Departmental Papers (ESE)

Abstract

In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent’s heading is updated using a local rule based on the average of its own heading plus the headings of its “neighbors.” In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent’s set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.

Document Type

Journal Article

Subject Area

GRASP

Date of this Version

June 2003

Comments

Copyright 2003 IEEE. Reprinted from IEEE Transactions on Automatic Control, Volume 48, Issue 6, June 2003, pages 988-1001.
Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=27134&puNumber=9

This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

Keywords

Cooperative control, graph theory, infinite products, multiagent systems, switched systems

Additional Files

j2.pdf (143 kB)
Correction to

Share

COinS
 

Date Posted: 15 November 2004

This document has been peer reviewed.