An Adaptive Optimal Backstepping \& Sliding Mode Control for Trajectory Tracking of a Differential Drive Autonomous Mobile Robot using Cross-Entropy and Neural Network

In the paper, an adaptive optimal backstepping \& sliding mode controller (AOBSC) using a neural network is proposed for trajectory tracking of a differential drive autonomous mobile robot (DDAMR) in the presence of unstructured uncertainties. The backstepping control is designed based on the kinematic model to disqualify the pose deviations in trajectory tracking progress of the robot. At the dynamic control level, a sliding mode controller is employed in velocity tracking and steering control of the robot. Parameters of the backstepping and sliding mode controllers are optimized by the cross-entropy (CE) method. A radial basis function (RBF) neural network for approximation of unknown nonlinearities is proposed as an adaptive controller which is integrated with the backstepping and sliding mode controllers to resolve unstructured uncertainties of continuous time unknown nonlinear components. Experiments are conducted with the prototype of a differential mobile robot which designed by authors in real-world environments. Real-world experimental results confirm the effectiveness of the proposed AOBSC approach in markedly enhancing tracking precision and concurrently ensuring the efficiency and reliability for the robot in terms of small distance error, rapid response, high stability, and trajectory tracking more accuracy.