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Robust Policies for a Multiple-Pursuer Single-Evader Differential Game

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Abstract

Analysis of the pursuit–evasion differential game consisting of multiple pursuers and single evader with simple motion is difficult due to the well-known curse of dimensionality. Policies have been proposed for this scenario, and we show that these policies are global Stackelberg equilibrium strategies. However, we also show that they are not saddle-point equilibria in the feedback sense. The argument is twofold: cases where the saddle-point condition is violated and cases where the strategy profiles are not time consistent (subgame perfect). The issue of capturability is explored, and sufficient conditions for guaranteed capture are provided. A new pursuit policy is proposed which guarantees capture while also providing an upper bound for capture time. The evader policy corresponding to the global Stackelberg equilibrium is shown to provide a lower bound for capture time. Thus, these policies are robust from the pursuer and evader perspectives, respectively, should they implement them. Several other interesting pursuit and evasion policies are explored and compared with the robust policies in a series of experiments.

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Notes

  1. 1.

    M. Pachter et al. Two-on-One Pursuit, submitted to the Journal of Guidance, Control, and Dynamics, Aug 2018.

  2. 2.

    Von Moll et al. The Multi-Pursuer Single-Evader Game: A Geometric Approach, submitted to the Journal of Intelligent & Robotic Systems in September 2018.

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Correspondence to Alexander Von Moll.

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This paper is based on work performed at the Air Force Research Laboratory (AFRL) Control Science Center of Excellence. Distribution Unlimited. 19 Oct 2018. Case #88ABW-2018-5299. The views expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the United States Government.

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Von Moll, A., Pachter, M., Garcia, E. et al. Robust Policies for a Multiple-Pursuer Single-Evader Differential Game. Dyn Games Appl 10, 202–221 (2020). https://doi.org/10.1007/s13235-019-00313-3

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Keywords

  • Pursuit evasion
  • Differential game
  • Multiple pursuers
  • Robust

Mathematics Subject Classification

  • 49N70
  • 49N90
  • 49N75