Cyclic pursuit without coordinates: Convergence to regular polygon formations

Maxim Arnold; Yuliy Baryshnikov; Daniel Liberzon

doi:10.1109/CDC.2014.7040359

Cyclic pursuit without coordinates: Convergence to regular polygon formations

Maxim Arnold, Yuliy Baryshnikov, Daniel Liberzon

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We study a multi-agent cyclic pursuit model where each of the identical agents moves like a Dubins car and maintains a fixed heading angle with respect to the next agent. We establish that stationary shapes for this system are regular polygons. We derive a sufficient condition for local convergence to such regular polygon formations, which takes the form of an inequality connecting the angles of the regular polygon with the heading angle of the agents. A block-circulant structure of the system's linearization matrix in suitable coordinates facilitates and elucidates our analysis. Our results are complementary to the conditions for rendezvous obtained in earlier work [Yu et al., IEEE Trans. Autom. Contr., Feb. 2012].

Original language	English (US)
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6191-6196
Number of pages	6
Edition	February
ISBN (Electronic)	9781479977468
DOIs	https://doi.org/10.1109/CDC.2014.7040359
State	Published - 2014
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/Territory	United States
City	Los Angeles
Period	12/15/14 → 12/17/14

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Online availability

10.1109/CDC.2014.7040359

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Arnold, M., Baryshnikov, Y., & Liberzon, D. (2014). Cyclic pursuit without coordinates: Convergence to regular polygon formations. In 53rd IEEE Conference on Decision and Control,CDC 2014 (February ed., pp. 6191-6196). [7040359] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7040359

Cyclic pursuit without coordinates : Convergence to regular polygon formations. / Arnold, Maxim; Baryshnikov, Yuliy ; Liberzon, Daniel.

53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 6191-6196 7040359 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Arnold, M, Baryshnikov, Y & Liberzon, D 2014, Cyclic pursuit without coordinates: Convergence to regular polygon formations. in 53rd IEEE Conference on Decision and Control,CDC 2014. February edn, 7040359, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., pp. 6191-6196, 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 12/15/14. https://doi.org/10.1109/CDC.2014.7040359

Arnold M, Baryshnikov Y , Liberzon D. Cyclic pursuit without coordinates: Convergence to regular polygon formations. In 53rd IEEE Conference on Decision and Control,CDC 2014. February ed. Institute of Electrical and Electronics Engineers Inc. 2014. p. 6191-6196. 7040359. (Proceedings of the IEEE Conference on Decision and Control; February). doi: 10.1109/CDC.2014.7040359

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Cyclic pursuit without coordinates: Convergence to regular polygon formations

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