Optimal Model‐Free Adaptive Sliding Mode Control Based on an Extended State Observer for Three‐Wheel Omnidirectional Mobile Robots

ABSTRACT Precision‐driven industries increasingly rely on agile and flexible three‐wheeled omnidirectional mobile robots, but their control remains challenging because of complex dynamics, nonlinearities, uncertainties, and external disturbances. Therefore, this paper introduces optimal model‐free adaptive sliding mode control (OMF‐ASMC) to enhance their trajectory tracking accuracy and robustness. The framework synergistically combines an extended state observer (ESO)‐based ultra‐local model (ULM) for dynamic estimation, ASMC for controlling nonlinearities and mitigating chattering, and the marine predators algorithm (MPA) for parameter optimization. The ULM facilitates a model‐free approach, with the ESO estimating unmeasured states and disturbances. The ASMC ensures robustness, while the MPA optimally tunes controller parameters using Lévy and Brownian strategies. Furthermore, Lyapunov theory is employed to rigorously verify closed‐loop stability. Numerical simulations in MATLAB/Simulink demonstrate that the proposed OMF‐ASMC approach achieves superior trajectory tracking accuracy, smoother control signals, and improved velocity response compared with conventional intelligent proportional‐integral controllers and those combined with sliding mode control.