Linear Quadratic Optimal Regulator for Steady State Drifting of Rear Wheel Drive Vehicle

Abstract

Drifting is a large sideslip cornering technique with counter steering, which is advantageous in some driving conditions where vehicle-handling capability over linear tire slip-friction characteristics is imperative. In this paper, the dynamics of a rear-wheel-drive (RWD) vehicle cornering at steady states was simplified using a single-track vehicle model. In addition, tire frictions in any slip conditions were estimated from the combination of the Pacejka’s magic formula and the modified Nicolas-Comstock tire model. A computer program was developed, on the basis of the equations of motion (EOMs) derived via the body-fixed coordinate so that the suitable cornering speed and its corresponding steady-state driving control inputs (the steering angle and rear wheel slip ratio) could be calculated automatically for any given radius of curvature and vehicle sideslip. The other set of EOMs was derived via the normal-tangential coordinate and then linearized so that the state space description could be constructed. Eventually, the linear quadratic optimal regulator was designed and simulated via MATLAB for various regulation problems where the initial condition of each individual state deviated from its desired steady-state value. According to the simulation results, the physical explanation of the control inputs can be used as guidance for adjusting vehicle behavior in manual driving.