## 2 Intent-Estimation- and Motion-Model-Based Collision Avoidance Method
### Intent Estimation  
Detected moving vehicles can be extracted from sensor information, and their moving features become accessible. All of the detected vehicles can be modelled with a state vector in the form of Equation (1), as shown in Figure 2.  
\[\overrightarrow{\xi}=[ \begin{array}{cccccc}x_{p}&y_{p}&\theta&v&a&w\end{array} ] \tag{1}\]  
where \((x_{p},y_{p})\) is the position, \(\theta\) represents the moving direction of the vehicle, \(v\) and \(a\) are the velocity and acceleration, respectively, and \(w\) is the yaw rate of the vehicle. For a vehicle moving along a straight lane, as shown in Figure 3a, the trajectory of the vehicle can be predicted with its moving state, although the trajectory may fail when subject to the conditions in Figure 3b,c. In Figure 3b, the vehicle performs a left lane change, and the vehicle in Figure 3c moves along a winding road. In addition to the moving state, the road structure should be considered when estimating the driving intents of detected vehicles. Figure 1: Structure of the collision avoidance method. Driving intent estimation and trajectory prediction are the two main components of this method. By matching the lane marks and road edges with an accurate lane-level map, the accurate position of the vehicle on the map is accessible, as well as the lane number and the road shape. The trajectories of the moving vehicles are strongly influenced by the road shape because drivers tend to follow the center line of a lane, which can be modeled with a quadratic curve, as shown in Equation (2). \[y=k_{2}x^{2}+k_{1}x+k_{0} \tag{2}\]  
where \(k_{2}\), \(k_{1}\) and \(k_{0}\) are coefficients. In urban environments, the trajectory of a vehicle is decided by the driver and can be divided into the following categories. * Normal moving (moving along the lane)
* Left change
* Right lane change
* Turn  
For most turns at intersections, the driving intent can be estimated by identifying the lane being driven on. For a driver who wants to turn left, he/she will enter the left-turn lane before entering the intersection. Therefore, we mainly discuss normal moving and lane changes in this paper. For a  
Figure 3: Typical trajectory: (**a**) normal moving; (**b**) lane change; (**c**) normal moving on a winding road. Figure 2: Moving state of a vehicle. normally moving vehicle, the trajectory is similar to the center line of the lane. On the other hand, a vehicle that is changing its lane is leaving the center line and will enter an adjacent lane. A set of lane change trajectories, obtained from the onboard sensors, are shown in Figure 4. It can be seen that the shapes of the change trajectories are different in both longitudinal and horizontal directions, which increases the difficulty of intent estimation. To estimate the intent of the driver, a state vector of the moving vehicle is constructed. \[X_{car}=[ \begin{array}{cccc}d_{l}&d_{r}&\theta&\gamma\end{array} ] \tag{3}\]  
where \(d_{l}\) are distances between the vehicle and the left lane mark and \(d_{r}\) corresponds to the distance between the vehicle and the right lane mark. \(\theta\) is the heading direction of the vehicle, and \(\gamma\) is the current curvature of its path. \[\gamma=w/v \tag{4}\]  
The center line of the lane where the vehicle is moving can also be represented with a state vector:  
\[X_{lane}=[ \begin{array}{cccc}d_{l}&d_{r}&\theta_{lane}&\gamma_{lane}\end{array} ] \tag{5}\]  
where \(\theta_{lane}\) is the road direction and \(\gamma_{lane}\) is the road curvature. Besides, \(d_{l}\) and \(d_{r}\) are set as half of the lane width. These variables can be obtained with the mentioned quadratic curve mentioned in Equation (1) and road information from the map. The computation of \(\theta_{lane}\) and \(\gamma_{lane}\) is attached in Appendix A, and the results are shown in Equations (6) and (7).