## 3 Intra-Platoon Potential Field  
The intra-platoon potential field (IPF) is a physical field that denotes the spatial distribution of risk between targets in complex traffic environments. The targets refer to objects, such as vehicles, pedestrians, and cyclists, that could collide or their current status could result in significant losses. Microscopic driving behavior in the traffic environment was mapped to potential field theory [19; 24; 25]. The vehicle will be affected by its environment in the process of driving. Generally speaking, no matter what kind of driving behavior the vehicle displays, its purpose is to achieve its movement purpose under the premise of ensuring driving safety. Taking lane-changing behavior as an example, during the process, the key to determining whether lane-changing behavior can be successful is to keep a safe distance between the vehicle and other vehicles around it. Although there is no substantial physical contact between the lane-changing vehicles and their surrounding vehicles, their motion state changes due to the surrounding position state. This indicates that there is a virtual force acting on the lane-changing vehicle, which causes it to change its motion state, where the virtual force is provided by the surrounding vehicles. The virtual force can be mapped to the field force because it is not determined by contact but due to the distribution of spatial positions. This shows that there is a potential field in the lane-changing scene and even in the traffic system, which represents the driving risk caused by the traffic environment. In the traditional model of the acceptable gap theory, the field model usually only considers the repulsion field between the lane-changing vehicles and other vehicles around it to obtain the critical minimum safe distance during lane changing. However, the difference between platoon lane changing and non-platoon-vehicle lane changing is that the vehicles in the platoon can tolerate smaller safety distances because of the characteristics of the platoon and CAVs. An inappropriate safety distance may occur when there is no lane-changing model specifically for platoon vehicles. On an expressway, an inappropriate distance between vehicles in a platoon even means the dissolution of the platoon. Therefore, this study considered the design of the IPF model, which is composed of the repulsive force field between each vehicle and the gravitational potential field between vehicles in the platoon. On the premise that the platoon does not dissolve, it can complete the lane-changing maneuver of all vehicles in the platoon. Therefore, this study combined the repulsive force field to establish the IPF expression of the interaction between platoon vehicles, as follows:  
\[E_{v}=\left(\frac{1}{2}\big{(}E_{r}+E_{g}\big{)}+c\right)\frac{k^{\prime}}{| k^{\prime}|} \tag{1}\]  
where \(E_{v}\) stands for the intra-platoon potential field, \(E_{r}\) represents the repulsive potential field, \(E_{g}\) refers to the gravitational potential field, and \(c\) is a value related to scale correction. The repulsive potential field is a typical potential field that was widely applied in the traffic environment. In a previous study [16], the existing repulsive potential field model was established by considering the spatial position of surrounding vehicles and their motion state.