# Automatic Vertical Parking Reference Trajectory Based on Improved Immune Shark Smell Optimization
## 4 Experimental Verification
### Results and Analysis of the Automatic Parking Experiment  
To verify the optimization effect of the proposed parking optimization algorithm, with clear weather and no wind, the proposed IISSO, an IIMPO proposed in [15], the traditional shark smell optimization [18], the traditional moth flame optimization [22], an improved PSO proposed in [16], and the traditional PSO [23] were used to optimize the parking reference trajectory. Fuzzy proportional-integral-derivative (Fuzzy PID) control was selected as the reference trajectory tracking control mode of the above algorithms. To ensure a reasonable comparison of the performance differences, the optimization models of the optimization reference trajectory of the different algorithms were configured with the same parameters, as detailed in Table 1.  
To ensure that the experiment comparison results were fairly compared, the vehicle coverage areas at the fixed points of P4, P7, and P10 in the automatic parking tracking control process were selected for analysis and comparison, and their ordinate ranges were [5.95, 6.05] meters, [4.45, 4.55] meters, and [2.30, 2.50] meters, respectively. The experimental results of the automatic vertical parking included the trajectory optimization results and tracking control results displayed by the upper computer, as well as the UAV aerial images for the vehicle coverage areas at the fixed points in the tracking process. The optimized reference trajectory and tracking control curve of the whole parking process for the two AVP experiments are shown in Figures 5-8, respectively. The display images of the upper computer and aerial photography images of the vehicle overlay areas at the three fixed points of the parking tracking control process for the two AVP experiments are shown in Figures 9-12, respectively. The fixed point coordinates and path length results of the optimized trajectory curve and its tracking control curve can be seen in Tables 2-5, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Symbol** & **Value** \\ \hline Vehicle coverage area collected times & \(ns\) & 10 \\ Parking inclination angle threshold & \(\Delta\angle_{\text{Smax}}\) & \(\frac{\pi}{20}\) \\ Parking process period & \(\Delta t\) & \(1.5\times 10^{-3}\)s \\ Parking interval threshold & \(\Delta L_{\text{max}}\) & \(10^{-3}\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter configuration of the automatic vertical parking optimization model. Figure 5: Reference trajectory optimization curves for the AVP at the pre-selected points obtained via the upper computer (scene 1). Figure 6: Reference trajectory optimization curves for the AVP at the pre-selected points obtained via the upper computer (scene 2). Figure 7: Reference trajectory tracking control curves for the AVP at the pre-selected points obtained via the upper computer (scene 1). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Parking Point Vector (m, m)** & **Path Length (m)** & **Parking Position Error (m)** & **Realization Time (s)** \\ \hline IISSO & (1.55, 2.39, 0.40) & 9.035 & \(-\)0.01 & 9.47 \\ IIMFO & (1.49, 2.43, 1.57) & 9.182 & 0.03 & 9.88 \\ SSO & (1.41, 2.44, 2.82) & 9.293 & 0.04 & 10.62 \\ MFO (1.33, 2.39, 2.44) & 9.411 & \(-\)0.01 & 10.09 \\ IPSO & (1.24, 2.35, 2.07) & 9.498 & \(-\)0.05 & 10.44 \\ PSO & (1.17, 2.35, 1.79) & 9.553 & \(-\)0.05 & 10.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Reference trajectory optimization results for the AVP process (scene 2). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Parking Point Vector (m, m)** & **Path Length (m)** & **Parking Position Error (m)** \\ \hline IISSO & (1.53, 2.40, 0.53) & 9.109 & 0 \\ IIMFO & (1.47, 2.44, 2.72) & 9.292 & 0.04 \\ SSO & (1.40, 2.46, 2.85) & 9.358 & 0.06 \\ MFO (1.32, 2.41, 1.51) & 9.443 & 0.01 \\ IPSO & (1.23, 2.38, 1.29) & 9.502 & \(-\)0.02 \\ PSO & (1.20, 2.41, 0.72) & 9.544 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Reference trajectory tracking control results for the AVP process (scene 2).