In this work a smoothly interpolating controller for autonomous vehicle steering is proposed. The paper concentrates on dealing with the parameter uncertainty which is introduced by variable speed. A further primary goal is the development of a non-linear controller in which the speed of response is dependent on the distance from the lane centre. A smoothly switching (interpolating) controller is employed where switching depends on the measured speed, and also on the deviation from course setpoint. In this way parameter variations caused by varying speed can be taken into account, and the trade-off between comfort and safety is also explicitly addressed; a higher gain is associated with larger tracking errors to ensure fast recovery from dangerous deviations (safety), while low gain is used when the tracking error is 'small' (comfort).