Sliding Mode Control of Underactuated Vehicles in Three-Dimensional Space

This paper describes the derivation of a trajectory tracking sliding mode control law for general three-dimensional vehicle models with one degree of underactuation, which allows the control law to be applied to different vehicle models. The method is based on the transformation of the problem into a reduced order error dynamics. We then prove that the stabilization of the error dynamics results in tracking all the system states in the presence of bounded modeling uncertainties and disturbances. The method is then applied to a generic underwater vehicle model and simulated to verify its performance.