journal article·2026-07-01Open access

Hybrid SMC-ESO-RBF-Based Robust Adaptive Control for Tanker Robots Under Liquid Sloshing and Terrain Disturbances

Do Khac Tiep, Nguyen Van Tien, Pham Duc Anh, Seung-Hun Han

Applied Sciences· Volume 16· Issue 13

Abstract

This paper proposes a hybrid SMC + ESO + RBF control architecture designed to evaluate trajectory tracking and liquid sloshing suppression in tanker robots navigating complex terrains within a simulated environment. A multi-variable dynamic model integrates the differential drive mobile platform with an equivalent mass-spring-damper sloshing system under terrain disturbances. To achieve robust stability, an Extended State Observer (ESO) neutralizes baseline generalized disturbances, while a Radial Basis Function (RBF) neural network adaptively compensates for residual nonlinear coupled sloshing errors. Practical stability and uniform ultimate boundedness (UUB) of the closed-loop system are proven via Lyapunov theory under bounded network approximation errors and observer uncertainties. Numerical simulations in MATLAB/Simulink demonstrate that the proposed controller achieves a baseline Root Mean Square Error (RMSE) of 0.0109 m, representing an 84.1% improvement over traditional Sliding Mode Control (SMC). Parametric sensitivity analysis under variable liquid filling ratios (30%, 50%, and 70%) and a circular steering topology indicates notable adaptability, with the tracking RMSE bounded between 0.0085 m and 0.0129 m under the considered virtual scenarios. Within the simulated environment, the system successfully smooths control profiles and dampens liquid oscillations, demonstrating a promising potential to support transport safety and mitigate actuator chattering under virtual constraints. However, these qualitative observations serve as preliminary hypotheses and must be formally verified through future hardware-in-the-loop (HIL) experiments to evaluate the impact of physical non-idealities, including sensor noise, actuator saturation, communication delays, and wheel slip. These findings confirm the competitive analytical robustness of the SMC + ESO + RBF framework in stabilizing tanker robots within highly uncertain simulated operational environments.
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Research context

OpenAlex topics: Fluid Dynamics Simulations and Interactions · Vibration Control and Rheological Fluids · Adaptive Control of Nonlinear Systems

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Faculty of Electrical and Electronic Engineering, Vietnam Maritime University, Haiphong 18000, Vietnam

Department of Mechanical System Engineering, Gyeongsang National University, Tongyeong 53064, Republic of Korea

Funding

the Ministry of Education (MOE) and the Gyeongsangnam-do Provincial Government, Republic of Korea

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