This paper investigates the lane keeping control and the lateral control of autonomous ground vehicles, robots or the like considering the road agency formation unit (RAFU) functions. A strategy based knowing the real position of several points of the trajectory is proposed to achieve the lateral control purpose and maintain the lane keeping errors within the prescribed performance boundaries. The RAFU functions are applied to achieve these goals. The stability of these functions, their applicability to approach any arbitrary trajectory and the easy control of the possible error made on the approximation are useful advantages in practice.