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

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.