Backstepping sliding mode lane keeping control of lateral position error with dynamic of tire steering device

A kind of backstepping sliding mode control law was proposed to solve the lane keeping problem where the automatic driving system was simplified to be a kind of linear lateral dynamic model. And the dynamic response characteristic of tire steering system was described to be a first order system with a proper delay time constant. First, the complex system was divided into a relative accurate subsystem and an uncertain subsystem. Second, the proposed backstepping sliding mode method was proposed to eliminate the lateral position error which can make use of the advantage of sliding mode method that it can improve the robustness of the whole system. The backstepping strategy was adopted for the accurate inertial delay dynamic of tire steering system. Third, a kind of soft function was used to reduce the oscillation caused by sliding mode control. And a Lyapunov function was constructed to guarantee all signals of close loop system are stable. At last, 100 times of random numerical simulations were done to testify the rightness and stability of the proposed method applied in the situation that the tire coefficients are uncertain.