Effective path planning is essential for autonomous mobile robots navigating unknown environments. Fuzzy Logic Controllers (FLCs) are well-suited for this task due to their robustness in handling uncertainty, vagueness, and nonlinearities. Among the core elements that influence FLC behaviour are membership functions (MFs), which define how sensory inputs are translated into fuzzy linguistic terms. Despite their importance, specific impact of different MF shapes on navigation performance remains underexplored. This study investigates the effect of three widely used MF types i.e., triangular, trapezoidal, and Gaussian on the traversal efficiency of a nonholonomic wheeled mobile robot operating in a static, obstacle filled environment. A series of simulations were conducted using MATLAB and CoppeliaSim, with traversal time serving as the primary performance metric. One-way ANOVA results (F = 342.33, p < 0.001) revealed statistically significant differences across MF types, with triangular MFs yielding the shortest average traversal time of 177.95 s, followed by trapezoidal with 179.08 s and Gaussian at 181.05 s. These findings highlight that MF shape significantly influences control responsiveness and path efficiency. By isolating MF type within a consistent rule base and simulation setup, this work provides baseline guidance for MF selection and sets the stage for future research involving hybrid MFs, real-world validation, and adaptive fuzzy systems.