The Game of Two Identical Cars: An Analytical Description of the Barrier

In this study, a pursuit-evasion game of two players, known as a game of two identical cars, is examined. It is assumed that the game proceeds in a two-dimensional plane. Both players have a constant speed and a limited turn radius. The goal of the first player (pursuer) is to ensure that the second player (evader) enters the capture circle as quickly as possible. The goal of the evader is to avoid or delay capturing for as long as possible. The kinematics of both players are described using the same equations. Thus, the game has only one free parameter: capture radius. This study aims to provide an exhaustive analytical description of the barrier surface for all values of capture radius. Previously, Merz analytically investigated the barrier in a game of two identical cars. In this work, it was found that there is a certain critical value of the capture radius, above which the barrier is qualitatively different from Merz’s example. In addition, we obtained an explicit analytical description of the optimal feedback controls for the barrier.