Time optimal trajectory design for unmanned underwater vehicle

Abstract

This paper presents the design of time optimal trajectories for the depth control of an unmanned underwater vehicle. Its approach stems from the fact that the minimum time to destination can be attained when the thruster(s) of the vehicle always operates at maximum thrust levels during the maneuver. Therefore, the nonlinear second order differential equation of depth motion of the vehicle with appropriate constant thrust forces will be analytically solved to find the time optimal trajectories. These resulting trajectories are explicit functions which offer a solution for achieving the shortest travel time provided that a robust trajectory tracking controller is used along. The paper also presents the design of trajectory tracking controller using the sliding mode method. It is shown that this controller forces the vehicle to track the designed time optimal trajectories very well, even with uncertainties. Its robustness can be guaranteed if bounds of the uncertainties are known. The effectiveness of the proposed designs will be demonstrated via simulation results.