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A controller is developed for underactuated surface ships with only surge force and yaw moment available to globally asymptotically track a reference trajectory generated by a suitable virtual ship in a frame attached to the ship body. The reference trajectory is allowed too be a curve including a straight line. The control development is based on Lyapunov's direct method and backstepping technique, and utilizes several properties of ship dynamics and their interconnected structure. Numerical simulations are provided to validate the effectiveness of the proposed controller.
Do et al. (Sun,) studied this question.