This paper concerns the low-speed maneuvering of autonomous ground vehicles. A novel guidance method is introduced based on the fluid flow analogy; in this approach, both path topology and motion reference are derived at a single step. Motion control then results from obtaining a best fit to the fluid motion distribution taking account of three constraints: boundary avoidance, rigidity of the vehicle and non-holonomic velocity constraints due to the steering system. Combined with weighted-least-squares fitting, an analytical solution is obtained for the steering angle. The methodology has the advantage of being applicable to both low-speed precision maneuvering and for dynamic control at highway speeds.