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Multiplayer Pursuit-Evasion Games in Three-Dimensional Flow Fields

Author

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  • Wei Sun

    (University of Oklahoma)

  • Panagiotis Tsiotras

    (Georgia Institute of Technology)

  • Anthony J. Yezzi

    (Georgia Institute of Technology)

Abstract

In this paper, we deal with a pursuit-evasion differential game between multiple pursuers and multiple evaders in the three-dimensional space under dynamic environmental disturbances (e.g., winds, underwater currents). We first recast the problem in terms of partitioning the pursuer set and assign each pursuer to an evader. We present two algorithms to partition the pursuer set from either the pursuer’s perspective or the evader’s perspective. Within each partition, the problem is reduced into a multi-pursuer/single-evader game. This problem is then addressed through a reachability-based approach. We give conditions for the game to terminate in terms of reachable set inclusions. The reachable sets of the pursuers and the evader are obtained by solving their corresponding level set equations through the narrow band level set method. We further demonstrate why fast marching or fast sweeping schemes are not applicable to this problem for a general class of disturbances. The time-optimal trajectories and the corresponding optimal strategies can be retrieved afterward by traversing these level sets. The proposed scheme is implemented on problems with both simple and realistic flow fields.

Suggested Citation

  • Wei Sun & Panagiotis Tsiotras & Anthony J. Yezzi, 2019. "Multiplayer Pursuit-Evasion Games in Three-Dimensional Flow Fields," Dynamic Games and Applications, Springer, vol. 9(4), pages 1188-1207, December.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:4:d:10.1007_s13235-019-00304-4
    DOI: 10.1007/s13235-019-00304-4
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    References listed on IDEAS

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    1. Ibragimov, Gafurjan I. & Salimi, Mehdi & Amini, Massoud, 2012. "Evasion from many pursuers in simple motion differential game with integral constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 505-511.
    2. Efstathios Bakolas, 2014. "Optimal Guidance of the Isotropic Rocket in the Presence of Wind," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 954-974, September.
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    Cited by:

    1. Gafurjan Ibragimov & Azamat Holboyev & Tolanbay Ibaydullaev & Bruno Antonio Pansera, 2022. "Pursuit Differential Game with Slow Pursuers on the 1-Skeleton Graph of the Icosahedron," Mathematics, MDPI, vol. 10(9), pages 1-12, April.

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