# Modeling of Lane Changing Behavior of Connected Driving Based on Vehicle Interaction Potential
## 2 Research of Vehicle Interaction Potential Based on Lennard-Jones Potential  
### Vehicle Interaction Potential Based on Lennard-Jones Potential  
The molecular force between molecules is the attraction and repulsion interaction between molecules, which is the main reason for the different physical properties of molecules. The equilibrium distance is denoted as the zero distance of the resultant force of molecular attraction and repulsion. When the distance between molecules is greater than the equilibrium distance, the intermolecular force as a whole appears as gravity. When the distance between molecules is less than the equilibrium distance, the intermolecular force as a whole behaves as a repulsive force. The motion of the traffic flow is reduced to the level of particles; just like the current particle is pushed by the particles behind and pulled by the particles in front of the forward movement, the vehicles are not easy to get close to and not easy to stay away from, and from the dynamic point of view the movement is under the combined action of gravity and repulsion. The interaction between vehicles on the road has similar characteristics to the mechanical relationship between molecules. In this paper, microscopic vehicles in traffic flow are compared to molecules, and a vehicle interaction potential model is established on the basis of molecular dynamics. The Lennard-Jones molecular action potential function is widely used in modeling research based on molecular dynamics. Based on the intermolecular Lennard-Jones potential, [PERSON] [15] established a molecular interaction potential model between following vehicles:  
\[U=4\epsilon\left[\left(\frac{X_{r}}{L}\right)^{12}-\left(\frac{X_{r}}{L} \right)^{6}\right] \tag{1}\]  
where: \(\epsilon\) is the depth of the potential well; \(L\) is the distance between the front and rear cars; and \(X_{r}\) is the required safe distance for following. However, 6-12 potential is only a special form of Lennard-Jones potential. Although it conforms to the interaction between microscopic particles in fluids, it is directly applied to the interaction behavior of real vehicles, ignoring the large differences in mass, velocity, and acceleration of the objects studied in the two scenarios. The model results in a strong sensitivity of the vehicle to each parameter. Therefore, [PERSON] [16] sets the powers of gravitational and repulsive forces in the original model as undetermined parameters, and the vehicle interaction potential function is constructed. \[U=\frac{\epsilon}{v-u}\left[u\left(\frac{X_{r}}{L}\right)^{v}-v\left(\frac{X_{ r}}{L}\right)^{u}\right] \tag{2}\]  
where: \(v\) and \(u\) are powers of the gravitational and repulsive force terms, and \(v>u\). The research shows that when the actual distance between two vehicles is less than the required safety distance, different degrees of short-range repulsion are displayed. The closer the distance, the greater the repulsive force. The contour projection state of the potential field, as shown in Figure 1, indicates that the risk of approaching the vehicle from any direction is the same, but this is obviously unreasonable. Therefore, consider the following factors that may affect the vehicle potential distribution to modify the model. (1) In the actual road driving environment, the action potential  
Figure 1: Schematic diagram of initial stationary vehicle potential field. of vehicles at the front and rear of the same lane on the target is significantly higher than that of vehicles in adjacent lanes approaching from the side; (2) dynamic vehicles should show a different acting potential to static vehicles. The coordinate system is established with the position of the leftmost lane line of the road as the \(Y\) axis, as shown in Figure 2.  
Taking distance, velocity, and longitudinal acceleration into account in the correction of the model, the vehicle action potential function is obtained as follows:  
\[\left\{