## 6 Conclusions  
This study focused on the feasible gap in platoon lane-changing maneuvers in CAVs systems. First, conflicts that may happen in scenes of platoon lane changing were listed and the typical rear-end collision and side crash were selected as core scenarios for this study. Second, a gravitational potential field brought by the traction inside the platoon was proposed for the platoon vehicles. Combined with the repulsive potential field, the IPF method was established, which represents the risk distribution around the platoon vehicle under its current moving state. Third, a safety lane-changing process for the platoon was designed and a dynamic gap in the process was proposed, which was composed of intra-platoon and inter-platoon distances. The distance between non-platoon vehicles was studied in many pieces of research, but it is necessary to also study the gap between intra-platoon vehicles. On the basis of the IPF, this study deeply analyzed the critical distances between vehicles in different conflict scenarios, namely, rear-end collisions and side crashes. It was found that the critical distance in the platoon was an interval with an upper bound and a lower bound, which was quite different from the results in previous studies about non-platoons. Therefore, this study proposed a critical lane-changing distance model for platoon vehicles under each of the two collision scenarios. Finally, experiments were carried out, namely, numerical experiments of critical distances between intra-platoon vehicles and that of the dynamic gap in the entire platoon lane-changing process, which showed that the proposed model effectively represented the relationship between the critical distances and the motion state. Compared with other models, it was verified that the critical distance model proposed ensured the safety of a lane-changing maneuver and that it could maintain a shorter gap compared with non-platoon vehicle lane changing.  
The method can be applied further in many scenarios, including up and down ramps, avoiding construction areas ahead, and even the lane-changing behavior strategy of a self-organizing platoon. Furthermore, future work intends to do further research on trajectory planning and stability control in the platoon lane-changing process under the CAVs environment.  
Conceptualization, R.W.; methodology, R.W.; software, L.L.; validation, L.L. and W.L.; formal analysis, R.W.; writing--original draft preparation, R.W. and L.L.; writing--review and editing, W.L. and B.R.; visualization, R.W., L.L. and W.L.; supervision, Y.R. and B.R.; project administration, Y.R. and B.R.; funding acquisition, Y.R. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Key Research and Development Program of Shandong Province (grant no. 2020 CXGC010118), the National Natural Science Foundation of China (grant no. 41971342), the Fundamental Research Funds for the Central Universities (grant no. 2242021k30055), and the Postgraduate Research and Practice Innovation Program of Jiangsu Province (grant no. KYCX21_0140).  
Data Availability Statement: Data sharing is not applicable. No new data were created or analyzed in this study.  
We would like to thank the anonymous reviewers whose insightful comments have helped to significantly improve the quality of the analysis and presentation of this study.  
The authors declare no conflict of interest.