An asymmetric version of the two car pursuit-evasion game

In this paper we consider a differential game of pursuit and evasion involving two players with constant, but different, speeds, and different maneuverability constraints. Specifically, the evader has limited maneuverability, while the pursuer is completely agile. This problem is an asymmetric version of the well-known Game of Two Cars. The aim of this paper is to derive the optimal strategies of the two players and characterize areas of initial conditions that lead to capture if the pursuer acts optimally, and areas that guarantee evasion regardless of the pursuer's strategy. It is shown that the problem reduces to a special version of Zermelo's Navigation Problem (ZNP) for the pursuer. Therefore, the well-known ZNP solution can be used to validate the results obtained through the differential game framework as well as to characterize the time-optimal trajectories. The results are directly applicable to collision avoidance problems.