This paper presents a simple and systematic approach to steer an underwater vehicle model by considering two different cases: (i) when all actuators are functional, and (ii) when one actuator is not working. In first case, the model of an underwater vehicle is steered by employing a Lie bracket extension of the original system and the resulting feedback law is as a composition of a standard stabilizing feedback control for the extended system and a periodic continuation of a parameterized solution to an open loop, finite horizon control problem stated in the logarithmic coordinates of flows. In second case (which represents a physical example where second level Lie bracket is necessary for controllability), the original system is decomposed into two subsystems; one subsystem, which is fifth dimensional, steered by a similar approach used in case (i) and the second subsystem, which is one dimensional, steered by using sinusoidal inputs. The mixture of both type of control is utilized to steer the actual system. The synthesis method is general, in that it applies to a large class of drift free, completely controllable systems, for which the associated controllability Lie algebra is locally nilpotent.