Bifurcation analysis of a car and driver model negotiating a curve

The paper deals with the bifurcation analysis of a validated simple model describing a vehicle+driver negotiating a curve. The mechanical model of the car has two degrees of freedom and the related equations of motion contain the nonlinear tyre characteristics. The driver is described by a well known model proposed in the literature. Bifurcation analysis is adopted as the proper procedure for analysing steady-state cornering. Two independent parameters referring to running conditions, namely steering angle and forward speed, are varied. The importance of properly computing steady-state equilibria is highlighted. The general result is the following: the effect of a skilled driver is to broaden the basin of attraction of stable equilibria and, in some cases, to stabilize originally unstable behaviours. Moreover, the proposed analysis allows one to better understand which behaviours should be avoided at the design stage in order to increase safety.