Pride of Lions and Man Differential Game
E. Garcia, D. W. Casbeer, A. Von Moll, M. Pachter
Published in Conference on Decision and Control, 2020
A reach-avoid differential game with multiple players is considered in this paper. A group of defenders is in charge of capturing a spy before it leaves the game set. This paper addresses cooperation among the defenders which protect a circular area on interest and try to intercept an intelligent adversary/intruder. The optimal strategies for each team, the defenders team and the spy, are obtained. These strategies and the Value function are obtained in analytical and explicit form. Furthermore, it is verified that the Value function is continuously differentiable and it is the solution of the Hamilton-Jacobi-Isaacs equation. Finally, the Barrier surface that separates the winning regions of each team is explicitly obtained as well. Illustrative examples show the Barrier surface cross-sections of this high dimensional differential game.