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

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 Erdös-Renyi network, demonstrate the existence of stable coherent patterns that can be achieved only 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.

Active particle condensation by non-reciprocal and time-delayed interactions

“…For example, an individual agent of a flock can be slow enough to respond to a signal coming from its neighbour. This causes communication-delay [38,39,40,41]. It has been shown that in presence of a noise induced transition from translatory to rotatory motion of agents [42], the time-delayed communication among them can introduce further instabilities where the harmonically interacting agents can form dynamic clusters or swarms, with a high degree of polarity [38].…”

A Simple Proof of Asymptotic Consensus in the Hegselmann--Krause and Cucker--Smale Models with Normalization and Delay

“…Agent i's opinion is represented by the quantity x i = x i (t) ∈ R d , with d ∈ N the space dimension, which is a function of time t ≥ 0. For many applications in biological and socio-economical systems or control problems (for instance, swarm robotics [11,23]), it is natural to include a time delay in the model reflecting the time needed for each agent to receive information from other agents. We therefore assume that agents' communication takes place subject to a variable delay τ = τ (t) ≥ 0, i.e., agent i with opinion x i (t) receives at time t > 0 the information about the opinion of agent j in the form x j (t − τ (t)).…”

Swarm Shedding in Networks of Self-propelled Agents

“…Typically, such systems involve sharing speed and heading data directly among agents, and are somewhat limited in their dynamics, e.g., to flocking, where consensus forms around a network-wide velocity. On the other hand, physically inspired models, where collective motion emerges from the more basic interplay of position-dependent forces and self-propulsion energy, have typically assumed global, homogeneous, or lattice communication topology [39][40][41][42][43][44][45] . Since the latter class of models derive from basic physical principles, they showcase a broader spectrum of emergent motion patterns, and they can more easily incorporate, e.g., active-matter dynamics 15,43 and collective motion on arbitrary surfaces 46 .…”

“…To make progress, we consider a generic system of mobile agents moving under the influence of self-propulsion, friction, and pairwise interaction forces 41,43,47,49 mediated through a network 42,48 . In the absence of interactions, each swarmer will tend to a fixed speed, which balances its self-propulsion and friction but has no preferred direction 46 .…”