<p>This paper proposes an adaptive optimal backstepping and sliding mode controller (AOBSC) using a neural network for trajectory tracking of a differential drive autonomous mobile robot (DDAMR) under unstructured uncertainties. The backstepping controller is designed based on the robot’s kinematic model to reduce pose deviations during the trajectory tracking process. At the dynamic level, a sliding mode controller is employed for velocity tracking and steering control. The parameters of both controllers are optimized using the cross-entropy method. To approximate unknown nonlinearities, a radial basis function (RBF) neural network is integrated as an adaptive component, enabling the system to handle unstructured uncertainties in continuous time nonlinear elements. Experiments are conducted on a prototype DDAMR designed by the authors in real-world environments. The experimental results confirm that the proposed AOBSC significantly enhances tracking accuracy while ensuring fast response, high stability, and overall robustness.</p>