# 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 Potential Field Distribution under Different States  
When the distance between vehicles is less than the required safety distance, it is represented as a short-range repulsive force. The potential field of vehicles under different  
Figure 2: Road environment diagram. moving states is projected onto the plane to draw its potential field contour diagram, as shown in Figure 3.  
Taking the center of mass of the research vehicle as the origin point, the contour lines of the vehicle potential field under the five motion states of stationary, constant speed, acceleration, deceleration, and steering are shown, respectively. The color represents the difference in the size of the potential field, which is white near the center of mass, indicating that the potential field approaches infinity, which means that a vehicle is bound to collide when it appears at this position. This is in line with practical significance. The following analyzes the spatial distribution of the vehicle potential field according to the above five driving states. 1. Static state. Figure 3a shows the vehicle at rest, when the vehicle is equivalent to a stationary obstacle. Because the risk of approaching the vehicle from the front and rear is greater than that of approaching the vehicle from the side, the distance is corrected in this paper, so the potential field as a whole is oval. 2. State of uniform velocity. Figure 3b,c show the scene when the vehicle is traveling at a constant speed \(v=10\) m\(\cdot\)s\({}^{-1}\) and \(v=15\) m\(\cdot\)s\({}^{-1}\) along the axes \(y\). comparing Figure 3b,c, it can be found that the potential field increases with the increase in speed in the direction of the vehicle. This also well reflects that the vehicle at high speed has a larger risk range for interactive vehicles than that at low speed. Therefore, the potential field as a whole presents an oval shape elongated along the direction of vehicle motion. Figure 3: Distribution diagram of vehicle potential field under different motion states. 3. Accelerated state. Figure 3d,e show a vehicle with a speed of \(v=10\) m\(\cdot\)s\({}^{-1}\) accelerating along the axes \(y\) with \(a=1.5\) m\(\cdot\)s\({}^{-2}\) and \(a=2\) m\(\cdot\)s\({}^{-2}\) accelerations, respectively. By comparison with Figure 3b, it can be found that the potential field of the vehicle presents an obvious forward-leaning phenomenon under accelerated motion. This means that the risk to the vehicle in front of the vehicle is significantly greater than that of the vehicle behind, so the required safety distance in front of the vehicle should be greater than that behind the vehicle. By comparing Figure 3d,e, it can be found that with the increase in acceleration, the degree of forward tilt of the vehicle potential field increases. It indicates that the greater the acceleration of the vehicle, the greater the risk to the front. 4. Deceleration state. Figure 3g,h shows the scenario of a vehicle with a speed of \(v=10\) m\(\cdot\)s\({}^{-1}\) decelerating along an axis with an acceleration of \(a=-1.5\) m\(\cdot\)s\({}^{-2}\) and \(a=-2\) m\(\cdot\)s\({}^{-2}\), respectively. By comparison with Figure 3b, it can be found that the potential field of the vehicle shows an obvious backward tilt in the decelerating motion state. This means that the vehicle poses a significantly greater risk to the vehicle behind than to the vehicle in front. So the required safety distance behind the vehicle should be greater. By comparing Figure 3g,h, it can be seen that the potential field of the vehicle increases with the increase in the deceleration value, that is, the risk degree of the rear vehicle increases with the increase in the deceleration speed. Therefore, in the network environment, when the rear vehicle obtains the deceleration information of the front vehicle, it can decelerate in advance to improve driving safety. 5. Turning state. Figure 3f,i show the vehicle turning to the left while accelerating and decelerating, respectively.