A non-linear, reduced-dimension steering controller is derived through a sliding mode control theory for an automobile with unknown parameters driving on a course consisting of smoothly connected arcs. A specific, headway viewpoint is introduced to define deviations from the course, and the controller is proven stable and robust. Stationaly values are calculated analytically. Simulation results are given to demostrate a good performance of the proposed controller. Clothoid connections of arcs further improve the performance.