Title :
Coherent Pattern Prediction in Swarms of Delay-Coupled Agents
Author :
Mier-y-Teran-Romero, Luis ; Forgoston, Eric ; Schwartz, Ira B.
Author_Institution :
Johns Hopkins Bloomberg Sch. of Public Health, Baltimore, MD, USA
Abstract :
We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatiotemporal scales of the swarm structures, as well as demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In particular, our studies show that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent.
Keywords :
bifurcation; delays; multi-agent systems; alignment transition; coherent pattern prediction; communication time delay; coupling amplitude; coupling strength; coupling-time delay plane; delay-coupled agents; dynamical behaviors; general swarm model; mean field approximation; noise intensity threshold; pattern bifurcation; self-propelling agents; spatiotemporal scales; swarm structures; Approximation methods; Bifurcation; Delay effects; Eigenvalues and eigenfunctions; Mathematical model; Noise; Autonomous agents; bifurcation; delay systems; nonlinear dynamical systems; pattern formation;
Journal_Title :
Robotics, IEEE Transactions on
DOI :
10.1109/TRO.2012.2198511