Capturing a Dubins Car With a Differential Drive Robot

Abstract

In this paper, we study the problem of capturing a Dubins Car with a Differential Drive Robot in minimum time. The two vehicles are represented like unitary discs moving in the plane without obstacles. Both agents have the same maximum speed and a bounded turning ratio. We frame the problem as a pursuit-evasion game. The Differential Drive Robot plays as a pursuer and aims to capture the Dubins Car as soon as possible. The Dubins Car, on the contrary, takes the evader’s role and tries to avoid capture. Using differential game theory, we compute the players’ time-optimal motion strategies to accomplish their tasks and provide analytical expressions describing them. In particular, we reveal four singular surfaces in this game. Two evader’s dispersal surfaces (EDS) where the evader can choose between two controls and the pursuer must react accordingly, leading to trajectories with the same cost. One pursuer’s dispersal surface (PDS) where the evader must select its control based on the pursuer’s choice. And a transition surface (TS), where the DDR switches its controls. Some examples of the players’ time-optimal motion strategies are shown in numerical simulations.