## 4 Numerical Experiments
Figure  
**Scenario II**: In this scenario, all the following vehicles are distributed in the right lane of the leading vehicle at the initial state and are controlled to gradually merge into the lane where the leading vehicle is located one by one by adjusting their own positions. To show the advantages of the model in considering the complex road environment, in this scenario, we added double yellow lines on the road to simulate the plator formation process in the merging area. The spatial distribution \(\left[X^{i},Y^{i}\right]\) and the velocity \(\left[v_{x}^{i},v_{y}^{i}\right]\) of each \(i\)-\(th\) CAV at the initial state were set as follows:  
\[\left[ \begin{array}{cc}X^{0}&Y^{0}\\ X^{1}&Y^{1}\\ X^{2}&Y^{2}\\ X^{3}&Y^{3}\\ X^{4}&Y^{4}\\ X^{5}&Y^{5}\end{array} \right]=\left[ \begin{array}{cc}86&2\\ 60&6\\ 40&10\\ 38&6\\ 25&10\\ 5&10\end{array} \right](m),\left[ \begin{array}{cc}v_{x}^{0}&v_{y}^{0}\\ v_{y}^{1}&v_{y}^{1}\\ v_{x}^{2}&v_{y}^{2}\\ v_{y}^{3}&v_{y}^{3}\\ v_{x}^{4}&v_{y}^{4}\\ v_{x}^{5}&v_{y}^{5}\end{array} \right]=\left[ \begin{array}{cc}6.0&0.0\\ 8.0&0.0\\ 14.0&0.0\\ 8.5&0.0\\ 8.0&0.0\\ 9.5&0.0\end{array} \right](m/s). \tag{18}\]  
Figures 7 and 8 present the trajectories and the lateral and longitudinal velocities of the CAVs during the platoon formation process, respectively. Similar to scenario I, all the vehicles except for the gray vehicle out of the communication range can be gradually merged into the same lane to form a platoon through our proposed control strategy in Section 4. Note that the first, second, third and fourth vehicles are controlled to maintain the car-following state in the double yellow line area where lane changing is prohibited. They start to change lanes when reaching the dotted line area and gradually merge into the lane of the leading vehicle. Compared with the previous study of platoon formation based on graph theory, consideration of the driving risk in the surrounding environment of the vehicle can better ensure traffic safety. This advantage comes from the accurate description of the safety risk of the driving environment by the safety potential field model. Figure 7: The trajectories of the CAVs during the platoon formation process (scenario II). **Scenario III**: In this scenario, the following vehicles are randomly distributed in the different lanes (left and right sides of the leading vehicle) at the initial state and are controlled to gradually merge into the lane where the leading vehicle is located one by one by adjusting their own positions. The spatial distribution \(\left[X^{i},Y^{i}\right]\) and the velocity \(\left[v_{x}^{i},v_{y}^{i}\right]\) of each \(i\)-\(th\) CAV at the initial state were set as follows:  
\[\left[ \begin{array}{cc}X^{0}&Y^{0}\\ X^{1}&Y^{1}\\ X^{2}&Y^{2}\\ X^{3}&Y^{3}\\ X^{4}&Y^{4}\\ X^{5}&Y^{5}\end{array} \right]=\left[ \begin{array}{cc}70&6\\ 60&6\\ 48&2\\ 40&10\\ 22&2\\ 5&10\end{array} \right](m),\left[ \begin{array}{cc}v_{x}^{0}&v_{y}^{0}\\ v_{x}^{1}&v_{y}^{1}\\ v_{x}^{2}&v_{y}^{2}\\ v_{x}^{3}&v_{y}^{3}\\ v_{x}^{4}&v_{y}^{4}\\ v_{x}^{5}&v_{y}^{5}\end{array} \right]=\left[ \begin{array}{cc}6.0&0.0\\ 4.3&0.0\\ 7.8&2.0\\ 6.4&-1.0\\ 9.15&1.0\\ 12.15&-1.0\end{array} \right](m/s). \tag{19}\]  
Figures 9 and 10 depict the trajectories and the lateral and longitudinal velocities of the CAVs during the platoon formation process, respectively. Similar to scenario I and scenario II, all the vehicles can also be controlled to gradually merge into the same lane to form a platoon through our proposed control strategy in Section 4. The simulation results of scenarios I to III show that the platoon formation method proposed in this paper can be applied to the preliminary platoon formation of multiple CAVs in different initial states. A stable platoon is formed after approximately 20 s in all three scenarios.