Modelling Emergent Swarm Behavior Using Continuum Limits for Environmental Mapping

Abstract

Robotic swarms are comprised of simple, individual robots but can collectively accomplish complex tasks through frequent interactions with other robots and the environment. One pertinent objective for swarms is mapping unknown, potentially hazardous environments. We show that even without communication or localization, the emergent behavior of a swarm observed at one area can be used to infer the presence of obstacles in an unknown environment. The main body of this work focuses on how partial differential equation (PDE) models of emergent swarm behavior can be derived by applying continuum limits to approximate discrete-time rules for individual robots in continuous-time. We illustrate our approach by demonstrating how obstacles can be located by comparing swarm observations to a base library of PDE models. As supported in this work, the PDE models accurately capture identifying characteristics of the emergent behavior and are solved in a few seconds allowing for fast feature identification.