Collective Motion of Self-Propelled Particles: Stabilizing Symmetric Formations on Closed Curves

Derek Paley, Naomi Ehrich Leonard and Rodolphe Sepulchre

Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, December 2006, pp. 5067-5072.
We provide feedback control laws to stabilize formations of multiple, unit speed particles on smooth, convex, and closed curves with definite curvature. As in previous work we exploit an analogy with coupled phase oscillators to provide controls which isolate symmetric particle formations that are invariant to rigid translation of all the particles. In this work, we do not require all particles to be able to communicate; rather we assume that inter-particle communication is limited and can be modeled by a fixed, connected and undirected graph. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. The methodology is demonstrated using a superellipse, which is a type of curve that includes circles, ellipses, and rounded rectangles. These results can be used in applications involving multiple autonomous vehicles that travel at constant, arbitrary speed particles around fixed beacons.

(7.2 MB pdf)
Back to home page
Copyright 2007 IEEE. 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 to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.