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This paper proposes a novel adaptive variable power sliding mode observer-based model predictive control (AVPSMO-MPC) method for the trajectory tracking of a Mecanum-wheeled mobile robot (MWMR) with external disturbances and model uncertainties. First, in the absence of disturbances and uncertainties, a model predictive controller that considers various physical constraints is designed based on the nominal dynamics model of the MWMR, which can transform the tracking problem into a constrained quadratic programming (QP) problem to solve the optimal control inputs online. Subsequently, to improve the anti-jamming ability of the MWMR, an AVPSMO is designed as a feedforward compensation controller to suppress the effects of external disturbances and model uncertainties during the actual motion of the MWMR, and the stability of the AVPSMO is proved via Lyapunov theory. The proposed AVPSMO-MPC method can achieve precise tracking control while ensuring that the constraints of MWMR are not violated in the presence of disturbances and uncertainties. Finally, comparative simulation cases are presented to demonstrate the effectiveness and robustness of the proposed method. • kinematic and dynamic constraints are handled efficiently. • The improved observer has a fast convergence rate without chattering. • The method can improve tracking performance. [ABSTRACT FROM AUTHOR]