Adaptive Fuzzy Sliding Mode Trajectory Tracking Control Using Hexagonal Fuzzy Numbers

Abstract This paper presents an adaptive fuzzy sliding mode controller (AFSMC) designed for precise trajectory tracking of an omnidirectional mobile robot operating within dynamic and uncertain environments. The control strategy integrates a sigmoid-based sliding mode switching function with an integral component to enhance system convergence speed and effectively mitigate chattering. A novel fuzzy gain adaptation mechanism employs a hexagonal fuzzy number (HFN) representation, facilitating more flexible and nonlinear shaping of membership functions. This methodology enables multi-objective gain tuning, assisting the controller in balancing robustness, responsiveness, and smoothness of control signals. The AFSMC architecture combines both equivalent and switching control laws to ensure robust resilience against model uncertainties, parameter variations, sensor noise, and external disturbances. Extensive simulations under diverse conditions, including disturbance injection, payload variations, and external force application, demonstrate that the proposed HFN-based AFSMC consistently attains lower root mean square error (RMSE), reduced overshoot, and significantly diminished chattering relative to conventional fuzzy sliding mode controllers employing triangular and trapezoidal membership functions. These findings affirm that the integration of HFN-based fuzzy adaptation within the sliding mode framework provides a robust and efficient solution for the accurate trajectory tracking of omnidirectional mobile robots in real-world and unpredictable scenarios.Impact: The method offers a practical framework for precision mobile robotics control, with potential extensions to autonomous navigation under soft-sensing and unstructured terrain conditions.