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Multiplayer Pursuit-Evasion Games in Three-Dimensional Flow Fields

A Correction to this article was published on 22 March 2019

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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.

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  • 22 March 2019

    Unfortunately, the acknowledgement text was not submitted during the acceptance of the manuscript.


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Correspondence to Wei Sun.

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This work has been supported by NSF award CMMI-1662542.

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Sun, W., Tsiotras, P. & Yezzi, A.J. Multiplayer Pursuit-Evasion Games in Three-Dimensional Flow Fields. Dyn Games Appl 9, 1188–1207 (2019).

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  • Multiplayer pursuit-evasion
  • Flow field
  • Differential game
  • Reachable set
  • Level set method