A pursuit game with range-only measurements

Abstract—We address a discrete-time, pursuit-evasion game with alternate moves played between two kinds of players: the pursuer and the evader. The pursuer wishes to capture the evader while the evader’s goal is to avoid capture. By capture, we mean that the distance between the players is no greater than 1 unit. We assume simple, first-order motion kinematics for the players. The pursuer can move with a step size of at most 1 unit while the evader can move with a maximum step size of β < 1 units. The pursuer is able to measure only its distance from the evader, before and after the evader’s move. We propose a capture strategy and first show that for the game played in R2, if β < 0.5, then a single pursuer captures the evader in finite time. Next, we show that if the game is played in R3 and if β < 0.5, then with a modified strategy, two identical cooperative pursuers capture the evader in finite time. Finally, we shed light on the performance of the capture strategy in the case of β ∈ [0.5, 1 [ and the case of sensing errors via simulations. We also present a simulation study of a version of this game with simultaneous moves. I