## 1 Introduction  
Due to the simple structure design and strong movement ability, mobile platforms have been extensively applied in various fields, including agricultural production [1], environmental detection [2], and industrial production [3]. Due to the differences in the number of motors and the structure shape, differential mobile robots controlled by two driving wheels have become the mainstream mobile robot. In the movement of the mobile platform, there are two actual input control variables: the speeds of the driving wheels on the left side and the right side [4]. However, the actual positioning of the mobile platform requires three parameters: the position of the \(xy\) plane and the rotation angle of the \(z\) axis [5]. Therefore, a differential mobile robot with two driving wheels is a typical non-holonomic constraint system [6]. In solving various problems associated with this mobile robot, trajectory tracking is an important research problem with a high application value in many fields. With mobile robots, uncertain parameters are unavoidable, which are caused by many factors, such as physical error in the machining [7], external disturbances in the environment [8], equipment wear during working [9], and disturbances in the control signals [10]. To deal with these uncertainties parameters, various controllers have been proposed, such as the back-stepping controller [11], model predictive controller [12, 13], sliding mode controller [14; 15], fuzzy controller [16; 17], adaptive tracking controller [18; 19; 20], and the neural network controller [21; 22; 23]. Compared with the kinematic controller, the dynamic controller has more uncertain parameters, a more complex construction, and worse adaptability to different environments. The kinematic controller also needs to be designed before the dynamic controller can be designed for realizing trajectory tracking. However, the design of most kinematic controllers is based on the structural parameters of the mobile robot. Therefore, designing a simple kinematic controller and reducing the disturbance due to uncertain parameters remains a significant research challenge. In various kinematics controllers, an iterative learning controller can ignore the robot's structure parameters and realizes high-precision trajectory tracking by continuously adjusting the input control signals and optimizing the output result. Furthermore, iterative learning controllers mainly focus on specific task requirements and movement characteristics instead of the basic parameters of the system. As an advanced control theory, iterative learning controllers have been widely applied to various robots, such as a parallel Delta robot [24], manipulator robot [25], mobile platform, and self-balancing mobile robot [26]. Additionally, iterative learning controllers have demonstrated effectiveness in solving many research problems, such as trajectory tracking problems [27; 28], and trajectory planning problems [29; 30]. Currently, the typical iterative learning controllers mainly include the P-type, PD-type, and PID-type [31; 32]. In addition, iterative learning controllers have widely used in solving the trajectory tracking problems of mobile platforms. The authors in [33] first applied the P-type iterative learning controller to realize the sine-type trajectory tracking of a mobile platform. Another article [34] revised the design of P-type iterative control into the typical PD-type control design for realizing rectangular trajectory tracking. [PERSON] [35] proposed different error signals to optimize the P-type iterative learning controller for completing various types of trajectory tracking control with mobile platforms. Then, researchers [36] added the PID coefficient in the iterative learning controller to improve the effectiveness of arc-shaped trajectory tracking. At the same time, researchers [37] changed the forgetting factor to reduce the correction of the error parameters at the initial moment of each iteration process.