Cyclic pursuit without coordinates: Convergence to regular polygon formations

Maxim Arnold, Yuliy Baryshnikov, Daniel Liberzon

Research output: Contribution to journalConference articlepeer-review

6 Citations (Scopus)


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 languageEnglish
Article number7040359
Pages (from-to)6191-6196
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Issue numberFebruary
Publication statusPublished - Jan 1 2014
Externally publishedYes
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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