Reinforcement Learning-Based Sliding Mode Control of Underwater Vehicles with Bow Rudders and X-Stern Rudders

Ren, Hao; Liu, Jie; Gao, Jian; Pan, Guang; Ding, Haixu

doi:10.3390/jmse14030321

Open AccessArticle

Reinforcement Learning-Based Sliding Mode Control of Underwater Vehicles with Bow Rudders and X-Stern Rudders

by

Hao Ren

¹,

Jie Liu

^1,*

,

Jian Gao

¹

,

Guang Pan

¹ and

Haixu Ding

²

¹

School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

²

Institute of Kunming Haiwei Electromechanical Technology, Kunming 650217, China

^*

Author to whom correspondence should be addressed.

J. Mar. Sci. Eng. 2026, 14(3), 321; https://doi.org/10.3390/jmse14030321

Submission received: 13 January 2026 / Revised: 30 January 2026 / Accepted: 2 February 2026 / Published: 6 February 2026

(This article belongs to the Section Ocean Engineering)

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Abstract

This paper addresses the motion control for an x-rudder underwater vehicle, which features a bow rudder and four independent x-shaped stern rudders. To achieve coordinated operation of bow and stern rudders of the x-rudder underwater vehicle, the motion controller is divided into two parts: dynamic controller and control distributor. A model-free sliding mode parameter optimization control algorithm for underwater vehicles based on reinforcement learning (RL) is proposed. The proposed algorithm integrates a fast terminal sliding mode controller based on prior model knowledge with a model-free, data-driven input derived from reinforcement learning, ensuring both efficiency and adaptability. The control allocator employs an improved sequential quadratic programming approach to tackle the mixed minimization problem, considering various evaluation criteria and constraints. The effectiveness of the proposed control method is validated through numerical simulations across different conditions, and its performance is compared in terms of accuracy, convergence, and computational complexity.

Keywords: X-rudder; model-free; parameter optimization; reinforcement learning; data-driven

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MDPI and ACS Style

Ren, H.; Liu, J.; Gao, J.; Pan, G.; Ding, H. Reinforcement Learning-Based Sliding Mode Control of Underwater Vehicles with Bow Rudders and X-Stern Rudders. J. Mar. Sci. Eng. 2026, 14, 321. https://doi.org/10.3390/jmse14030321

AMA Style

Ren H, Liu J, Gao J, Pan G, Ding H. Reinforcement Learning-Based Sliding Mode Control of Underwater Vehicles with Bow Rudders and X-Stern Rudders. Journal of Marine Science and Engineering. 2026; 14(3):321. https://doi.org/10.3390/jmse14030321

Chicago/Turabian Style

Ren, Hao, Jie Liu, Jian Gao, Guang Pan, and Haixu Ding. 2026. "Reinforcement Learning-Based Sliding Mode Control of Underwater Vehicles with Bow Rudders and X-Stern Rudders" Journal of Marine Science and Engineering 14, no. 3: 321. https://doi.org/10.3390/jmse14030321

APA Style

Ren, H., Liu, J., Gao, J., Pan, G., & Ding, H. (2026). Reinforcement Learning-Based Sliding Mode Control of Underwater Vehicles with Bow Rudders and X-Stern Rudders. Journal of Marine Science and Engineering, 14(3), 321. https://doi.org/10.3390/jmse14030321

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Reinforcement Learning-Based Sliding Mode Control of Underwater Vehicles with Bow Rudders and X-Stern Rudders

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