Designing discrete-time control-based strategies for pursuit-evasion games on the plane

Abstract

Two-player discrete-time pursuit-evasion games are proposed with control-based strategies on the plane, where each player's position is determined by the discrete-time version of the kinematic equation related to the moving structure of vehicles. In this regard, the first game is built in a one-target fashion where the high-speed pursuer tries to reach the running evader in optimal discrete time, whereas the second game is constructed from a two-target perspective where the evader becomes an attacker whose ultimate aim is to build a control-based strategy to capture the high-speed pursuer who follows the shortest tracking policy within his target region. Each player's winning and losing strategies are designed under certain playability conditions. Later, the main results are generalized for players sharing various discrete-time speeds during the game. The motivation of the study is to investigate the losing and winning strategies of the evader against the high-speed pursuer, who tries to capture his opponent in optimal discrete time on the plane. Numerical experiments are performed on four different unmanned aerial vehicles (UAVs) flying at the same altitude with various airspeeds and turning radii, where several capture scenarios and control-based strategies for each UAV are constructed according to the main results.