# Automatic Vertical Parking Reference Trajectory Based on Improved Immune Shark Smell Optimization
## 1 Introduction  
AVP performance is a significant performance evaluation index used to determine the safety and comprehensive quality of intelligent vehicles. It is divided into two parts: the optimization of the parking reference trajectory and tracking control [1]. It is crucial to obtain a reference trajectory with collision avoidance and a smooth and short length, prerequisites for achieving high AVP performance [2]. Designing an AVP optimization algorithm with high performance is a research hotspot for scholars in the field of intelligent driving. The successful implementation of AVP requires three steps: the first is to determine whether the parking feasibility constraint is established (available parking space detection); the second is to obtain an optimized reference trajectory for parking (parking trajectory optimization); and the third is to effectively track the path to the allowable parking range (parking trajectory tracking). In recent years, scholars have produced valuable research results on the problem of automatic parking. A parking space detection method suitable for underground and indoor parking environments was put forward in [3]. This method combined parking space marking and free space detection; however, a large number of vehicle sensors needed to be configured. A parking space detection method based on probabilistic occupancy filter was proposed, which overcame the defect of obstacle occlusion in the detection of traditional around view monitoring (AVM) sensors to a certain extent [4]. A swarm intelligence optimization framework combining gradient arithmeticand an adaptive parameter controller for multi-objective automatic parking operation planning was proposed in [5]. Based on driving experience and discrete kinematic differential equations, a parking trajectory optimization scheme suitable for a narrow environment was proposed in [6]. A parking trajectory tracking controller based on multi-constrained model predictive control (MMPC) was proposed in [7]. A three-layer framework was proposed to address the challenges of high nonholonomic constraints, unstable reverse dynamics, and non-convex obstacle avoidance constraints in parking tractor-trailer vehicles in extremely narrow environments [8]. Based on the switching control algorithm and backstepping theory, a control method for the fully automatic parking of vehicles was proposed in [9]. Improved A* and dynamic window approaches were proposed to enhance the accuracy and speed of tracked vehicle automatic parking [10]. Utilizing a recursive network structure, deep neural networks (DNNs) were used to approximate the optimal parking trajectory [11]. A novel adaptive pseudospectral (NAP) method was proposed to solve the time-energy optimal control model problem, minimizing the vehicle parking time and the energy output [12]. Restrictions on parking spaces can make parking more challenging. Algorithms for parallel parking and forward perpendicular parking path planning considering the parking corridor space were proposed in [13]. A geometric path plan consisting of two stages for the automatic execution of vertical and parallel parking in narrow spaces using reverse paths was proposed in [14]. In fact, in terms of emerging automatic parking technology, researchers pay attention to the detection and tracking control technology related to the success of parking. However, with the development of highway public transportation, people have more demanding requirements for parking quality such as collision avoidance, a smooth and short path, etc., and parking trajectory optimization technology has also attracted more attention as it matures. In order to improve the area utilization rate, vertical parking spaces are used in parking lots and garages. Combining cubic spline interpolation and an intelligent optimization algorithm (IOA), it is easy to design an AVP trajectory optimization algorithm with high parking quality.