IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v198y2023i3d10.1007_s10957-023-02278-1.html
   My bibliography  Save this article

The Game of Two Identical Cars: An Analytical Description of the Barrier

Author

Listed:
  • Maksim Buzikov

    (V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences)

  • Andrey Galyaev

    (V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences)

Abstract

In this study, a pursuit-evasion game of two players, known as a game of two identical cars, is examined. It is assumed that the game proceeds in a two-dimensional plane. Both players have a constant speed and a limited turn radius. The goal of the first player (pursuer) is to ensure that the second player (evader) enters the capture circle as quickly as possible. The goal of the evader is to avoid or delay capturing for as long as possible. The kinematics of both players are described using the same equations. Thus, the game has only one free parameter: capture radius. This study aims to provide an exhaustive analytical description of the barrier surface for all values of capture radius. Previously, Merz analytically investigated the barrier in a game of two identical cars. In this work, it was found that there is a certain critical value of the capture radius, above which the barrier is qualitatively different from Merz’s example. In addition, we obtained an explicit analytical description of the optimal feedback controls for the barrier.

Suggested Citation

  • Maksim Buzikov & Andrey Galyaev, 2023. "The Game of Two Identical Cars: An Analytical Description of the Barrier," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 988-1018, September.
  • Handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02278-1
    DOI: 10.1007/s10957-023-02278-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02278-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-023-02278-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. T. Tarnopolskaya & N. Fulton, 2010. "Synthesis of Optimal Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Turn Capabilities," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 367-390, February.
    2. Ritwik Bera & Venkata Ramana Makkapati & Mangal Kothari, 2017. "A Comprehensive Differential Game Theoretic Solution to a Game of Two Cars," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 818-836, September.
    3. Thomas L. Vincent & Douglas J. Sticht & Willy Y. Peng, 1976. "Aircraft Missile Avoidance," Operations Research, INFORMS, vol. 24(3), pages 420-437, June.
    4. Meir Pachter & Sean Coates, 2019. "The Classical Homicidal Chauffeur Game," Dynamic Games and Applications, Springer, vol. 9(3), pages 800-850, September.
    5. T. Tarnopolskaya & N. Fulton, 2009. "Optimal Cooperative Collision Avoidance Strategy for Coplanar Encounter: Merz’s Solution Revisited," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 355-375, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. T. Tarnopolskaya & N. Fulton & H. Maurer, 2012. "Synthesis of Optimal Bang–Bang Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Linear Speeds," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 115-144, October.
    2. A. Miele & T. Wang & J. A. Mathwig & M. Ciarcià, 2010. "Collision Avoidance for an Aircraft in Abort Landing: Trajectory Optimization and Guidance," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 233-254, August.
    3. Alireza Rangrazjeddi & Andrés D. González & Kash Barker, 2023. "Applied Game Theory to Enhance Air Traffic Control in 3D Airspace," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1125-1154, March.
    4. Erick J. Rodríguez-Seda & Dušan M. Stipanović & Mark W. Spong, 2016. "Guaranteed Collision Avoidance for Autonomous Systems with Acceleration Constraints and Sensing Uncertainties," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 1014-1038, March.
    5. T. Tarnopolskaya & N. Fulton, 2010. "Synthesis of Optimal Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Turn Capabilities," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 367-390, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02278-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.