Path following control of an underactuated AUV: a prescribed performance and tunable prescribed time-based approach

This paper proposes a prescribed performance and tunable prescribed time-based approach for the horizontal path following control of an underactuated autonomous underwater vehicle with the influence of unknown disturbances. Firstly, an improved piecewise prescribed performance function and its corresponding error transformation function considering the sign of initial errors are introduced into line-of-sight guidance to confine the kinematics tracking errors to the prescribed performance within a tunable prescribed time. Subsequently, an adaptive dynamics controller is designed by combining the asymmetric time-varying barrier Lyapunov function and the tunable prescribed-time stability theory. Furthermore, the entire path following controller is demonstrated to be tunably prescribed-time stable and both position tracking errors and heading tracking error are consistently kept within the predefined constraints. Finally, three groups of comparative numerical simulations are presented to demonstrate the validity and outperformance of the designed control scheme and approach.