The major problem dealing with mobile robots is the trajectory tracking control problem, in the presence of random disturbance and unmeasurable angular velocity. In this paper, we propose a Sliding Mode Control (SMC) based on a Nonlinear Disturbance Observer (NDO) and a Neural State Observer (NSO). The (SMC-NDO) controller displays limitations in mitigating external disturbances. Therefore, this research contribution suggests a novel approach that integrates a Neural State Observer (NSO) into the (SMC-NDO) controller, to significantly enhance the performance of a control system. The combined approach improves disturbance reduction while simultaneously estimating the unmeasurable angular velocity, ultimately leading to more accurate path tracking. Furthermore, the Lyapunov method is used to ensure the stability of the closed-loop control on the one hand, and the stability of the Neural State Observer based on the Backpropagation algorithm on the other hand. Numerical simulations and the implementation of the Simulator in ROS/Gazebo demonstrate better performance of our proposed approach (SMC-NSONDO) compared to the Sliding Mode control-based Disturbance Observer (SMC-NDO) and the Sliding Mode Control (SMC). The control proposal in this work is ready for use on most ROScompatible robots. This experiment should offer an enlightening perspective to robotics researchers.