## 1 Introduction
Due to the many limitations not considered in the actual modeling and controller design, these iterative learning controllers produced in the above studies are not fully suitable for trajectory tracking with mobile platforms. These shortcomings can be summarized as follows:  
1. The discrete kinematics model does not conform to the actual physical model of the mobile robot. The gravity center may not wholly coincide with the midpoint of the driving wheels in the actual mobile robot. Therefore, the previous modeling methods and iterative learning controllers based on the gravity center are different from the actual model and control of the mobile platform. 2. The output variables of the iterative controller cannot directly control the motion of the mobile platform. The actual control variable of the mobile platform is the rotation speed of the driving wheels, whereas the output variables in these literatures are the forward speed and rotation speed of the mobile robot. The output variables produced by the above controllers need to be converted into the rotation speed of the driving wheels. 3. The solution speed may not meet the actual physical constraints of the motor. Since the selected control parameters are the mobile robot's forward speed and rotation speed in these literatures, they cannot be effectively limited by the driving wheels. Therefore, the solution in the above-described studies cannot be converted into the actual rotation speed of two wheels considering the actual physical constraints. 4. The above-mentioned studies did not analyze the influence of the various parameters of the iterative controller on the trajectory tracking task of the mobile robot. These researchers only analyzed and verified the effectiveness of the designed controller,but did not study the influence of the controller parameters, such as the parameter uncertainty, speed limitation, structural parameter uncertainty, and initial error. It is necessary to conduct in-depth research so that the iterative controller can be more widely used in trajectory tracking. To overcome the shortcomings in earlier studies, we established a new discrete kinematic model of a mobile platform to directly choose the speed of the driving wheels as the control variable for trajectory tracking, instead of controlling the forward speed and angular rotation speed. Furthermore, we explicitly analyzed multiple constraints in actual trajectory tracking tasks, and established a new type of iterative learning controller in the presence or absence of the initial error. With the initial error, a corresponding compensatory mechanism was designed for the learning controller to correct the error at the start time; otherwise, the other error signals were added in the iterative learning law to improve the effectiveness of the controller. According to the theoretical analysis, the proposed controller has convergence and stability under certain conditions. In the simulation experiment, the effectiveness of the proposed controller was verified using various typical trajectories, such as a circular trajectory, a combination trajectory of arc and straight, a cardioid-like trajectory, and a spiral-like trajectory. Then, in-depth research on the iterative learning controller was specifically conducted by comparing the performance of the circular trajectory tracking task with different control parameters, which mainly included the selection of the control coefficient, the choice of various error signals, and the impact of speed constraints. This paper is organized as follows: Section 2 describes the specific structure and basic assumptions of a non-holonomic wheeled mobile platform, establishes the discrete kinematics of the differential drive mobile platform, and analyzes the control constraints of the drive wheels. In Section 3, we explicitly design the iterative learning controller and prove the effectiveness and robustness of the new controller through theoretical analysis.