A Bio-Inspired Sliding Mode Algorithm with Lateral Velocity Tracking Differentiator for Formation Control of Underactuated USVs

Jiaying Niu; Lanqing Xu; Guiyin Chen; Jinhua Lv; Yiming Tang

doi:10.2478/pomr-2026-0018

.blurhash-client-img { display: none !important; }

A Bio-Inspired Sliding Mode Algorithm with Lateral Velocity Tracking Differentiator for Formation Control of Underactuated USVs

Polish Maritime Research

Volume 33 (2026): Issue 2 (June 2026)

By: Jiaying Niu , Lanqing Xu , Guiyin Chen , Jinhua Lv and Yiming Tang

Open Access

|May 2026

Abstract

An advanced control framework is presented to solve the challenge of trajectory tracking in underactuated unmanned surface vehicles (USVs) operating in a formation. Three key innovations are featured: (1) Complex derivative calculations are effectively eliminated by a bio-inspired model approximating virtual longitudinal/lateral velocities; (2) Severe initial control chattering is significantly mitigated by a lateral velocity tracking differentiator (LVTD); (3) These techniques are integrated within a disturbance-observer-compensated dynamic surface sliding mode control (SMC) under a virtual framework. In addition, trajectory tracking errors are defined using desired and actual USV states, while virtual control laws are developed based on nonlinear backstepping. Meanwhile, the bio-inspired model is incorporatedto approximate virtual velocities, avoiding complex differentiation. Subsequently, the LVTD is employed to smooth lateral velocity derivatives. Furthermore, the robustness of the SMC algorithm is ensured by a marine disturbance observer providing real-time observing and compensation for environmental disturbances. Finally, an exponentially stable SMC law is designed and the global uniform stability is rigorously proven via Lyapunov theory. Extensive simulation experiments in different working conditions validate the algorithm’s superior effectiveness, stability, and tracking precision over existing methods, attributable to its core innovations.

