Lanekeeping at the Limits of Handling: Stability via Lyapunov Functions and a Comparison With Stability Control

Abstract

Lanekeeping assistance systems and stability control systems both seek to control the yaw behavior of the vehicle. However, lanekeeping systems are typically thought of as linear systems, while stability control systems are explicitly designed to work at the limits of handling. In order to bring these two systems together, there is a need to investigate lanekeeping up to and beyond the limits of handling. This paper presents a nonlinear tire model suitable for analyzing the behavior of a lanekeeping system at all points along the tire curve and a method for finding common quadratic Lyapunov functions to prove stability. The results show that the lanekeeping system is stable well into the nonlinear tire region. This stability holds even under changes in the lanekeeping gain and the understeering/oversteering characteristics of the vehicle. The results suggest that future safety systems could benefit from incorporating integrated lanekeeping and stability control functionality.