## 7 Conclusions and Future Work  
In this study, we proposed a path-planning method for intelligent semi-trailers that consider the surrounding traffic conditions and vehicle roll stability, aiming to address the issue of potential rollover during lane-changing in complex traffic. The experimental results comprehensively demonstrate the effectiveness of our proposed method across multiple aspects. \begin{table}
\begin{tabular}{c c c} \hline
**Case Study 4** & **Our Method** & **Sigmoid Method** \\ \hline Average curvature of the path & 0.00175 & 0.00395 \\ Maximum of LTR & 0.83893 & 1 \\ Average steering angle & 7.01638 & 16.21332 \\ Average yaw rate & 1.14704 & 2.80779 \\ Average lateral acceleration & 0.04652 & 0.08669 \\ \hline \end{tabular}
\end{table} 
Table 8: Comparison of case study 4 data. In terms of path tracking performance, as shown in the comparison with the Sigmoid function-based optimization method in different case studies (case study 1-4), our method exhibits a better-fitting trajectory. This indicates that our method can generate a smoother path, facilitating more accurate vehicle control during lane-changing maneuvers. Regarding vehicle roll stability, a crucial aspect for semi-trailers, our method has achieved remarkable results. By setting the roll stability boundary based on the maximum LTR, we ensure that the planned paths meet the roll stability requirements. In all case studies, the maximum LTR values of our method are well below 0.9 (e.g., 0.73249 in case study 1, 0.74934 in case study 2, 0.63285 in case study 3, and 0.83893 in case study 4), while those of the comparison method are close to or reach 1. This significant reduction in LTR effectively supports the roll stability of intelligent semi-trailers throughout the driving process, greatly reducing the risk of rollover accidents. Driving comfort is also improved by our path-planning method. The average steering angle, which is an important indicator of driving comfort, is significantly reduced compared to the Sigmoid-based method. A smaller steering angle not only reduces the driver's physical burden but also provides a more stable and comfortable driving experience for passengers or cargo. In addition, the lateral dynamic stability of the vehicle is enhanced. Although the lane-changing distance of our method may be slightly longer in some cases, the substantial decrease in the average curvature of the path reduces the steering burden of the intelligent semi-trailer. As a result, the tracking performance of the vehicle is improved, as evidenced by the lower average yaw rate and lateral acceleration values in all case studies. This improvement in lateral dynamic stability is crucial for maintaining vehicle control and safety during lane changing. Our method also shows a good adaptability to different traffic conditions. It can flexibly adjust the lane-changing paths according to various driving parameters such as the road adhesion coefficient, vehicle velocity, and load capacity. This adaptability ensures that the path-planning results are always suitable for the current traffic environment, further enhancing the practicality and reliability of the method. However, it should be noted that this study has certain limitations. Although the current framework is mainly applicable to straight-road lane-changing scenarios with constant vehicle speeds, real-world driving conditions are much more complex, including curved roads, variable speeds, and dynamic interactions with other traffic participants. Moreover, simulation experiments rely on predefined environmental parameters, which may not fully reflect real-world unpredictability. Future work will extend the proposed method to address more complex scenarios, such as:  
1. Curved road adaptation: Incorporating path planning for curved roads and dynamic speed adjustments. 2. Dynamic obstacle interaction: Enhancing the decision-making system to handle real-time interactions with moving obstacles and multi-vehicle coordination. 3.