## 5 Conclusions  
This study proposes a novel graph and safety potential field theory-based platoon formation and optimization method. Graph theory is applied to describe the information topology between CAVs and control the trajectory of CAVs during the platoon formation process. Safety potential field theory is exploited to characterize the driving risk of CAVs during the platoon formation process. A four-step platoon formation and optimization control strategy based on the G-SPF model is proposed. This platoon control method increases the consideration of the complex driving environment during the formation of the platoon, which ensures the driving safety of vehicles in the CAVs environment. CAVs distributed in different lanes can be aggregated into the lane where the leading vehicle is located according to the information between the CAVs without any collisions. The \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Performance Indicators**} & \multicolumn{3}{c}{**Control Strategies**} \\ \cline{2-4}  & **Constant Spacing** & **Constant Time** & **Potential** \\  & **Strategy** & **Headway Strategy** & **Field-Based** \\ \hline Average time headway & & & \\ (s/veh) & 0.839 & 1.011 & 0.698 \\ Travel time (s) & 110.7 & 113.5 & 108.6 \\ Velocity deviation (m/s) & 0.071 & 0.057 & 0.013 \\ Average jerk (m/s\({}^{3}\)) & 0.215 & 0.193 & 0.202 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comprehensive performance for different control strategies. optimized control after the formation of the platoon shows obvious advantages in traffic efficiency and exhibits strong platoon stability, compared with the traditional fixed spacing or fixed headway control method. From the perspective of platoon configurations in the future connected and automated environment, safe and efficient platooning has always been the research direction we are pursuing. The findings of this study illustrate that the safety potential field model, considering the multiple pieces of motion information of vehicles (velocity, acceleration, steering angle, etc. ), can be well applied to vehicle platoon control. There are some limitations to this study that would need further improvements. More available field data need to be collected for the purpose of calibration and validation of our proposed model. In addition, there is no discussion of platoon formation under different vehicle information topologies. Therefore, further studies may focus on the analysis of multi-type topologies based on real vehicle experiments and try to combine different types of advanced control methods to further expand the research of this study. Nevertheless, this paper provides a new idea and method for platoon formation and optimization in the future autonomous driving environment. Conceptualization, L.L. and J.G. ; methodology, L.L. ; software, P.M.; validation, J.G., Z.Y. and X.Q. ; formal analysis, L.L. ; writing--original draft preparation, L.L. and J.G. ; writing--review and editing, X.Q. ; visualization, L.L., P.M. and Z.Y. ; supervision, X.Q. and B.R. ; project administration, X.Q. ; funding acquisition, X.Q. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Key R&D Program in China (Grant No. 2018 YFB1600600), the MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Project No. 20 YJAZH083) and the National Natural Science Foundation of China (Grant No.51878161). Part of the research was conducted at the University of Wisconsin-Madison where the first author spent a year as a visiting student funded by the China Scholarship Council. Informed consent was obtained from all subjects involved in the study. Data Availability StatementData sharing not applicable. No new data were created or analyzed in this study. Data sharing is not applicable to this article. We would like to thank the anonymous reviewers whose insightful comments have helped significantly improve the quality of the analysis and presentation of this study.