References

Dong Z, Zhang Z, Qi S, Zhang H, Li J, Liu Y. Autonomous cooperative formation control of underactuated USVs based on improved MPC in complex ocean environment. Ocean Engineering 2023. https://doi.org/10.1016/j.oceaneng.2023.113633.
Search in Google Scholar Back to article
Liu B, Chen Z, Zhang H, Wang X, Geng T, Su H, Zhao J. Collective dynamics and control for multiple unmanned surface vessels. IEEE Transactions on Control Systems Technology 2020. https://doi.org/10.48550/arXiv.1905.01215.
Search in Google Scholar Back to article
Dong Z, Ding Y, Liu W, Hu Z, Lu S, Liu Y. Manoeuvreability parameter identification of a water-jet USV based on truncated weighted LSSVM integrated with adaptive mutation PSO algorithm. Ocean Engineering 2025. https://doi.org/10.1016/j.oceaneng.2025.120474.
Search in Google Scholar Back to article
Lapandic D, Verginis C, Dimarogonas D, Wahlberg. Kinodynamic motion planning via funnel control for underactuated unmanned surface vehicles. IEEE Transactions on Control Systems Technology 2024. https://doi.org/10.1109/TCST.2024.3396027.
Search in Google Scholar Back to article
Batkovic I, Ali M, Falcone P, Zanon M. Safe trajectory tracking in uncertain environments. IEEE Transactions on Automatic Control 2023. https://doi.org/10.48550/arXiv.2001.11602.
Search in Google Scholar Back to article
Dong Z, Tan F, Zhou W, Wang B, Liu Y. Distributed formation control of underactuated UMVs based on nonlinear model prediction algorithm with obstacle avoidance strategy incorporating relative velocity constraints. Ocean Engineering 2024. https://doi.org/10.1016/j.oceaneng.2024.119272.
Search in Google Scholar Back to article
Przybylski M. Validation of control of course and depth of biomimetic underwater vehicle with two side and two tail fins. Polish Maritime Research 2025. https://doi.org/10.2478/pomr-2025-0033.
Search in Google Scholar Back to article
Taner M, Gursel T. A comparative study of biomimicry-inspired design forms for autonomous underwater vehicles. Polish Maritime Research 2025. https://doi.org/10.2478/pomr-2025-0034.
Search in Google Scholar Back to article
Qin J, Du J. Minimum-learning-parameter-based adaptive finite-time trajectory tracking event-triggered control for underactuated surface vessels with parametric uncertainties. Ocean Engineering 2023. https://doi.org/10.1016/j.oceaneng.2023.113634.
Search in Google Scholar Back to article
Meng J, Tan H, Jiang L, Qian C, Xiao H, Hu Z, Li G. Robust finite-time sliding mode control of unmanned surface vehicle with active compensation of pose estimation uncertainty. Ocean Engineering 2024. https://doi.org/10.1016/j.oceaneng.2024.117831.
Search in Google Scholar Back to article
Dong Z, Tan F, Yu M, Xiong Y, Li Z. A bio-inspired sliding mode method for autonomous cooperative formation control of underactuated USVs with ocean environment disturbances. Journal of Marine Science and Engineering 2024. https://doi.org/10.3390/jmse12091607.
Search in Google Scholar Back to article
Yang W, Shen T, Pan T, Hu G, Xu D. Distributed model predictive consensus control of unmanned surface vehicles with post-verification. Drones 2023. https://doi.org/10.3390/drones7010042.
Search in Google Scholar Back to article
Li J, Fu MY, Xu YJ. Disturbance-observer-based adaptive prescribed performance formation tracking control for multiple underactuated surface vehicles. Journal of Marine Science and Engineering 2024. https://doi.org/10.3390/jmse12071136.
Search in Google Scholar Back to article
Dong Z, Qi S, Yu M, Zhang Z, Zhang H, Li J, Liu Y. An improved dynamic surface sliding mode method for autonomous cooperative formation control of underactuated USVs with complex marine environment disturbances. Polish Maritime Research 2022. https://doi.org/10.2478/pomr-2022-0025.
Search in Google Scholar Back to article
Zhang Q, Zhang SH, Liu Y, Zhang Y, Hu Y. Adaptive terminal sliding mode control for USV-ROVs formation under deceptive attacks. Frontiers in Marine Science 2024. https://doi.org/10.3389/fmars.2024.1320361.
Search in Google Scholar Back to article
Duan H, Yuan Y, Zeng Z. Distributed robust learning control for multiple unmanned surface vessels with fixed-time prescribed performance. IEEE Transactions on Systems Man Cybernetics-Systems 2024. https://doi.org/10.1109/TSMC.2023.3321119.
Search in Google Scholar Back to article
Sui B, Zhang J, Liu Z, Wei J. Distributed prescribed-time cooperative formation tracking control of networked unmanned surface vessels under directed graph. Ocean Engineering 2024. https://doi.org/10.1016/j.oceaneng.2024.117993.
