## 1 Introduction  
The increase of car ownership in urban areas and the challenges of traffic congestion and insufficient parking spaces are great concerns to urban planners and managers. Consequently, the size of parking space in most urban centers is becoming smaller to overcome the difficulty of inadequate parking space, and the following problem is usually associated with parking difficulties and accidents, such as scuffing and collisions [1; 2; 3]. Facing these challenges, automatic parking technology for intelligent vehicles receives extensive attention from both the automotive industry and research institutions. Automatic parking technology refers to the parking process that completes the parking operations safely and quickly without a driver and can effectively improve driving comfort while greatly reducing the probability of accidents during parking. Also, the promotion of automatic parking technology can promote the development and deployment of autonomous driving and intelligent vehicles [4; 5; 6; 7; 8; 9; 10]. A major component of automatic parking technology is parking path planning and tracking control, which significantly affects the requirements of the parking space size and parking success rate. Parking path planning is widely investigated in previous researches with most studies based on the three-segmented path. The three-segment path is composed of two segments of arcs with constant curvature and one segment of a straight line between two arcs. The curvature of the connecting point of the arc and the line in the path is discontinuous. Therefore, the vehicle has to stop and turn in situ to match the planned path, which makes the parking procedure discontinuous and time-consuming in addition to aggravating tire wear. To address this issue, numerous path planning methods based on different theories are proposed. However, most of these methods have certain limitations, and with the nature of only method research and simulation. The real validity of the algorithm has not been verified by real vehicle tests, therefore, the problem is well solved yet. For example, [PERSON]. [PERSON] et al. [11] planned the parking path by the combination of arc and straight line, and used the cycloid curve to smooth the parking path, thus avoiding in-situ turning during parking. [PERSON] et al. [12] obtained the parking path by comparing the two paths planned by different constraints and found the parking path of a vehicle robot. [PERSON] et al. [13] designed an automatic parking system which focuses on the path planning method. However, their research did not consider the parking space constraints. [PERSON] and [PERSON] [14] also investigated the parallel parking path planning based on the B-spline theory. Their study justified the curvature continuity of parking path in the regular parking space limitations in its application to an irregular parallel parking slot. Furthermore, [PERSON] [15] conducted the path planning of parallel parking based on continuous curvature, and the curvature outliers were smoothed using the transition curve. However, the speed control of the transition curve path was required to be high. [PERSON] et al. [16] used a heuristic search algorithm to design a parking path under irregular and narrow conditions, and the optimization method was used to smooth the parking path. [PERSON] et al. [17] researched the path planning by transforming the path planning problem caused by narrow environment into a constrained optimization problem before providing the solution, and the parking success rate of automatic parking system is then improved. However, their research only uses a limited number of narrow parking scenarios to verify the feasibility and effectiveness of the proposed method, besides, the parking success rate of the automatic parking system in the conventional environment has not been effectively reflected. To effectively track the planned path, investigations on path tracking control systems are implemented based on advanced algorithms in the literature.