Dynamics of four-wheel-steering vehicles

Abstract

In this paper we present an optimised 3 degrees-of-freedom non-linear dynamic model of a four-wheel-steering (4WS) vehicle. As variables, we retain the lateral velocity V, the rolling velocity p and yaw velocity r. The front steer angle δf and rear steer angle δr are considered to be linear functions of the steering wheel angle θs and of dθs/dt, the proportionality parameters being k1f, k2f for δf and k1r, k2r for δr. The parameters k1f, k2f, k1r, k2r are optimised by use of the BOX mathematical algorithm. In a first optimisation loop we minimise the sideslip angle β of the vehicle and in a second optimisation loop we assure, that the resultant (taken in the centre of gravity of the vehicle) of all the transversal forces Fy applied on the wheels of the vehicle (reaction forces contained in the road plane), give a component Fyx along the longitudinal axis of the vehicle, that takes a non negative value. This assures, that the motor of the vehicle will not waste fuel to overcome resistance forces originating from the steering system of the vehicle. A numerical application is also presented for a 4WS vehicle negotiating a curve at constant velocity. The results are compared to those obtained by two models frequently used in the literature. The comparison testifies on the superiority of our model for the application presented here.