Lyapunov-based adaptive path tracking control of wheeled mobile robots using a self-organizing recurrent Gaussian-gating functional-link fuzzy neural network

A recurrent Gaussian gating functional-link fuzzy neural network (RGFL-FNN) is developed into a two-channel path-tracking controller for nonholonomic mobile robots. The six-layer structure combines Gaussian grade-field gating of fuzzy grades, a first-order recurrent state, and trigonometric functional-link consequents. A normalized descent rule updates the parameters online. On the fully specified discrete-time Pioneer 3-DX study, the controller is compared with three fuzzy-neural networks and an adaptive neural sliding-mode design. On the lemniscate it has the lowest and most consistent error, over twenty noisy trials and wins every paired comparison against the four alternatives. In the noisy run it lowers mean-absolute-error by 51.6% and 66.0% relative to the functional-link and conventional baselines while using three rules instead of five and nine. Ablation results associate the Gaussian grade-field layer with lower error in the tested noisy configuration. Each update executes in 73–146 $$\:\mu\:s$$ within a 10 ms sampling period. An additional MuJoCo run is retained only as an exploratory simulation.