Time delay effects on vehicle-and-driver stability

The loss of vehicle stability is a major cause of road accidents, with over one million fatalities recorded yearly in the world. A complete mathematical characterisation of the behaviour of road vehicle-and-driver under the action of severe perturbations, e.g. wind gusts or evasive maneuvers, is still lacking. Studies on global stability of road vehicle-and-driver are in their infancy, offering numerous avenues for enhancing the active safety of vehicles, whether human-driven or automated. This paper aims to start providing a substantial contribution in the field. Considering a simple vehicle-and-driver model, a subcritical Hopf bifurcation is found at high forward speed, caused by the driver's delayed steering action. Both rectilinear and circular motions of the system are characterized by a saddle-type limit cycle. A region of attraction of stable equilibria of the system is thus computed, both numerically and with experimental tests performed at the driving simulator. Copyright (c) 2024 The Authors.