Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves

Derek A. Paley, Naomi Ehrich Leonard, Rodolphe J. Sepulchre

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

14 Scopus citations

Abstract

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 speed around fixed beacons.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5067-5072
Number of pages6
ISBN (Print)1424401712, 9781424401710
DOIs
StatePublished - 2006
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: Dec 13 2006Dec 15 2006

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
CountryUnited States
CitySan Diego, CA
Period12/13/0612/15/06

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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    Paley, D. A., Leonard, N. E., & Sepulchre, R. J. (2006). Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 5067-5072). [4177474] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/cdc.2006.377462