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

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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.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Ritwik Bera

  2. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0150, USA

    Venkata Ramana Makkapati

  3. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Mangal Kothari

Authors
  1. Ritwik Bera
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  2. Venkata Ramana Makkapati
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  3. Mangal Kothari
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Correspondence to Mangal Kothari.

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Communicated by Bruce A. Conway.

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Bera, R., Makkapati, V.R. & Kothari, M. A Comprehensive Differential Game Theoretic Solution to a Game of Two Cars. J Optim Theory Appl 174, 818–836 (2017). https://doi.org/10.1007/s10957-017-1134-z

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  • DOI: https://doi.org/10.1007/s10957-017-1134-z

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