# An Adaptive Control Based on Improved Gray Wolf Algorithm for Mobile Robots
## 1 Introduction  
With the characteristics of moving ability, high efficiency, and flexible control, mobile robots, which can assist or take the place of people to complete some repetitive and dangerous work and improve the production efficiency and safety of the working environment [1], have been deeply researched and widely applied in the service industry, industry, defense, agriculture, and other fields [2; 3; 4]. An intelligent, accurate, safe, and reliable control system, as the key to the execution of tasks, is crucial to promote the development and application of mobile robot technology. The objective of the robot movement control system is to obtain the information of the robot's traveling speed and angle in real time, and constantly reduce the distance and angle deviation between the robot and the target point, while guiding the robot to move accurately, smoothly, and quickly to the stationary or moving target point. Lots of research on the motion control of mobile robots has been carried out, and various motion control techniques and solutions for nonholonomic mobile robots have been proposed. In [5], a robust output feedback controller, which can ensure the system status asymptotically converges to the origin by treating the disturbance as an extended state and constructing an extended state observer (ESO), is proposed for mobile robotic systems with parameter uncertainty, measurement angle deviation, and non-zero external disturbances. In [6], the authors focus on designing an action tracking control method for nonholonomic mobile robots, taking into account the actuator dynamics, and the feasibility of the nonholonomic mobile robot following the specified trajectory is verified by designing a trajectory tracking controller at the actuator aspect. In [7], a robot kinematics controller based on Lyapunov theory and a PID controller for DC motors are discussed. And, by estimating localizationthrough integrating the robot movement into a fixed sampling frequency, the method of precise control of the mobile robots is given. In [8], a robust synchronization controller that can be simply tuned and adapted to various control scenarios is developed. Then, an algorithm for recognizing the system parameters for both online and offline scenarios using particle swarm optimization is proposed and evaluated. The method, which can successfully improve its convergence speed, accuracy, and stability without prior knowledge, is implemented on the Ballbot robot. In [9], the robust adaptive neural network tracking controller is developed and adaptive laws are introduced to estimate a local upper bound of the mechanical subsystem and the electrical subsystem of the nonholonomic mobile robot. In [10], a robust adaptive controller that addresses the parameter uncertainty of a wheeled mobile robot (WMR) is proposed. And, utilizing a smooth finite-time control technique, a trajectory following controller is proposed. Additionally, in order to deal with the system uncertainties of the nonholonomic WMR, the method of combining an observer and compensator is adopted in the design of the tracking controller. In [11], for the sake of improving the motion control accuracy and robustness of the system, a hierarchical improved fuzzy dynamic sliding mode control method, which can incorporate a tuning mechanism and operate in a similar way to the online processing of uncertainties without imposing a significant computational burden, is proposed for automated guided vehicles (AGVs) to deal with the uncertainty of the system. To significantly enhance the convergence speed and robustness of the controller, computational intelligence technology has been favored by many scholars; especially, heuristic algorithms have been well applied, such as particle swarm optimization (PSO) [8; 12; 13], genetic algorithm (GA) [14; 15], be colony optimization [16; 17; 18], ant colony optimization (ACO) [19; 20; 21], gray wolf optimizer (GWO) [22; 23], etc.