In this paper, an adaptive control scheme based on using neural networks is designed to guarantee the desired behavior of a micro-robot which is equipped with vibrating actuators and follows the principle of slip-stick movement. There are two tiny shaking motors which have been utilized to run the micro-class robotic system. Dynamic modeling equations are expressed by considering the spring coefficient of the bases. After that, the effect of the spring on the foundations was investigated. In addition to designing neural-based controller, an AI-based system identifier has been developed to help the controller update its parameters and achieve its desired targets. Using this method, several specific paths for the movement of this micro robot are simulated. Based on the simulation results, the proposed controlling strategy guarantees acceptable performance for tracking different paths due to plotted near-zero errors and handles the nonlinear behavior of the micro-robot system.