

In this paper, we examine a class of counter-swarm problems featuring small teams of antagonists. The objective of the counter-swarm algorithm is to minimize the connectivity of the team using a single adversarial pursuer. We devise a novel criterion for the connectivity of an undirected graph, based on an augmentation of its Laplacian. We prove theoretically how the criterion depends on the size and the connectivity of the graph. Next, we pose optimal control problems which use this criterion as well as the eigenvalues of the Laplacian. We show how the properties of the team dynamics and their interaction with the pursuer define an envelope within which the pursuer achieves the desired objectives.