Pursuit evasion game of two players under an external flow field

In this paper, we address the differential game of pursuit and evasion between two players in the presence of an external flow field. It is assumed that the two players move on the plane at fixed but different speeds, and they are both agile. That is, they steer by choosing at each instant their direction of travel and abrupt heading changes are allowed. The external flow field is approximated by a time-invariant affine function. By utilizing standard techniques from differential game theory, we characterize the regions of initial conditions that lead to capture, as well as the regions that result in evasion when the two players act optimally. We derive the optimal strategies of the pursuer and the evader within the capture regions. Finally, we present numerical simulations of the resulting pursuer and evader trajectories for several values of the parameters of the external flow field.