Collective motion patterns of swarms with delay coupling: theory and experiment

TL;DR

This paper investigates how delay-coupled interactions influence pattern formation in swarms, combining theoretical modeling, simulations, and experimental validation in mixed-reality large-scale swarm systems.

Contribution

It introduces a model and experimental setup for delay-coupled swarms, revealing stable patterns dependent on delay and network connectivity, with analysis of heterogeneity effects.

Findings

Stable coherent patterns emerge only with delay coupling.

Pattern stability is robust to network connectivity and agent heterogeneity.

Experimental results confirm delay-induced pattern formation.

Abstract

The formation of coherent patterns in swarms of interacting self-propelled autonomous agents is a subject of great interest in a wide range of application areas, ranging from engineering and physics to biology. In this paper, we model and experimentally realize a mixed-reality large-scale swarm of delay-coupled agents. The coupling term is modeled as a delayed communication relay of position. Our analyses, assuming agents communicating over an Erdos-Renyi network, demonstrate the existence of stable coherent patterns that can only be achieved with delay coupling and that are robust to decreasing network connectivity and heterogeneity in agent dynamics. We also show how the bifurcation structure for emergence of different patterns changes with heterogeneity in agent acceleration capabilities and limited connectivity in the network as a function of coupling strength and delay. Our results are verified through simulation as well as preliminary experimental results of delay-induced pattern formation in a mixed-reality swarm.