Multi-agent coordination using nearest neighbor rules: revisiting the Vicsek model

TL;DR

This paper refines the mathematical understanding of the Vicsek model, demonstrating that multi-agent coordination occurs under a weaker connectivity condition than previously established, emphasizing the importance of eventual linking of all agents.

Contribution

It improves existing theoretical results by showing that eventual linking of all agents suffices for coordination, relaxing earlier connectivity requirements.

Findings

Coordination achieved under weak linking conditions

All agents eventually linked is sufficient for consensus

Refinement of the Vicsek model analysis

Abstract

Recently, Jadbabaie, Lin, and Morse (IEEE TAC, 48(6)2003:988-1001) offered a mathematical analysis of the discrete time model of groups of mobile autonomous agents raised by Vicsek et al. in 1995. In their paper, Jadbabaie et al. showed that all agents shall move in the same heading, provided that these agents are periodically linked together. This paper sharpens this result by showing that coordination will be reached under a very weak condition that requires all agents are finally linked together. This condition is also strictly weaker than the one Jadbabaie et al. desired.