Asymptotic Trajectory Tracking of Underactuated Non-minimum Phase Marine Vessels

Abstract

This paper presents a trajectory tracking scheme for a class of underactuated non-minimum phase marine vessels. Through proper coordinates transformations, the vessels tracking model can be transformed into two-input-two-output strict-feedback form for which general backstepping method can be applicable to solve the control problem. To avoid possible singularity problem in the recursive control design, an AMO (asymptotic modification of orientation) concept is applied. In this case, the vessels are forced to track this modified trajectory instead of directly tracking the predefined reference trajectory. Since the vessels’ tracking model is transformed into two-input-two-output strict-feedback form with invertible control gain matrix, the non-minimum phase problem can be easily handled by the proposed method. Proposed tracking method can guarantee the asymptotic stability of closed-loop system in terms of polar coordinates. Simulation studies are also carried out to demonstrate the effectiveness of presented tracking scheme.