This paper presents a feasibility study of the robust predictive control with and without parameter adaptation for the design of an automatic steering system. The involved vehicle is a full-scale nonlinear model and the feedback is only on the lateral displacement unlike in the available studies where an additional feedback on the yaw rate is commonly used to improve the performance. The robustness feature is particularly motivated by variations in velocity, tyre-road contact and vehicle mass. The underlying control design is performed using a sensitivity function shaping oriented procedure that heavily borrows from the robust control culture. Intensive simulations are carried out to emphasize the performance of the proposed automatic steering system.