Lateral stability analysis of on-road vehicles using the concept of Lyapunov exponents

This paper deals with the application of the concept of Lyapunov exponents in vehicle lateral stability analysis. The constructive nature of the available methods for calculating Lyapunov exponents as the `invariant´ measure of the dynamics is the main advantage of this concept. The vehicle model has two degrees of freedom (2-DOF), and its non-linearity is caused by the third-order polynomial expression between the sideslip forces on the the tires and the tire sideslip angles. In this paper, firstly, the concept of Lyapunov exponents and the standard algorithm to calculate them are presented. Then, by applying this concept to the case of a straight-line motion, the lateral stability region of the vehicle model is estimated. Moreover, the effects of driving conditions such as the vehicle longitudinal velocity, road friction and steering angle on the stability region are investigated. The comparison of the results obtained by the concept of Lyapunov exponents with those given in literature by simulation based methods verifies the effectiveness of this concept for vehicle lateral stability analysis.