## 3 Methodology
### Platoon Formation and Optimization Control Strategy  
In order to achieve efficient vehicle formation operation, the control of the leading vehicle and the following vehicles is subsequently discussed to construct a completeplatoon formation control model. The entire control model based on graph theory and safety potential field theory consists of four steps: the identification of vehicles that can potentially form a platoon, the recognition of the leading vehicle in a platoon, the formation of a preliminary platoon and the implementation of an optimal driving strategy for vehicles in a platoon accounting for traffic efficiency and traffic safety. Figure 4 illustrates the flow chart of our proposed method. The variable t represents the time interval for each vehicle to judge whether there is a chance to form a platoon. The indicator of the end of the algorithm is the horizontal and vertical distances between the vehicles when they reach the desired distance. Step 1: The identification of vehicles that may form a platoon  
The arrival of vehicles on the road is a random phenomenon, and the longitudinal and lateral distances between adjacent vehicles are uncertain in the initial stage. Therefore, some basic constraints should be established to identify those vehicles that may form a platoon. Two microscopic traffic indexes (i.e., vehicle headway and vehicle velocity) are commonly used to identify the vehicles which can form a platoon [4]. In this paper, we additionally use the transmission distance of the information flow as the third index to  
Figure 4: Flow chart of the platoon formation control strategy. describe the limitation of the communication distance between vehicles in a platoon. The constraints in Equation (15) should be satisfied with the vehicles in a platoon as follows:  
\[\left\{ \begin{array}{l}H_{i}\leq H_{0}\\ V_{i}\leq V_{0}\\ D_{l-i}\leq D_{\max}\\ V_{i}=|v_{i}-v_{i-1}|\end{array} \right. \tag{15}\]  
where \(H_{i}\) is the space headway (\(m\)) of two adjacent vehicles (vehicle \(i\) and vehicle \(i-1\)) in the same platoon, \(H_{0}\) is the critical value of the space headway (\(m\)) of two adjacent vehicles, \(V_{i}\) is the absolute difference in velocity (\(m/s\)) between two adjacent vehicles (vehicle \(i\) and vehicle \(i-1\)), \(v_{i}\) and \(v_{i-1}\) are the velocities of vehicle \(i\) and vehicle \(i-1\), respectively, \(V_{0}\) is the critical value of the absolute difference in velocity (\(m/s\)) between two adjacent vehicles, which can ensure that the vehicle generates as little disturbance (from the sudden increase or decrease in vehicle velocity) as possible during the platoon formation process, \(D_{l-i}\) is the distance (\(m\)) between the leading vehicle and the following vehicle \(i\) and \(D_{max}\) is the maximum transmission distance (\(m\)) that the leading vehicle can transmit in the information flow topology of a platoon. According to the constraint requirements in Equation (15), we can make a preliminary judgment on whether vehicles have the possibility of forming a platoon. Step 2: Identification and control of the platoon leader  
According to the result of Step 1, if it can be determined that a group of vehicles can have the potential to form a platoon, then the leading vehicle of the platoon can be determined based on the natural spatial location of the vehicle. The first vehicle in the positive direction of the platoon is automatically recognized as the leading vehicle. For the special situation that some vehicles can form a platoon with the vehicles in front or with the vehicles behind, this article chooses the first vehicle in the driving direction as the leading vehicle selection criterion to form the first platoon. If the vehicles outside the communication range of platoon 1 meet the judgment condition of Step 1 with their following vehicle, this will automatically form a second platoon. Step 3: The preliminary formation of a platoon  
After exploring the identification and control of the leading vehicle, the preliminary formation of a platoon is constructed.