## 5 Test Verification
### Simulation Results and Comparative Analysis from ARP  
To further validate the effectiveness of the proposed algorithm, simulation verification for ARP trajectory optimization and actual tracking control was conducted using the Matlab simulation platform. A monitoring platform based on Visual Studio was employed to monitor the entire ARP trajectory optimization process, with communication established using Visual C++ 6.0 and the communication medium being Office Excel. The simulation environment was configured as follows: Matlab version 2016b, Visual Studio version VS2015, computer processor model Core i7-9800X @ 3.80 GHz, and Office Excel version Office Excel 2017. The ARP-optimized trajectory model based on Matlab simulation and  
Figure 11: Designated fixed-point regions’ curves for ARP trajectory tracking control  
Figure 10: Designated fixed-point regions’ curves for ARP trajectory optimizationthe key parameters of IDMMFO-GM are described in Table 2 and Table 3, respectively. The pchip function was utilized to construct the cubic spline interpolation function, while the integral fitting method was adopted to solve parking curve length calculations.  
This study selected parking space No. 155 at Dalian Shell Museum in Xinghai Square, Dalian, as the test scenario for automatic parking. The lengths of both the near-side and far-side boundary lines of the test garage were measured as 5.0 m, while the length of the rear boundary line was recorded as 2.7 m, with the width of the parking space markings being 0.1 m. The test vehicle used was a Volkswagen Tiguan (2016 model, 1L variant), with its length, width, and height being specified as 3540 mm, 1645 mm, and 1509 mm, respectively. The initiating position of the vehicle was such that the horizontal distance between the bottom right corner of its coverage area and the far corner of the parking space was measured as 2.2 m, while the longitudinal distance was recorded as 1.0 m.  
Under the aforementioned simulation conditions, comparative tests were conducted between the proposed IDMMFO-GM and three algorithms: IIMFO-GC, IISSO, and IPSO. The trajectory optimization simulation curves and related results are presented in Figure 13 and Table 8.  
As illustrated in Figure 13 and Table 8, compared with IIMFO-GC, IISSO, and IPSO, the simulation-optimized trajectory obtained through IDMMFO-GM demonstrates a shorter berthing trajectory length, and closer proximity to the garage's near-side boundary line. This indicates that the proposed IDMMFO-GM possesses superior optimization capabilities, enabling the identification of more desirable parking trajectories and achieving enhanced ARP trajectory optimization outcomes.  
Figure 12: Actual unmanned aerial image for ARP trajectory tracking control fixed-point regions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithms** & **Center Point Coordinates (m)** & **Path Length (m)** \\ \hline IDMMFO-GM & (1.55, 2.44), (1.53, 3.84), (2.07, 6.01) & 9.19 \\ IIMFO-GC & (1.20, 2.45), (1.21, 3.95), (1.92, 6.15) & 9.75 \\ IISSO & (1.32, 2.49), (1.35, 3.86), (2.02, 6.15) & 9.63 \\ IPSO & (1.11, 2.45), (1.22, 3.93), (1.89, 6.15) & 9.88 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Fixed-point positions and path lengths for ARP trajectory optimization in Matlab simulation environment.