Kinematics of four-wheel-steering vehicles

In this paper, we review some aspects of the kinematical theory of four-wheel-steering (4WS) vehicles and present some new results and conclusions that we came across during our research on the subject. In a first paragraph, we compare the turning radius of two-wheel-steering (2WS) and 4WS vehicles and draw some interesting conclusions on the manoeuvring ability of either of them. In a second paragraph, we present a general kinematical analysis of 4WS vehicles by considering either the simplified two-wheel (bicycle) model or the more complete four-wheel model. In this analysis, we assume the sideslip angles of the wheels as non-negligible and we derive the general formulae relating the steering angles of the wheels to the geometrical data of the vehicle. By taking as zero the steering angles of the rear wheels, we derive from the above relations the well-known formulae of Ackermann-Jeantaux that are valid for 2WS vehicles.