Stability analysis of one-dimensional asynchronous swarms

Coordinated dynamical swarm behavior occurs when certain types of animals forage for food or try to avoid predators. Analogous behaviors can occur in engineering systems such as in groups of autonomous mobile robots or air vehicles. In this paper we characterize swarm "cohesiveness" as a stability property and provide conditions under which convergence can be achieved for an asynchronous swarm with swarm members that have proximity sensors and neighbor position sensors that only provide delayed position information. Such stability analysis is fundamental to understand the coordination mechanisms for groups of autonomous vehicles or robots where inter-member communication channels are less than perfect.