Lyapunov Exponent Based Stability Analysis for a High-Dimensional Nonlinear Vehicle System Under Extreme Condition

<div class="section abstract"><div class="htmlview paragraph">The vehicle stability assessment system is an indispensable component to ensure driving safety and enhance vehicle motion control, whether for automated or human-driven vehicles, especially in extreme operating conditions. However, the existing stability assessment methods tend to be conservative and often ignore the coupled longitudinal and lateral dynamics, as well as the nonlinear characteristics of tires. To evaluate the vehicle stability accurately and quickly, an 8-degree-of-freedom (DOF) vehicle dynamic model is constructed first, considering the nonlinear characteristics of tires through a physics-based approach. Subsequently, the vehicle and environment parameters are auto-tuned using Bayesian optimization with field test data. Based on the adjusted vehicle model, a Lyapunov exponent (LE) based vehicle stability analysis method is proposed to quantitatively assess the stability of the vehicle state and determine the corresponding stability boundary. Within this framework, 3-dimensional LEs, encompassing lateral velocity, yaw rate, and roll rate, are employed to comprehensively evaluate the stability of vehicle state. This approach ensures evaluation accuracy while reducing computational complexity. Experimental results demonstrate that the proposed method is validated by field test data from a typical scenario on the ice-snow road, i.e., evasive maneuver test, through the values of 3-dimensional LEs. Negative LE values indicate that the vehicle states fall within the stability boundary, while the magnitude of LE represents the degree of stability.</div></div>