Pursuit-evasion of an Evader by Multiple Pursuers

In this paper, we extend the well-studied results of the two-pursuer, single-evader differential game to any number of pursuers. The main objective of this investigation is to exploit the benefits of cooperation amongst the pursuers in order to reduce the capture time of the evader. Computational complexity is a chief concern as this problem would need to be solved in an online fashion, e.g., in the case of autonomous unmanned aerial vehicles. A new geometric approach to solving the game is introduced and analyzed, which changes the problem of optimizing over continuous domains to a discrete combinatoric optimization. While past efforts at solving multiple pursuer problems have suffered from the curse of dimensionality, the geometric algorithms put forth here are shown to be scalable. Categorization and removal of redundant pursuers is the primary means by which scalability is achieved. The solution of this problem serves as a stepping stone to more complex problems such as the M-pursuer N-evader differential game.