Trajectory Tracking for Autonomous Vehicles based on Frenet Frame

Abstract

This paper investigates a trajectory tracking control problem of autonomous vehicles. Existing methods can suffer from complex control algorithms and a lack of tracking stability at high speed, which negatively affects tracking performance. This study decouples the vehicle's motion by considering the Frenet frame and Frenet equations. A lateral control law based on the linear-quadratic-regulator (LQR) imposes the tracking errors to converge to zero stably and quickly, providing the optimal solution in real-time due to adaptive gains. Regarding the steady-state errors, they are eliminated through the correction of the feedforward term. Furthermore, the designed double proportional-integral-derivative (PID) controller realizes not only the longitudinal control but also the velocity tracking. By the proposed strategy, the tracking accuracy and stability can be enhanced regardless of the vehicle speed, verified by the simulation results from different driving scenarios.