Abstract:
Objectives With the intensification of the global energy crisis and environmental degradation issues, the development of low-carbon shipping technology has become an inevitable trend in the transformation of the shipping industry. As a result, the application of the sail-assisted vehicles, which harness the power of wind energy, has gradually become a prominent research topic globally. However, despite the promising potential of sail-assisted vehicles, challenges such as time-varying marine environmental disturbances and limited signal transmission significantly affect their path following control performance. Traditional control strategies often struggle to address the complexities of ocean dynamics and communication constraints, resulting in reduced tracking accuracy and energy efficiency. To overcome these limitations, this study proposes an adaptive tracking control algorithm based on rotor rate regulation for the rotor-assisted vehicles, which utilize the Magnus effect generated by rotating drum sails to achieve efficient propulsion and possess advantages such as simple structure and strong environmental adaptability.
Methods Firstly, a modified guidance law is constructed by improving the traditional logic virtual ship (LVS) guidance principle. This improvement involves the incorporation of an intervention method based on a finite boundary circle, which effectively reduces the communication load of the guidance system. The modified guidance law ensures that when the vessel enters the coverage area of the boundary circle, the guidance signal is no longer updated, thus preventing unnecessary signal transmission and conserving communication resources. Meanwhile, to address the issue of actuator input saturation, a saturation compensation function is integrated into the guidance law, which helps to ensure that the system remains within the operational limits of the actuators, thus enhancing the robustness of the control system. Secondly, the radial basis function (RBF) neural networks are employed for the online approximation of the system uncertainties. The RBF neural networks can respond in real time to the changing dynamic conditions, thereby providing an effective mechanism to compensate for unmodeled dynamics or external disturbances that may affect the vessel’s tracking trajectory. To avoid the “explosion of computational complexity” inherent in traditional backstepping control, the dynamic surface control (DSC) technique is introduced. This technique simplifies the control law by using first-order filters, which significantly reduces the computational burden and prevents the growth of intermediate variables that would otherwise increase the computational complexity. Furthermore, a robust adaptive control algorithm is designed by combining neural damping and adaptive techniques. This is coupled with an integral event-triggered mechanism, which is particularly important in dealing with slight fluctuations in system states. Traditional event-triggered mechanisms, which rely on instantaneous state measurements, may fail to trigger updates in cases of minor state fluctuations, leading to long periods without signal updates, thus degrading the system’s closed-loop performance. The proposed integral event-triggered mechanism can effectively avoid long periods of non-triggering caused by minor state fluctuations. Its triggering effect is more natural and efficient, thus significantly reducing the frequent transmission of control commands and mechanical wear of actuators. Finally, the stability of the proposed control algorithm is rigorously analyzed using the Lyapunov theory to guarantee that all error signals are semi-global uniform and ultimately bounded (SGUUB). To validate the proposed control strategy, numerical simulations are conducted in the MATLAB, where the marine environmental disturbance under a sea state level of 4 is simulated based on the NORSOK wind spectrum and the JONSWAP wave spectrum.
Results The results of the simulations demonstrate that the proposed algorithm significantly enhances the path following performance of sail-assisted vehicles. The proposed algorithm exhibits high control accuracy and fast response, maintaining the position and heading errors within a range of \pm 3 m and \pm 5°, respectively. Notably, due to the introduction of the event-triggered mechanism and the servo systems, the control inputs remain within the allowable range of actuator operations and signal chattering is significantly reduced, effectively minimizing mechanical wear on the actuators. Additionally, the adaptive laws embedded in the control algorithm demonstrate effective convergence, ensuring that the system can reach a stable operating condition despite the dynamic disturbances present in the marine environment. The utilization of the proposed sail-assisted navigation strategy can achieve an 11.6% improvement in propulsion efficiency under a sea state level of 4, substantially reducing energy consumption and promoting sustainable maritime operations.
Conclusions The path following performance of the proposed system exhibits not only low communication load but also strong robustness, making it highly suitable for practical deployment in maritime navigation. The research findings provide a practical and feasible technical pathway for the green transformation of marine vessels, contributing to the development of more sustainable and energy-efficient shipping technologies. Therefore, the proposed control algorithm and sail-assisted strategy could play a vital role in advancing the future of green maritime transportation.