## 6 Conclusions  
ARP systems have a broad spectrum of practical applications across various fields including commercial, civilian, military, and ceremonial domains. However, trajectory optimization for ARP systems presents a multi-objective, non-linear, and extremely difficult optimization challenge. Consequently, obtaining an ideal reference trajectory that makes its curve collision-avoidance smoothness and short path lengths, is particularly difficult. To effectively enhance the performance of ARP trajectory optimization, a gene modification optimization algorithm, IDMMFO-GM, is proposed in this study. In contrast to current research achievements on optimizing reference trajectories for automatic parking, the key contributions of this study can be summarized as follows:  
A novel reference trajectory optimization model for ARP is developed. Integrating cubic spline interpolation with the standardized parking plane coordinate system, an effective and practical reference trajectory optimization framework is established, which takes into account the feasibility constraints of parking, including the initiating region and berthing tilt angle; hence, it can effectively describe and optimize ARP trajectory. To address the issue of infeasible solutions and balance the algorithm's global exploitation and local development capabilities, an IDMMFO-GM is introduced. This algorithm organically integrates the gene modification mechanism, the non-linear decreasing weight coefficient strategy, and the directional mutation strategy, which can effectively utilize infeasible solutions encountered during computation, thus improving its global optimization performance and avoiding local convergence. While the IDMMFO-GM algorithm exhibits excellent performance in optimizing automatic parking trajectories, it still possesses certain constraints: (I) Concerning parameter sensitivity, the algorithm's empirical coefficients require manual tuning. This not only raises deployment expenses but might also compromise the algorithm's adaptability in parking scenes. To achieve dynamic parameter adjustment, the implementation of online calibration technology is essential. (II) Regarding the constraint of dynamic adaptability, the current research is primarily grounded in the static environment hypothesis and does not account for real-time interference factors such as pedestrian movement and dynamic obstacles. In future work, mechanisms for predicting and avoiding dynamic obstacles will be incorporated. (III) Considering the sensitivity of sensor errors, the precision of transforming into a standardized coordinate system largely relies on the quality of sensor calibration. This reliance becomes more significant under extreme conditions, such as low  
Figure 13: ARP trajectory optimization curves in Matlab simulation environment. light or adverse weather like rain and snow, where error accumulation is more likely to occur. Therefore, adopting a multi-source sensor fusion approach is essential for enhancing the stability of the system. (IV) At the multi-objective optimization level, the current model focuses solely on path length as its optimization goal and does not adequately account for various factors, including the rate of change in steering angle and energy consumption efficiency. This could result in practical issues, such as decreased comfort during application. Moving forward, the integration of multi-objective optimization algorithms will aim to address and harmonize the diverse performance requirements across dimensions. To validate the efficacy of the proposed IDMMFO-GM, an automatic parking test is conducted for verification. Actual vehicle tests show that IDMMFO-GM outperforms three high-performance comparative optimization algorithms in parking trajectory optimization. Additionally, its trajectory tracking control performance is markedly improved. The study was undertaken in partnership between all contributing authors. [PERSON].