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A Comprehensive Differential Game Theoretic Solution to a Game of Two Cars

Author

Listed:
  • Ritwik Bera

    (Indian Institute of Technology Kanpur)

  • Venkata Ramana Makkapati

    (Georgia Institute of Technology)

  • Mangal Kothari

    (Indian Institute of Technology Kanpur)

Abstract

In this paper, a pursuit-evasion game involving two non-holonomic agents is examined using the theory of differential games. It is assumed that the two players move on the Euclidean plane with fixed but different speeds and they each have a lower bound on their achievable turn radii. Both players steer at each instant by choosing their turn radii value and directions of turn. By formulating the game as a game of kind, we characterize the regions of initial conditions that lead to capture as well as the regions that lead to evasion, when both the players play optimally. The game is then formulated as a game of degree to obtain time-optimal paths for the pursuer and evader inside a capture region. Besides, all possible scenarios are considered for both players that differ in speed ratios and maneuverability constraints. Solutions are provided for those cases using appropriate simulation parameters, which aid in understanding the characteristics of the game of two cars under a wide range of constraints.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1134-z
    DOI: 10.1007/s10957-017-1134-z
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    References listed on IDEAS

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    1. Ioannis Exarchos & Panagiotis Tsiotras & Meir Pachter, 2015. "On the Suicidal Pedestrian Differential Game," Dynamic Games and Applications, Springer, vol. 5(3), pages 297-317, September.
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    Cited by:

    1. 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.

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