# Goal Estimation of Mandatory Lane Changes Based on Interaction between Drivers
## 3 Proposed Method
### Feature Extraction for the Interaction  
The proposed method applies a potential field method, which is a general method in the robotics field, for assessing the interaction between drivers [12; 13; 14]. A potential field method considers two types of potential energies: attractive and repulsive. The attractive potential energy is generated from the goal, whereas the repulsive potential energy is generated from an obstacle. The total energy that a robot has can be derived as follows. \[U_{total}=U_{a}+U_{r}, \tag{1}\]  
where \(U_{total}\) denotes the sum of potential energies, \(U_{a}\) is the attractive potential energy from the goal, and \(U_{r}\) is the repulsive potential energy. The proposed method does not consider attractive potential energy since the goal is independent of the interaction between drivers. In this paper, the lead and rear vehicles are defined as obstacles. Consequently, the repulsive energy is emitted from each vehicle, and the potential field is generated by combining the two energies. As a navigation method for robots, the repulsive energy is represented as  
\[U_{r}=\frac{1}{2\pi\sigma^{2}}\exp\left[-\frac{r}{2\sigma}\right], \tag{2}\]  
where \(r\) denotes the distance from a robot to an obstacle, and \(\sigma\) is its standard deviation. However, as this model assumes a static obstacle, it cannot handle the environment where dynamic obstacles exist such as traffic conditions. Considering this limitation, [PERSON] and [PERSON] proposed a dynamic characteristic potential field method [15]. This method uses the von Mises distribution and generates a potential field which changes the distribution according to the moving direction of the obstacle. Figure 4 shows the generated potential fields based on the dynamic model. Vehicles are dynamic obstacles, and their acceleration is significant information for assessing the interaction between drivers. At on-ramp of the highway, the lead or rear vehicle may decelerate when the driver intends to give passage for the target vehicle. Conversely, the target vehicle may accelerate to guarantee a safe distance from the lead and rear vehicles. In addition, the target vehicle may decelerate when the driver plans to change a lane after the lead or rear vehicle will pass. Based on this driver tendency, the proposed method generates the potential field drifted to the accelerating direction. The dynamic characteristic potential field method is applied, and the distribution is determined according to the level of acceleration (deceleration). If the level of acceleration is high, the potential field is largely drifted to the accelerating direction. In contrast, if the acceleration is low, the potential field  
Figure 3: Schematic of the proposed method. The proposed method is comprised of three parts. As the output, the goal of lane-changing performed by the target is estimated among the four candidates: \(A\), \(B\), \(C\), and \(D\). has low bias. If the vehicle maintains constant speed without acceleration (deceleration), the potential field has uniform distribution. Drivers generally show a tendency to maintain sufficient distance from the preceding vehicle when their vehicle is at high speed because of safety. Consequently, the proposed method is designed to generate potential energy according to the speed of the subject vehicle. If the vehicle drives with high speed, the large repulsive potential energy is generated. Summarizing the philosophies of our design, the drift direction of the potential field is determined according to the acceleration (deceleration) of the subject vehicle. In addition, the level of potential energy is determined according to the speed of the subject vehicle and its distance from the vehicle.