Autonomous underwater vehicles (AUVs) operating in dynamic ocean environments suffer from significant challenges due to model uncertainties and external disturbances, arising from factors such as hydrodynamic variability, sensor noise, and environmental forces. With this in mind, this paper designs a robust formation tracking control scheme that incorporates a distributed adaptive sliding mode predictive controller (DASMPC). Specifically, an auxiliary stabilizable control law based on adaptive sliding mode surface (ASMC) and extended state observer (ESO) is first designed. Considering that the traditional ESO-ASMC approach has a slow convergence rate and unsatisfied stability characteristics, a rolling time horizon optimization technique is incorporated, and the new ESO-DASMPC control scheme is designed, which greatly improves the stability and the convergence of the formation system while inheriting the robustness of the existing auxiliary controller. The recursive feasibility and stability of the ESO-DASMPC algorithm are guaranteed by constructing the constraints of the auxiliary controller and associated Lyapunov function. Finally, numerical experiments studies are conducted and the simulation results validate the superiority of control performance and the robustness of the proposed scheme.

The current state of underwater navigation equipment is very expensive. Even with traditional acoustic navigation methods, the total cost of autonomous underwater vehicle (AUV) cluster navigation will increase significantly with a set of underwater acoustic equipment with precisely timed beacons. To address the cost control issue of underwater cluster navigation, low-cost underwater cooperative navigation acoustic sensor research based on an implicit communication method was conducted. First, in three-dimensional inertial space, the azimuth and distance between the leader and follower were measured using Doppler shift and ultrasonic attenuation (DSUA). Additionally, the DSUA acoustic sensor was constructed, compared in terms of cost, and produced. Second, a variable formation and scalable underwater cooperative navigation and formation control method for DSUA-IVV is provided, based on the combination of the DSUA acoustic sensor and the virtual vector method to constrain the cluster control system. Lastly, to verify the performance of the formation using metrics such as formation control accuracy, position, and speed faults, simulation experiments were run on various formations and cluster numbers, proving the method’s efficacy. Sensitivity research was performed on the DSUA sensor to confirm its resilience and good stability in typical seawater settings. According to the simulation results, the navigation cost of the same scale is decreased by more than 12.6%, and the tracking error of the formation during the straight-line process is less than 0.04 m. The formation error during the formation transformation process is less than 0.7 m.