Autonomous underwater vehicles (AUVs) are powerful instruments that enable the exploration of the ocean. In recent years, AUVs have been developed considerably. Trajectory tracking control, which has been a major research focus for many decades due to its variety of applications, is one of the key advancements in the AUV technology. This paper presents six trajectory tracking control methods: PID (proportion integration differentiation) control, fuzzy control, adaptive control, sliding mode control, backstepping control, and neural network control. A few novel methods for trajectory tracking control are also introduced. First, the concept of trajectory tracking control for an AUV and the related basic theories are explained. Then, several methods that are currently used for tracking control are presented. The advantages and limitations of these methods are identified by evaluating the characteristics of the methods. Finally, on the basis of a summary of several main methods, the future development of the trajectory tracking control of AUVs is discussed.

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