Multiple Pursuer Multiple Evader Differential Games

Authors

Eloy Garcia, Control Science Center of Excellence, Air Force Research Laboratory
David Casbeer, Control Science Center of Excellence, Air Force Research Laboratory
Alexander Von Moll, Control Science Center of Excellence, Air Force Research Laboratory
Meir Pachter, Air Force Institute of TechnologyFollow

Document Type

Article

Publication Date

11-2019

Abstract

In this paper an N-pursuer vs. M-evader team conflict is studied. The differential game of border defense is addressed and we focus on the game of degree in the region of the state space where the pursuers are able to win. This work extends classical differential game theory to simultaneously address weapon assignments and multi-player pursuit-evasion scenarios. Saddle-point strategies that provide guaranteed performance for each team regardless of the actual strategies implemented by the opponent are devised. The players' optimal strategies require the co-design of cooperative optimal assignments and optimal guidance laws. A representative measure of performance is proposed and the Value function of the game is obtained. It is shown that the Value function is continuous, continuously differentiable, and that it satisfies the Hamilton-Jacobi-Isaacs equation - the curse of dimensionality is overcome and the optimal strategies are obtained. The cases of N=M and N>M are considered. In the latter case, cooperative guidance strategies are also developed in order for the pursuers to exploit their numerical advantage. This work provides a foundation to formally analyze complex and high-dimensional conflicts between teams of N pursuers and M evaders by means of differential game theory.

Comments

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DOI

Version of record: 10.1109/tac.2020.3003840 ; arXiv:1911.03806

Source Publication

IEEE Transactions on Automatic Control

Recommended Citation

E. Garcia, D. W. Casbeer, A. Von Moll and M. Pachter, "Multiple Pursuer Multiple Evader Differential Games," in IEEE Transactions on Automatic Control, vol. 66, no. 5, pp. 2345-2350, May 2021, doi: 10.1109/TAC.2020.3003840.