## 3 Intra-Platoon Potential Field
The specific expression of the model is shown in the following equation:  
\[E_{r}=M_{i}\lambda\cdot\frac{e^{-\beta a_{i}\cos\varnothing}}{|k^{\prime}|} \cdot\frac{k^{\prime}}{|k^{\prime}|} \tag{2}\]  
where \(E_{r}\) is the repulsive potential field, \(M_{i}\) is the equivalent mass of the ego vehicle \(i\), \(k^{\prime}\) refers to the virtual distance to donate the relationship between the ego vehicle's velocity \(v\) and the potential field intensity, \(a_{i}\) is the acceleration of the ego vehicle, and \(\varnothing\) is the clockwise angle of any point to the velocity direction of the ego vehicle, and \(\lambda\) and \(\beta\) are undetermined parameters that are related to the equivalent mass and the clockwise angle, respectively. Details of the parameters are given in Equations (4)-(6). The gravitational potential field between vehicles in the platoon was proposed. In order to keep the consistency between the gravitational potential field and repulsive potential field and reduce the number of parameters to be calibrated, the gravitationalpotential field model was modified based on the repulsive potential field model. The formula for the gravitational potential field model was as follows:  
\[E_{g}=M_{i}\gamma|k^{\prime}|\cdot e^{\beta a_{i}\ cos\beta}\cdot\frac{k^{\prime} }{|k^{\prime}|} \tag{3}\]  
where \(E_{g}\) refers to the gravitational potential field, \(k^{\prime}\) is the virtual distance between the ego vehicle velocity \(v\) and the potential field intensity, \(\varnothing\) represents the clockwise angle of any point to the velocity direction of the ego vehicle, \(a_{i}\) is the acceleration of the ego vehicle, \(\gamma\) refers to an undetermined parameter related to the virtual distance, and \(\beta\) is an undetermined parameter related to the clockwise angle. \(M_{i}\) is the equivalent mass of the ego vehicle \(i\) and is used to characterize the influence of the vehicle's mass and its motion state on the repulsive potential field [16]:  
\[M_{i}=m_{i}\Big{(}1.566\times 10^{-14}v_{i}^{,6687}+0.3345\Big{)} \tag{4}\]  
where \(m_{i}\) is the actual mass of the ego vehicle \(i\) and \(v_{i}\) is the velocity of the ego vehicle. In addition, numerical values in the above equation are consistent with our previous research [16]. The artificial bee colony algorithm (ABC) was used for the specific calibration process:  
\[|k^{\prime}|=\sqrt{\Big{[}\big{(}x^{*}-x_{ego}\big{)}\frac{\tau}{e^{\beta v_{i} }}\Big{]}^{2}+\big{[}\big{(}y^{*}-y_{ego}\big{)}\tau\big{]}^{2}} \tag{5}\]  
where \((x^{*},y^{*})\) is the transfer coordinate to describe the relationship between the coordinate of the ego vehicle and the steering angle, \(\big{(}x_{ego},y_{ego}\big{)}\) is the coordinate of the ego vehicle, \(v_{i}\) is the velocity of the ego vehicle, and \(\alpha\) and \(\tau\) are undetermined parameters that are related to the velocity and the lane width. \[\left[ \begin{array}{c}x^{*}\\ y^{*}\end{array} \right]=\left[ \begin{array}{cc}\cos\theta&\sin\theta\\ -\sin\theta&\cos\theta\end{array} \right]\left[ \begin{array}{c}x-x_{ego}\\ y-y_{ego}\end{array} \right] \tag{6}\]  
where \(\theta\) is the steering angle of the ego vehicle and \((x,y)\) is the coordinate of the subject point. In the CAVs system, the motion state of vehicles can be transmitted and shared in real time. Therefore, the potential field distribution of every vehicle can be obtained according to real-time information. Contours are numerical expressions of the potential energy field and are closed-loop rings, according to which, the vehicle makes decisions. In previous research [16], we built a lane-changing model based on the repulsive field for a single non-platoon vehicle and calibrated the values of each parameter. As is well known, platoon lane changing occurs in a hybrid environment of single vehicles and a platoon. Meanwhile, the IPF model of platoon lane changing in this study involved the combination of a repulsive potential field and gravitational potential field between single vehicles in the same platoon.