## 1 Introduction
However, all the tracking control methods were simulated by the design of control model, and the simulation results showed that the control model was available for an effective improvement of path tracking accuracy. Unfortunately, no real vehicle testing was carried out in these studies. Therefore, the effectiveness of the control model on a real vehicle and the tracking control efficiency are not established. For example, a tracking control rate based on the guidance path tracking control theory was proposed by [PERSON] et al. [18] which can guarantee the global uniform asymptotic stability of the controlled closed-loop system. Based on the fuzzy control algorithm, the path tracking controller was designed by [PERSON] [19], [PERSON] [20], [PERSON] [21] and [PERSON] [22] to carry out the control experiment. [PERSON] and [PERSON] [23] employed the neural network fuzzy theory to test the automatic parking system. However, the control logic in their study mainly depended on the driver's driving experience, and relies on a large number of parking test data to establish the control model. [PERSON] et al. [24] designed a parking path tracking control strategy based on nonlinear robust control using non-time-reference vehicle kinematics model, therefore, the impact of external interference and model uncertainty was reduced. [PERSON] [25] and [PERSON] [26] designed a path tracking controller based on the non-smooth control algorithm. [PERSON]. [PERSON] et al. [27] used the predictive model of two degree of freedom vehicle dynamics model to design the parking path tracking control strategy based on the model predictive control method. In general, the existing automatic parking systems show two major drawbacks. First, the curvature of the planned ideal parking path is not continuous. Secondly, the accuracy of automatic parking is poor, and vehicle control is low in terms of degree of automation. In addition to steering, existing parking systems require the driver to control the speed, gear, and brake during parking operation, which may result in poor path tracking efficiency. In order to improve the curvature continuity of parking path and the efficiency of path tracking, this study proposes a new path planning and tracking control method. In this paper, the preview optimization theory is applied to the parking path planning,that is, by previewing the curvature outliers in the parking path, the steering control is carried out in advance, thereby eliminating the problem of discontinuous curvature of the parking path. Meanwhile, the dual closed-loop sliding mode variable structure control algorithm is applied to path-following control. By combining the two control algorithms, a parking path planning and tracking control model is designed, which optimized the parking path and improved the path tracking control effect. Moreover, the automatic control of vehicle speed, steering, gear shifting, and braking during the parking process is realized. This advantage is utilized to improve the effect of path tracking and the parking accuracy, thus increasing the intelligence of automatic parking technology. The research methodology of this paper can be described by the flowchart shown in Figure 1.  
In order to ensure the effectiveness of the research method introduced in this article on vehicle parking control, some assumptions are made on the parking research in combination with the with actual parking restriction requirements. 1. Weather conditions are not heavy rain or heavy snow;
2. Parking slot is flat and the road slope does not exceed 10%;
3. Parking slot length \(\geq\) vehicle length + 0.8 m, parking slot width \(\geq\) vehicle width + 0.3 m;
4. Automatic parking speed does not exceed 3 km/h;
5. The distance between the obstacle on the opposite side of the parking slot and the vehicle is not less than 1.0 m.  
Figure 1: Flowchart of the Research Methodology.