Singularities and symmetry breaking in swarms

Abstract

A large-scale system consisting of self-propelled particles, moving under the directional alignment rule ͑DAR͒, can often self-organize to an ordered state that emerges from an initially rotationally symmetric configuration. It is commonly accepted that the DAR, which leads to effective long-range interactions, is the underlying mechanism contributing to the collective motion. However, in this paper, we demonstrate that a swarm under the DAR has unperceived and inherent singularities. Furthermore, we show that the compelled symmetry-breaking effects at or near the singularities, as well as the topological connectivity of the swarm in the evolution process, contribute fundamentally to the emergence of the collective behavior; and the elimination or weakening of singularities in the DAR will induce an unexpected sharp transition from coherent movement to isotropic dispersion. These results provide some insights into the fundamental issue of collective dynamics: What is the underlying mechanism causing the spontaneous symmetry breaking and leading to eventual coherent motion?

Accelerating consensus of self-driven swarm via adaptive speed

“…In addition, it is not economic to accelerate the consensus process merely by expanding the horizon radius, which implies higher requirement on both technology and the hardware cost. Considering the variability of particle speed [16,17], we propose a new consensus strategy which can effectively shorten the convergence time compared with the classical Vicsek model.…”

Consensus of Switched Multiagent Systems under Relative State Constraints

“…The definition of consensus implies that all the agents shall converge to a common value using a distributed interaction among these agents [3,4]. The practical applications of consensus are diverse and can be found in many fields, such as biology, physics, control systems, and robotics [5][6][7][8][9][10][11]. The consensus problem was first discussed for first order [12][13][14][15] and then generalized to second order [16,17], general linear dynamics [18,19], and nonlinear dynamics [20,21] in communication networks and sensor networks.…”

Fixed‐Time Consensus of Multi‐Agent Systems with Directed and Intermittent Communications

“…In the collective behaviors of multi-agent systems [1][2][3][4], the consensus problem has received considerable attention due to its wide applications, such as rendezvous, flocking [5], swarming [6,7], formation control and estimation of sensor networks [8][9][10][11]. One of the main tasks in consensus is to design distributed control protocols with some required performance [12][13][14][15][16][17], for example, the finite-time consensus, i.e., design a kind of protocols with finite settling time when exact control performance is required.…”