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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
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    References listed on IDEAS

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    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. Meir Pachter & Sean Coates, 2019. "The Classical Homicidal Chauffeur Game," Dynamic Games and Applications, Springer, vol. 9(3), pages 800-850, 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. 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.
    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)

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