Robust Relative Space Motion Control of Underwater Vehicles Using Time Delay Estimation

Cho, Gun Rae; Kang, Hyungjoo; Kim, Min-Gyu; Park, Sungho; Bae, Chulhee; Jin, Han-Sol; Jin, Seongho; Li, Ji-Hong

doi:10.3390/jmse13112214

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Open AccessArticle

Robust Relative Space Motion Control of Underwater Vehicles Using Time Delay Estimation

by

Gun Rae Cho

^*

,

Hyungjoo Kang

,

Min-Gyu Kim

,

Sungho Park

,

Chulhee Bae

,

Han-Sol Jin

,

Seongho Jin

and

Ji-Hong Li

Korea Institute of Robotics and Technology Convergence, Pohang-si 37666, Republic of Korea

^*

Author to whom correspondence should be addressed.

J. Mar. Sci. Eng. 2025, 13(11), 2214; https://doi.org/10.3390/jmse13112214

Submission received: 23 October 2025 / Revised: 17 November 2025 / Accepted: 19 November 2025 / Published: 20 November 2025

(This article belongs to the Special Issue Advanced Control Strategies for Autonomous Maritime Systems)

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Abstract

This paper presents a robust trajectory-tracking control framework for underwater vehicles operating in a relative coordinate system. Unlike conventional methods that define trajectories in the world frame, the proposed approach formulates the control problem directly in a moving reference frame, enabling accurate motion control with respect to dynamic and drifting objects affected by environmental disturbances such as ocean currents and waves. This relative-space formulation is particularly advantageous for tasks including diver guidance, floating-object inspection, and docking, where the reference itself is nonstationary.A coordinate transformation is introduced to consistently express the vehicle dynamics in the relative frame. Based on the transformed dynamics, a Time Delay Control (TDC) law is applied to estimate unmodeled dynamics and external disturbances without requiring precise system parameters. Theoretical stability analysis shows that the stability condition of the proposed controller is consistent with that of conventional TDC, allowing similar gain-tuning procedures. Simulation results demonstrate that the proposed controller achieves robust and smooth trajectory tracking even when the reference frame undergoes motion induced by ocean currents.

Keywords: underwater vehicle; relative motion control; coordinate transform; time delay control

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MDPI and ACS Style

Cho, G.R.; Kang, H.; Kim, M.-G.; Park, S.; Bae, C.; Jin, H.-S.; Jin, S.; Li, J.-H. Robust Relative Space Motion Control of Underwater Vehicles Using Time Delay Estimation. J. Mar. Sci. Eng. 2025, 13, 2214. https://doi.org/10.3390/jmse13112214

AMA Style

Cho GR, Kang H, Kim M-G, Park S, Bae C, Jin H-S, Jin S, Li J-H. Robust Relative Space Motion Control of Underwater Vehicles Using Time Delay Estimation. Journal of Marine Science and Engineering. 2025; 13(11):2214. https://doi.org/10.3390/jmse13112214

Chicago/Turabian Style

Cho, Gun Rae, Hyungjoo Kang, Min-Gyu Kim, Sungho Park, Chulhee Bae, Han-Sol Jin, Seongho Jin, and Ji-Hong Li. 2025. "Robust Relative Space Motion Control of Underwater Vehicles Using Time Delay Estimation" Journal of Marine Science and Engineering 13, no. 11: 2214. https://doi.org/10.3390/jmse13112214

APA Style

Cho, G. R., Kang, H., Kim, M.-G., Park, S., Bae, C., Jin, H.-S., Jin, S., & Li, J.-H. (2025). Robust Relative Space Motion Control of Underwater Vehicles Using Time Delay Estimation. Journal of Marine Science and Engineering, 13(11), 2214. https://doi.org/10.3390/jmse13112214

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Robust Relative Space Motion Control of Underwater Vehicles Using Time Delay Estimation

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