Objectives The safety of towing large ships to designated sea areas is of great significance for maritime navigation. However, traditional towing operations, which rely on manual scheduling, face challenges in complex marine environments. The towing system is characterized by non-linearity, large inertia, and under-actuation, making it vulnerable to external disturbances. This research aims to enhance the disturbance rejection performance of underactuated autonomous tugboats during large ship towing, aiming to ensure the safe navigation of the towing system along the planned path.

Methods Firstly, a three-degree-of-freedom coupled motion mathematical model of the towing system is established based on the ship MMG model, taking into account the surge, sway, and yaw motions of the ships in the horizontal plane. This model comprehensively considers the external disturbances and towing forces acting on the towed ship and the tugboat, providing a solid foundation for the design of subsequent control strategies. Secondly, a towed line-of-sight (TLOS) guidance method suitable for towing navigation is proposed. This method calculates the desired heading of the towed ship based on the target path deviation, the position, and heading of the towed ship. It converts the path-tracking problem into speed and heading control problems, thereby simplifying the control process. Then, a hierarchical anti-disturbance control strategy (HAD-CS) is designed. In the control layer of the towed ship, a top-level anti-disturbance control method combining linear active disturbance rejection control (LADRC) and sliding mode control (SMC) is designed. LADRC is used to control the heading of the towed ship by calculating the desired tow-cable angle based on the heading deviation and compensating for the heading disturbance. SMC based on the extended state observer (ESO-SMC) is used to control the longitudinal speed by observing and compensating for external disturbances, outputting the required longitudinal force. The output of the top-level control, which includes the desired tow-cable angle and force, is then transmitted to the bottom-level tugboat controller.In the control layer of the tugboat, a bottom-level anti-disturbance control method based on ESO-SMC is designed. The output of the top-level anti-disturbance control is used as the input to the bottom-level control. Considering the constraints of the tow-cable and thrusters, the method designs separate heading and speed controllers for the tugboat. For heading control, a sliding-mode surface is designed based on the heading error, and the control law is derived by estimating the disturbance. For speed control, a sliding-mode surface is designed based on the speed error, and the control law is derived by estimating the longitudinal disturbance.

Results Simulation experiments are carried out to compare the proposed HAD-CS with the existing single-level anti-disturbance control strategy (SAD-CS). The results show that both control strategies can follow the reference path. However, the HAD-CS shows better performance. In terms of path-tracking performance, the average lateral error of the towed ship under the HAD-CS is 1.448 m, while under the SAD-CS it is 1.743 m. The path-keeping performance of the towed ship under the HAD-CS improves by about 16.9% compared with the SAD-CS. In the presence of sudden constant disturbances, the HAD-CS ensures that the towed ship remains on the desired path, whereas the SAD-CS cannot. In terms of heading-keeping performance, during turns and in the presence of sudden disturbances, the HAD-CS enables the heading angles of the towed ship and the tugboat to converge to the target heading more quickly, with smaller overshoots. The average heading error of the towed ship decreases by 34.6%, and that of the tugboat decreases by 51.9%. In terms of speed-keeping performance, under the SAD-CS, the speeds of the two-ship towing system fluctuate greatly, especially during turns and in the presence of sudden disturbances. In contrast, under the HAD-CS, the speed error of the tugboat decreases by 52.2%, and that of the towed ship decreases by 68%. The ships can quickly converge to the predetermined speed with smaller fluctuations.

Conclusions The proposed HAD-CS can effectively compensate for the disturbances acting on the towed ship and the tugboat due to external environmental factors. It significantly improves the anti-disturbance ability of the towing system, verifying the feasibility of autonomous tugboats towing large ships. This research provides a theoretical reference for the application of autonomous towing by tugboats. Future research can focus on developing a more accurate tow-cable model, fully considering the impact of tow-cable motion on the system and external environmental disturbances, and introducing neural network methods to estimate disturbances to further enhance the anti-disturbance performance of the hierarchical anti-disturbance control strategy.