Stability of Controlled Road Vehicles: A Preliminary Fundamental Study

Abstract

A comparison of the lateral stability behaviour between an autonomous vehicle, a vehicle with driver and a vehicle without driver (fixed steering wheel) is made by introducing a simple mathematical model of a vehicle running on even road. The mechanical model of the vehicle 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. The autonomous vehicle has a virtual driver (robot) that behaves substantially like a human, but with its proper reaction time and gain. The road vehicle model has been validated. The study of vehicle stability has to be based on bifurcation analysis and a preliminary investigation is proposed here. The accurate computation of steady-state equilibria is crucial to study the stability of the three kinds of vehicles here compared. The stability of the bare vehicle without driver (fixed steering wheel) is studied in a rather complete way referring to a number of combinations of tyre characteristics. The (known) conclusion is that the understeering vehicle is stable at each lateral acceleration level and at each vehicle speed. The additional (partially unknown) conclusion is that the vehicle (model) with degradated tyres may exhibit a huge number of different bifurcations. The driver has many effects on the stability of the vehicle. One positive effect is to eliminate the many possible different equilibria of the bare vehicle and keep active one single equilibrium only. Another positive effect is to broaden the basin of attraction of stable equilibria (at least at relatively low speed). A negative effect is that, even for straight running, the driver seem introducing a subcritical Hopf bifurcation which limits the maximum forward speed of some understeering vehicles (that could run faster with fixed steering wheel). Both the mentioned positive and negative effects appear to be applicable to autonomous vehicles as well. Further studies could be useful to overcome the limitations on the stability of current autonomous vehicles that have been identified in the present research.