Shapes of cyclic pursuit and their evolution

Yuliy Baryshnikov, Cheng Chen

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

Abstract

We study the geometry of a 2-dimensional cyclic pursuit problem where n identical mobile agents modeled as unicycles are driven by a distributed control law. The agent i pursuits the agent i + 1 modulo n with the same constant forward speed. We propose, for the first time, a stable relative (1 : n)-periodic trajectory (RPT) for the polygonal chain formed by the system with a sufficiently large n. Unlike regular polygon, the polygonal chain evolves into the shape of figure-eight while the system follows this RPT. The shape of the figure-eight can be approximated by closed Euler elastica. We show several geometrical and dynamical properties of this polygonal chain such as curve length and configuration precession. In addition, it reveals that the rotation number of an unbroken polygonal chain is a geometric invariant when it converges to a stable formation.

Original languageEnglish
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2561-2566
Number of pages6
ISBN (Electronic)9781509018376
DOIs
Publication statusPublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

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All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

Cite this

Baryshnikov, Y., & Chen, C. (2016). Shapes of cyclic pursuit and their evolution. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 2561-2566). [7798648] (2016 IEEE 55th Conference on Decision and Control, CDC 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798648