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. 2025 Jan 9;25(2):351.
doi: 10.3390/s25020351.

ESO-Based Non-Singular Terminal Filtered Integral Sliding Mode Backstepping Control for Unmanned Surface Vessels

Jianping Yuan  1   2   3   4 , Zhuohui Chai  1 , Qingdong Chen  1 , Zhihui Dong  1   3 , Lei Wan  2
Affiliations

ESO-Based Non-Singular Terminal Filtered Integral Sliding Mode Backstepping Control for Unmanned Surface Vessels

Jianping Yuan et al. Sensors (Basel). .

Abstract

Aiming at the control challenges faced by unmanned surface vessels (USVs) in complex environments, such as nonlinearities, parameter uncertainties, and environmental perturbations, we propose a non-singular terminal integral sliding mode control strategy based on an extended state observer (ESO). The strategy first employs a third-order linear extended state observer to estimate the total disturbances of the USV system, encompassing both external disturbances and internal nonlinearities. Subsequently, a backstepping sliding mode controller based on the Lyapunov theory is designed to generate the steering torque control commands for the USV. To further enhance the tracking performance of the system, we introduce a non-singular terminal integral sliding mode surface with a double power convergence law and redesign the backstepping sliding mode controller for the USV heading control. Meanwhile, to circumvent the differential explosion issue in traditional backstepping control, we simplify the controller design by utilizing a second-order sliding mode filter to accurately estimate the differential signals of the virtual control quantities. Theoretical analysis and simulation results demonstrate that the proposed control algorithm improves the convergence speed, adaptive ability, and anti-interference ability in complex environments compared to traditional linear backstepping sliding mode control, thereby enhancing its engineering practicability. This research offers a more efficient and reliable method for precise heading control and path tracking of USVs in complex and dynamic environments.

Keywords: ESO; heading tracking; non-singular terminal sliding mode; path tracking; unmanned surface vessels.

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Conflict of interest statement

The authors declare no conflicts of interest.

Figures

Figure 1
Figure 1
Schematic of USV model motion coordinate system.
Figure 2
Figure 2
Controller structure diagram of this paper.
Figure 3
Figure 3
Power density spectrum of the noise added in Case 1.
Figure 4
Figure 4
Comparison of the tracking effect and error for Case 1. (a) Comparison of control effects under constant heading. (b) Comparison of tracking errors under constant heading. (c) Comparison of control effects under square heading. (d) Comparison of tracking errors under square headings.
Figure 5
Figure 5
Observation effect of ESO on total disturbance for Case 1.
Figure 6
Figure 6
Interference noise added in Case 2 for Case 1.
Figure 7
Figure 7
Comparison of tracking effect and error for Case 2. (a) Comparison of control effects under constant heading. (b) Comparison of tracking errors under constant heading. (c) Comparison of control effects under square heading. (d) Comparison of tracking errors under square headings.
Figure 7
Figure 7
Comparison of tracking effect and error for Case 2. (a) Comparison of control effects under constant heading. (b) Comparison of tracking errors under constant heading. (c) Comparison of control effects under square heading. (d) Comparison of tracking errors under square headings.
Figure 8
Figure 8
Observation effect of ESO on total disturbance for Case 2.
Figure 9
Figure 9
Comparison of USV linear path tracking results.
Figure 10
Figure 10
Comparison of USV linear path tracking errors.
Figure 11
Figure 11
Comparison of USV curve path tracking effectiveness.
Figure 12
Figure 12
Comparison of USV curve path tracking errors.
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