The Obstacle Avoidance Pursuit-Evasion Game with A Non-Quadratic Performance Index Based on Polynomial Approximation

In this paper, the pursuit-evasion problem under obstacle environment between two wheeled robots is investigated by the Stackelberg game. To address this problem, a linear non-quadratic differential game theorem with the general form is proposed, supplying a unified framework to obtain the analytical nonlinear control strategies. The Lyapunov function with a similar non-quadratic form, as the solution to the Hamilton-Jacobi-Isaacs equation, is designed by polynomial approximation methods. Therefore, Stackelberg Equilibrium (SE) can be reached and the stability is guaranteed with the closed-loop feedback control laws. The experiments on two wheeled robots demonstrate the effectiveness of the SE strategies.