2021
DOI: 10.1007/s10957-021-01899-8
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Revisiting a Three-Player Pursuit-Evasion Game

Abstract: We consider the game of a holonomic evader passing between two holonomic pursuers. The optimal trajectories of this game are known. We give a detailed explanation of the game of kind’s solution and present a computationally efficient way to obtain trajectories numerically by integrating the retrograde path equations. Additionally, we propose a method for calculating the partial derivatives of the Value function in the game of degree. This latter result applies to differential games with homogeneous Value.

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Cited by 6 publications
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“… Nath and Ghose (2022) and Zhang and Zha (2018) conducted pursuit-evasion game research under certain objectives or constraints in the two-dimensional plane. The differential game strategy in optimal control ( Fuchs et al, 2018 ; Szots et al, 2021 ; Yan et al, 2021 ; Zhang et al, 2023 ) was utilized to solve the three-player pursuit-evasion game. Wang et al (2020) , Wan et al (2021) , and Hamidoglu (2023) each applied different intelligent algorithms to achieve evasion, respectively.…”
Section: Introductionmentioning
confidence: 99%
“… Nath and Ghose (2022) and Zhang and Zha (2018) conducted pursuit-evasion game research under certain objectives or constraints in the two-dimensional plane. The differential game strategy in optimal control ( Fuchs et al, 2018 ; Szots et al, 2021 ; Yan et al, 2021 ; Zhang et al, 2023 ) was utilized to solve the three-player pursuit-evasion game. Wang et al (2020) , Wan et al (2021) , and Hamidoglu (2023) each applied different intelligent algorithms to achieve evasion, respectively.…”
Section: Introductionmentioning
confidence: 99%