Fixed-time velocity-free safe formation control of AUVs with actuator saturation and unknown disturbances

Abstract

This paper designs a fixed-time formation control law for multiple autonomous underwater vehicle (AUV) system (MAS) subjected to unmeasurable velocities, actuator saturation and time-varying disturbances. To address these challenges, the actuator saturation and time-varying disturbances are initially integrated into lumped disturbances, the initial step is to integrate actuator saturation and time-varying disturbances into lumped disturbances, followed by designing a fixed-time extended state observer (FTESO) to estimate the unavailable velocities and the lumped disturbances in fixed time. Moreover, a nonlinear filter is also utilized to eliminate the problem of computational explosion that arises due to derivatives in the controller design process. Additionally, a tan-type barrier Lyapunov function (TT-BLF) is presented to constrain the tracking errors within a predetermined time-varying constraint function. Then, a novel fixed-time formation control algorithm based on FTESO and TT-BLF is further designed to ensure that the formation tracking errors converge to a small neighborhood near origin in fixed time, and the fast formation task can be completed within a fixed time. Finally, the simulation experiments verify the effectiveness of the proposed controller.