Robust Policies for a Multiple-Pursuer Single-Evader Differential Game

Analysis of the pursuit–evasion differential game consisting of multiple pursuers and single evader with simple motion is difficult due to the well-known curse of dimensionality. Policies have been proposed for this scenario, and we show that these policies are global Stackelberg equilibrium strategies. However, we also show that they are not saddle-point equilibria in the feedback sense. The argument is twofold: cases where the saddle-point condition is violated and cases where the strategy profiles are not time consistent (subgame perfect). The issue of capturability is explored, and sufficient conditions for guaranteed capture are provided. A new pursuit policy is proposed which guarantees capture while also providing an upper bound for capture time. The evader policy corresponding to the global Stackelberg equilibrium is shown to provide a lower bound for capture time. Thus, these policies are robust from the pursuer and evader perspectives, respectively, should they implement them. Several other interesting pursuit and evasion policies are explored and compared with the robust policies in a series of experiments.