Evasion with terminal constraints from a group of pursuers using a matrix game formulation

Abstract

We consider a class of planar pursuit-evasion games with multiple pursuers and a single evader. The evader must reach a target set while avoiding the pursuers which relay the pursuit among themselves. We model this multi-player dynamic game as a two-player multi-stage game. In particular, all the pursuers are modeled as one entity, which we refer to as the super-pursuer, which can deploy only one pursuer of choice at each instant of time. We discretize the decision space of the players and formulate a zero-sum matrix game between the super-pursuer and the evader. In the construction of the matrix game, we explore a myopic solution approach to the game against one that is more far-sighted. In particular, the stage payoffs are constructed in two different ways, namely, with a planning horizon of one stage, and with a planning horizon which is taken to be the remaining stages of the game. We compare the performance of the evasion policies that are obtained in these two cases, against pursuers who engage in relay pursuit. Finally, we compare the pursuit policies obtained from the multi-stage matrix games using extensive numerical simulations.