Neural Backstepping Control for Trajectory Tracking of Wheeled Mobile Robots

This paper presents a Neural Backstepping control strategy for trajectory tracking of a differential-drive mobile robot. The proposed approach combines a dynamic-level backstepping controller with a lightweight single-hidden-layer adaptive neural network to compensate uncertain nonlinear dynamics through online adaptation. The backstepping component provides a Lyapunov-based stabilizing structure, whereas the neural approximator improves tracking performance without requiring deep architectures, offline training stages, or computationally demanding optimization procedures. The adaptive law for the neural output weights is derived from the stability analysis, ensuring bounded closed-loop signals and uniformly ultimately bounded tracking errors in the presence of bounded approximation uncertainties. The controller is evaluated through simulations using four reference trajectories: circular, lemniscate, Lissajous, and waypoint-based paths. The same control gains and neural network configuration are used in all cases, showing that the proposed scheme can track different trajectory geometries without trajectory-specific retuning. The simulation results show satisfactory tracking performance, with position RMSE values below 0.04 m for all evaluated trajectories. These results indicate that the proposed Neural Backstepping controller provides a suitable balance between tracking accuracy, online adaptation capability, and implementation simplicity for differential-drive mobile robot trajectory tracking.