# An Adaptive Control Based on Improved Gray Wolf Algorithm for Mobile Robots
## 1 Introduction
And the GA and PSO, which can be particularly used for self-tuning in controlling movement laws, are the most widely used algorithms in research. The GWO, which is a heuristic algorithm with a clear structure, fewer configuration parameters, and less likelihood of falling into local extremes, can offer superior performance advantages with regard to optimal control precision and convergence speed. However, due to its late introduction, few studies on methods based on the GWO have been implemented as adaptive processes, especially for the motion control of mobile robots. With the development of robotics technology and the increase in social demand, the performance requirements for mobile robot systems are becoming higher and higher. For example, electrical power substation inspection robots are required to be capable of smooth movement at high speeds in all weather conditions [24]. The weight of the heliostat cleaning robot [25; 26] is relatively large, and the robot is required to clean the solar mirrors stably on off-road surfaces such as sand and hard soil. The logistics transportation robot has a maximum payload capacity of up to 200 tons [27], and the Handle handling robot can achieve a speed of 15 km/h [28]. Some mobile robots with larger loads or faster speeds may be prone to tilting and rolling when operating in large-angle turns or complex environments where the upper bounds of the speed and load cannot be well estimated. Therefore, there are still some challenges and problems to be solved in the motion control of mobile robots under tilting and slipping conditions [29]. On the other hand, in order to solve the design problem of mobile robot controllers, which is exceptionally challenging due to the influence of highly time-varying uncertainties in the parameters of DC motors caused by strong coupling terms between electrical and mechanical systems, numerous classes of adaptive control methods have been proposed [30; 31]. However, unfortunately, only the time-varying uncertain parameter scalar terms of electromechanical coupling were considered. In this paper, using the techniques of a neural network and robust control, an intelligent controller for the motion control of a nonholonomic mobile robot with time-varying parameter uncertainty and external interference under the condition of tire hysteresis loss is proposed. At first, aimed at the motion control problem of a mobile robot with time-varying parameter uncertainty and external interference under the condition of tire hysteresis loss, based on the tire dynamics principle, dynamic and kinematic modelsof the nonholonomic mobile robot were established. The neural network approximation model of the system's nonlinear term, which is caused by many coupling factors when the robot rolls, is given. And, by estimating the local undetermined upper bounds that correspond to each of the subsystem perturbations as well as uncertainty terms such as the reducer gear clearance, changes in road friction coefficients, etc., a novel adaptive law for the real-time adaptive estimation of uncertainties and unknown upper bounds of perturbations of each subsystem is designed, while ensuring the system is able to stably track any desired trajectory in real time without requiring any previous understanding of its model. Furthermore, based on fuzzy system technology and the improved GWO, a self-tuning online optimization algorithm, whose learning space is used as the output variable by the fuzzy system to expand the search area of the gray wolf, is given. And the output of the algorithm can serve as the online input for the designed control law, which realizes the real-time self-tuning of any parameter and adapts to any desired trajectory. Finally, simulations are employed to confirm the suggested intelligent controller's efficacy. The remainder of this article is structured as follows. Description of the nonholonomic mobile robot system and some relevant characteristics and parameters is given in Section 2. The proposed controller is designed in Section 3.