Search in Google Scholar Back to article
Chang Z, Yao X, Park J. Fixed-time formation tracking for unmanned surface vehicles: A multi-layer neural networks approach. Neurocomputing 2024. https://doi.org/10.1016/j.neucom.2024.128220.
Search in Google Scholar Back to article
Piskur P, Szymak P, Kitowski Z, Flis L. Influence of fin’s material capabilities on the propulsion system of biomimetic underwater vehicle. Polish Maritime Research 2020. https://doi.org/10.2478/pomr-2020-0078.
Search in Google Scholar Back to article
Zhang H, Zhang X, Xu H, Soares C. Cooperative path following control of USV-UAVs with genetic algorithm extended state observer. Ocean Engineering 2025. https://doi.org/10.1016/j.oceaneng.2025.120332.
Search in Google Scholar Back to article
Cai W, Zhou X, Li Y, Qiu A. Event-triggered predefined-time neural network fault-tolerant formation control of uncertain heterogeneous USV-UAV systems. Ocean Engineering 2025. https://doi.org/10.1016/j.oceaneng.2025.120775.
Search in Google Scholar Back to article
Li F, Liu Z, Zhu Q. Adaptive fuzzy finite-time control for a QUAV with tracking error constraints and unknown actuator faults. Aerospace Science and Technology 2025. https://doi.org/10.1016/j.ast.2025.110054.
Search in Google Scholar Back to article
Mu D, Li L, Wang G, Fan Y, Zhao Y, Sun X. State constrained control strategy for unmanned surface vehicle trajectory tracking based on improved barrier Lyapunov function. Ocean Engineering 2023. https://doi.org/10.1016/j.oceaneng.2023.114276.
Search in Google Scholar Back to article
Zhang S, Zhang Q, Xu L, Xu S, Zhang Y, Hu Y. Dynamic sliding mode formation control of unmanned surface vehicles under actuator failure. Journal of Marine Science and Engineering 2025. https://doi.org/10.3390/jmse13040657.
Search in Google Scholar Back to article
Li M, Guo C, Yu H, Yuan Y. Line-of-sight-based global finite-time stable path following control of unmanned surface vehicles with actuator saturation. ISA Transactions 2022. https://doi.org/10.1016/j.isatra.2021.07.009.
Search in Google Scholar Back to article
Nie J, Zhang X, Wang H, Sheng C, Zhang C, Zhang C. Anti-saturation distributed fixed-time prescribed performance sliding mode formation control based on FXESO for uncertain USVs. Ocean Engineering 2025. https://doi.org/10.1016/j.oceaneng.2024.120101.
Search in Google Scholar Back to article
Ning J, Huang Y, Liu Z, Li W, Wei X. Adaptive distributed heterogeneous formation control for UAV-USVs with input quantisation. Journal of Marine Science and Engineering 2024. https://doi.org/10.3390/jmse12060975.
Search in Google Scholar Back to article
Fossen T, Breivik M, Skjetne R. Line-of-sight path following of underactuated marine craft. IFAC Proceedings Volumes 2003. https://doi.org/10.1016/S1474-6670(17)37809-6.
Search in Google Scholar Back to article
Hodgkin A, Huxley A. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 1952. https://doi.org/10.1016/S0092-8240(05)80004-7.
Search in Google Scholar Back to article
Mohammadi A, Tavakoli M, Marquez H, Hashemzadeh F. Nonlinear disturbance observer design of robotic manipulators. Control Engineering Practice 2013. https://doi.org/10.1016/j.conengprac.2012.10.008.
Search in Google Scholar Back to article
Zhu Y, Qiao J, Guo L. Adaptive sliding mode disturbance observer-based composite control with prescribed performance of space manipulators for target capturing. IEEE Transactions on Industrial Electronics 2018. https://doi.org/10.1109/TIE.2018.2838065.
Search in Google Scholar Back to article
Do K, Pan J. Global robust adaptive path following of underactuated ships. Automatica 2006. https://doi.org/10.1016/j.automatica.2006.04.026.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/pomr-2026-0018 | Journal eISSN: 2083-7429 | Journal ISSN: 1233-2585

Journal RSS Feed

Language: English

Page range: 28 - 41

Published on: May 6, 2026

Published by: Gdansk University of Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

underactuated unmanned surface vehicles (USVs),

trajectory tracking,

formation control,

sliding mode control (SMC),

bio-inspired model,

lateral velocity tracking differentiator (LVTD)

Related subjects:

Engineering,

Introductions and overviews,

Engineering, other,

Geosciences,

Atmospheric science and climatology,

Life sciences,

Life sciences, other

© 2026 Jiaying Niu, Lanqing Xu, Guiyin Chen, Jinhua Lv, Yiming Tang, published by Gdansk University of Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 33 (2026): Issue 2 (June 2026)