<p>This paper presents an adaptive fuzzy sliding mode controller (AFSMC) for accurate trajectory tracking of an omnidirectional mobile robot operating in dynamic and uncertain environments. The proposed control strategy integrates a sigmoid-based sliding mode switching function with an integral compensator, enabling fast convergence while effectively mitigating chattering. A novel fuzzy gain adaptation mechanism based on hexagonal fuzzy numbers (HFNs) provides flexible nonlinear shaping of membership functions, supporting multi-objective tuning that balances robustness, responsiveness, and smoothness of the control action. The AFSMC architecture combines equivalent and switching control laws to maintain resilience against model uncertainties, parameter variations, sensor noise, and external disturbances. Comprehensive simulation studies covering disturbance injection, payload variations, and external force perturbations demonstrate that the HFN-based adaptive gain yields reduced chattering, smoother control inputs, and improved heading and axial tracking performance compared to classical sliding mode control. These results indicate that embedding HFN-based adaptation within the sliding mode framework offers a robust and efficient solution for high-precision trajectory tracking in unpredictable real-world robotic applications. The method offers a practical framework for precision mobile robotics control, with potential extensions to autonomous navigation under soft-sensing and unstructured terrain conditions.</p>