A smooth robust controller for the path following of underactuated surface vehicles under disturbances
DOI:
https://doi.org/10.54939/1859-1043.j.mst.CSCE9.2025.3-12Keywords:
Path-following with bounded tracking error; Underactuated surface vehicles; Adaptive control; Stability analysis.Abstract
Trajectory tracking for underactuated surface vehicles (USVs) is challenging due to disturbances, system uncertainties, and underactuation. This paper proposes a smooth robust controller for USVs operating under such conditions. A translational velocity-based guidance law is designed, combined with a control handpoint technique [9] and the introduction of a small auxiliary term into the tracking error. A smooth adaptive force controller is developed to drive the USV to follow the desired trajectory. Unlike sliding mode control, the proposed controller produces continuous control signals and does not require prior knowledge of disturbance bounds. Lyapunov stability theory and Barbalat’s lemma are employed to analyze stability. Simulations in Matlab–Simulink for different values of ε, compared with the controller in [17], demonstrate that the USV tracks the desired trajectory with a small error while maintaining smooth control forces and moments.
References
[1]. M. Li, C. Guo, and H. Yu, “Extended state observer-based integral line-of-sight guidance law for path following of underactuated unmanned surface vehicles with uncertainties and ocean currents”, International Journal of Advanced Robotic Systems, vol. 18, no. 3, (2021).
[2]. T. I. Fossen, “An adaptive line-of-sight (ALOS) guidance law for path following of aircraft and marine craft”, IEEE Transactions on Control Systems Technology, vol. 31, no. 6, (2023).
[3]. T. Yamasaki, K. Enomoto, H. Takano, Y. Baba, and S. N. Balakrishnan, “Advanced pure pursuit guidance via sliding mode approach for chase UAV”, AIAA Guidance, Navigation, and Control Conference and Exhibit, (2009).
[4]. H. Xu, T. I. Fossen, and C. Guedes Soares, “Uniformly semiglobally exponential stability of vector field guidance law and autopilot for path-following”, European Journal of Control, vol. 53, pp. 88–97, (2020).
[5]. Y. Su, L. Wan, D. Zhang, and F. Huang, “An improved adaptive integral line-of-sight guidance law for unmanned surface vehicles with uncertainties”, Applied Ocean Research, vol. 108, Art. no. 102488, (2021).
[6]. H. Zhang, X. Zhang, and R. Bu, “Sliding mode adaptive control for ship path following with sideslip angle observer”, Ocean Engineering, vol. 251, p. 111106, (2022).
[7]. S. Li, Z. Xu, J. Liu, and C. Xu, “Learning-based extended dynamic mode decomposition for addressing path-following problem of underactuated ships with unknown dynamics”, International Journal of Control, Automation and Systems, vol. 20, no. 12, pp. 4076–4089, (2022).
[8]. Q. V. Tran, C. Lee, J. Kim, and H. Q. Nguyen, “Robust bearing-based formation tracking control of underactuated surface vessels: An output regulation approach”, IEEE Transactions on Control of Network Systems, vol. 10, no. 4, pp. 2048–2059, (2023).
[9]. D. S. Cao and Q. V. Tran, “Adaptive path-following control of underactuated surface vessels subject to unknown disturbances with uniform bounded lateral motion”, International Journal of Control, Automation and Systems, vol. 23, (2025).
[10]. C. Paliotta, E. Lefeber, K. Y. Pettersen, J. Pinto, M. Costa, and J. T. de Figueiredo Borges de Sousa, “Trajectory tracking and path following for underactuated marine vehicles”, IEEE Transactions on Control Systems Technology, vol. 27, no. 4, pp. 1423–1437, (2019).
[11]. P. Aguiar et al., “Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty”, IEEE Transactions on Automatic Control, (2007).
[12]. R. A. Horn et al., Matrix Analysis, Cambridge University Press, (2012).
[13]. P. Ioannou and J. Sun, Robust Adaptive Control, Dover Publications, (2012).
[14]. T. I. Fossen, Handbook of Marine Craft Hydrodynamics and Motion Control, Wiley, (2011).
[15]. Cao Duc Sang et al., “Điều khiển di chuyển bám quỹ đạo cho phương tiện nổi tự hành hụt dẫn động dựa trên kỹ thuật mô hình dự báo phi tuyến”, Journal of Science and Tecnology, Hanoi University of Industry, Vol. 61, No. 3, (2025) (in Vietnamese).
[16]. Quoc Van Tran, Duc Sang Cao et al., “Robust path-following of underactuated surface vehicles with an arbitrarily small position error”, International Conference on Sustainability and Emerging Technologies for Smart Manufacturing (SETSM), (2025).
[17]. Cao Duc Sang, Tran Thang Le, and Khuyen Nguyen Trong, “A robust adaptive controller for underactuated ASVs in loose path-following with an added error and a new control handpoint”, Journal of Military Science and Technology, no. 106, pp. 18–27, (2025).
