This paper proposes an advanced control method for autonomous mobile robots equipped with Mecanum wheels, which exhibit strong nonlinearities, multivariable dynamics, and significant susceptibility to wheel slip. The controller is designed based on a Dynamic Sliding Mode Control (DSC) framework, integrated with an adaptive fuzzy logic system and a radial basis function neural network (RBFNN), aiming to enhance adaptability and uncertainty compensation under real-world operating conditions. Specifically, the dynamic sliding mode controller is developed in the robot’s body-fixed coordinate frame to simplify the design. The fuzzy logic system adaptively tunes the control gains, and the RBFNN approximates the unknown, uncertain components of the system in real-time. The global stability of the proposed control system is guaranteed through Lyapunov theory. Simulation results demonstrate that the proposed controller (AFNNDSC) achieves higher trajectory tracking accuracy, significantly reduces position and orientation errors, and maintains superior disturbance rejection capability compared to conventional DSC and AFDSC approaches. These results indicate the practical potential of the proposed method in complex operating environments where wheel slip and unknown disturbances are prevalent.