Collective motion of ring-coupled planar particles

James Jeanne, Naomi Ehrich Leonard, Derek Paley

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

28 Scopus citations

Abstract

We study stabilization of collective motion of N constant-speed, planar particles with less than all-to-all coupling. Our interest is in circular motions of the particles around the fixed center of mass of the group, as has been studied previously with all-to-all coupling. We focus on coupling defined by a ring, i.e., each particle communicates with exactly two other particles. The Kuramoto model of coupled oscillators, restricted to "ring" coupling, serves as our model for controlling the relative headings of the particles. Each phase oscillator represents the heading of a particle. We prove convergence to a set of solutions that correspond to symmetric patterns of the phases about the unit circle. The exponentially stable patterns are generalized regular polygons, determined by the sign of the coupling gain K.

Original languageEnglish (US)
Title of host publicationProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages3929-3934
Number of pages6
DOIs
StatePublished - Dec 1 2005
Event44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain
Duration: Dec 12 2005Dec 15 2005

Publication series

NameProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume2005

Other

Other44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
CountrySpain
CitySeville
Period12/12/0512/15/05

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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    Jeanne, J., Leonard, N. E., & Paley, D. (2005). Collective motion of ring-coupled planar particles. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 3929-3934). [1582775] (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1582775