Evasion as a team against a faster pursuer

In this paper, we present an open-loop formulation of a single-pursuer-multiple-evader pursuit-evasion game. In this game, the pursuer attempts to minimize the total capture time of all the evaders while the evaders, as a team, cooperate to maximize this time. The information pattern considered here is conservative towards the evaders. One important advantage of this open-loop approach over the geometrical approach in the literature is that it provides guaranteed survival time of the evader team for all initial conditions, without the limitation that the pursuer must capture the evaders in a specific sequence. Another advantage of this approach is that under the open-loop framework, we can quickly generate controls for multiple players that the classical Hamilton-Jacobi-Isaacs (HJI) approach, due to its computational infeasibility, cannot handle. We also relax the conservatism inherent in this open-loop formulation by presenting an iterative open-loop scheme of the evaders' evasion strategy. Simulations for the open-loop, the iterative open-loop as well as the HJI approaches are presented, with the results on performance analyzed and discussed.