On recurrence of graph connectivity in Vicsek's model of motion coordination for mobile autonomous agents

Alireza Tahbaz-Salehi*, Ali Jadbabaie

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

24 Scopus citations

Abstract

In this paper we complete the analysis of Vicsek's model of distributed coordination among kinematic planar agents. The model is a simple discrete time heading update rule for a set of kinematic agents (or self-propelled particles as referred to by Vicsek) moving in a finite plane with periodic boundary conditions. Contrary to existing results in the literature, we do not make any assumptions on connectivity but instead prove that under the update scheme, the network of agents stays jointly connected infinitely often for almost all initial conditions, resulting in global heading alignment. Our main result is derived using a famous theorem of Hermann Weyl on equidistribution of fractional parts of sequences. We also show that the Vicsek update scheme is closely related to the Kuramoto model of coupled nonlinear oscillators.

Original languageEnglish (US)
Title of host publicationProceedings of the 2007 American Control Conference, ACC
Pages699-704
Number of pages6
DOIs
StatePublished - 2007
Event2007 American Control Conference, ACC - New York, NY, United States
Duration: Jul 9 2007Jul 13 2007

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2007 American Control Conference, ACC
Country/TerritoryUnited States
CityNew York, NY
Period7/9/077/13/07

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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