The Role of Memory in Stabilizing Swarms

In this paper, we analyze and evaluate swarm interactions using varying amounts of kinetic memory, defined as the stored velocity states for n discrete time steps in the past. We show that kinetic memory can play a key role in the dynamics of biological and artificial aggregations. It is reasonable to suppose that individuals possess a memory of the immediate past and use this information to their advantage when swarming. Similarly, in wireless robotic applications, the storage of past movements requires nocommunication and can be used to stabilize aggregations. In fact, in wireless robotic applications, the communication rate between nearby individuals is more limited than in many biological applications, so the time step used to update an individual's velocity is greater. In this paper, we develop and analyze updating schemes for interacting individuals in a swarm. We show that we can stabilize and destabilize coherent translating structures using suitable adjustments to the updating scheme. Using this framework, we design an updating scheme to provide maximum stability for coherent structures that arise from a three-zone swarming model. Finally, we verify the effectiveness of our updating methodology using realistic QualNet simulations of a swarm of networked robots.