Pattern-Acquisition in Finite, Heterogenous, Delay-Coupled Swarms

The self-organizing behavior of swarms of inter- acting particles or agents is a topic of intense research in fields extending from biology to physics and robotics. In this paper, we carry out a systematic study of how the stable spatio-temporal patterns of a swarm depend on the number of agents, in the presence of time-delayed interaction and agent heterogeneity. We show how a coherent pattern is modified as the number of agents varies, including the time required to converge to it starting from random initial conditions. We discuss the implications of our results for curve-tracking using autonomous robotic systems.