Fixed-time geometric tracking control of autonomous underwater vehicles on SE(3)

To achieve trajectory tracking with the high attitude maneuverability for autonomous underwater vehicles (AUVs) suffering from model uncertainties and unknown disturbances, a fixed-time geometric control scheme on SE(3) is proposed. Firstly, considering Euler angles and quaternion models lack globality or uniqueness, which restrict the ability to execute large-angle maneuvers of AUVs, the geometric controller is constructed on the special Euclidean group SE(3). Secondly, a novel configuration error function is proposed, which defines a promising configuration error vector to enhance the convergence performance of the AUV under large attitude errors. Then, a novel nonsingular terminal sliding mode (NTSM) based on error vectors is introduced, which boosts the convergence rate over the current NTSM by ensuring quick transient convergence both near and far from the origin. Finally, a robust fixed-time controller based on the designed NTSM is constructed that does not rely on exact model parameters. It can guarantee the almost global convergence of AUV tracking errors in a priori bounded time. Several numerical simulations are presented, demonstrating the superiority of the proposed control scheme in multiple aspects.