Bifurcation Analysis of a Nonlinear Vehicle Model on Banked Road

Towards the transition to automated driving, lateral stability of the vehicle represents a key requirement to guarantee the safety of passengers and vulnerable road users, especially during emergency operating conditions where nonlinearities arise. The present paper aims at investigating the effect of road banking angle on vehicle plane motion stability. To perform this analysis, a pure lateral nonlinear double track model is numerically derived for an oversteering vehicle. Lateral load transfer and its distribution among the axles are included for exploiting the tyre saturation region. The stability analysis is conducted by searching for the vehicle steady-state conditions and deriving the linearised equations around the equilibrium points. Moreover, the phase-plane plot is adopted to draw the states trajectories and to identify potential unstable regions. Finally, the bifurcation analysis as function of the road banking angle is investigated to highlight possible change of the phase portrait topology. The results show that a saddle-node bifurcation may occur when the vehicle is negotiating a certain level of bank road angle, affecting the vehicle yaw stability region.