# Goal Estimation of Mandatory Lane Changes Based on Interaction between Drivers
## 1 Introduction  
Although the traffic accident rates are declining, they remain a main factor of mortality. According to the conducted survey [1], nearly 90% of traffic accidents have been caused by human errors. To solve this problem, many researchers have developed autonomous driving and advanced driver-assistance systems (ADAS), and achievements to substitute or aid human drivers were obtained. For instance, a predictive system for future actions of surrounding vehicles is strongly required to improve driving safety. This system would support the cognition of the host driver and guarantees a sufficient reaction time with respect to the behaviors of surrounding traffic participants. Notably, the system could contribute to decreasing accidents that require an instant response, such as lane changes. If it is possible to forecast lane changes performed by surrounding vehicles, the accident rate can be significantly reduced. When a driver performs a lane change, there are two situations: mandatory and discretionary lane changing. In mandatory lane changing (MLC), a driver must perform a lane change, such as on-ramp or off-ramp. Conversely, discretionary lane changing (DLC) is usually performed when a driver desires to gain speed and improve the driving condition. According to the previous survey, the number of accidents caused by the MLC is twice compared to the DLC. For instance, in the merging situation, drivers may show a tendency to drive aggressively, performing risky lane changes as the end of the acceleration lane becomes closer. In contrast, the DLC does not force drivers to conduct lane changes if it may lead to a collision with vehicles on the target lane. Therefore, an estimation method for MLC is strongly required to improve driving safety. If it is possible to estimate a goal where the lane-changing driver attempts to overtake in front of the host driver, the target lane driver can be ready to react. Hence, the goal estimation of lane changing performed by other drivers may lead to better driving safety. The interaction between drivers is essential to forecast future actions [2,3]. Drivers control the speed and direction of their own vehicles depending on surrounding vehicles. Surrounding drivers also adjust their speed and direction according to the movement of the host vehicle. Figure 1 shows an example of the interaction between drivers at the on-ramp. When the vehicle on the mainstream lane is slowing down, it can be considered to give passage and allow a lane change to the front space of that as shown in Figure 1a. Conversely, if the vehicle on the mainstream lane maintains the speed or accelerates as shown in Figure 1b, the behavior can be interpreted as rejecting a lane change. Thus, the lane-changing vehicle should aim to cut-in to the behind space of that vehicle. However, some drivers may not abort the lane change in real circumstances. That driver accelerates further and forcibly enters the mainstream lane. In this case, the vehicle on the mainstream lane is forced to decelerate and give passage. Consequently, the interaction between drivers, who are on the acceleration lane and mainstream lane, should be considered for appropriately anticipating the goal of lane-changing. Among all the estimation model for MLC, a gap acceptance model (GAM) is the most widely used technique [4, 5, 6]. This model evaluates the probability of lane-changing performed by a vehicle located on the acceleration lane. The probability is derived by comparing the current gap with a critical gap distance, which is the minimum distance required to conduct lane changes. If the current gap is larger than the critical gap distance, the probability of lane-changing increases. However, this model does not consider the interaction between drivers. There are some drivers who perform a lane change even if the required gap distance is not ensured. Moreover, there is a possibility that the driver on the mainstream lane rejects the lane-changing and suddenly shortens the distance.