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A Two-Pursuer One-Evader Game with Equal Speed and Finite Capture Radius

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Abstract

In this paper, a two-pursuer one-evader game in the plane is considered. All the agents have simple motion and the same speed. As opposed to the game with superior pursuers, capture can occur in finite time only by defining a nonzero capture radius and for a subset of initial game states. Such a set is characterized and the full game solution is provided. In particular, the value function of the game and explicit expressions of the closed-loop optimal strategies of all the agents are derived. The results are validated via numerical simulations, comparing the optimal control actions with alternative strategies for both the evader and the pursuers.

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Acknowledgements

This work has been supported by the Italian Ministry for Research in the framework of the 2017 Program for Research Projects of National Interest (PRIN), Grant No. 2017YKXYXJ.

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Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, Via Roma 56, Siena, 53100, Italy

    Marco Casini & Andrea Garulli

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  1. Marco Casini
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  2. Andrea Garulli
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Contributions

Marco Casini: Conceptualization, Methodology, Software, Writing - review and editing. Andrea Garulli: Conceptualization, Methodology, Validation, Writing - original draft.

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Correspondence to Marco Casini.

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Casini, M., Garulli, A. A Two-Pursuer One-Evader Game with Equal Speed and Finite Capture Radius. J Intell Robot Syst 106, 77 (2022). https://doi.org/10.1007/s10846-022-01780-4

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