## 4 Trajectory Prediction Performance Evaluation  
This section evaluates the trajectory prediction performance by comparing it to other trajectory prediction methods. On-road data acquisition experiments were conducted at 31 urban intersections in Tokyo, Japan to evaluate the prediction performance in a real environment. For acquiring the driving data, an experiment vehicle was equipped with additional sensors: a LiDAR, two GPS antennae, and an inertia measurement unit (IMU). While the experiment vehicle drove into the intersection and made a right-turn, the vehicle speed, steering wheel angle, GPS position, yaw angle, accelerations, and point cloud data from LiDAR were acquired by a data recorder. From the acquired data, the driving paths of the experiment vehicle could be obtained. These driving paths were used as references to evaluate the prediction performances of the trajectory prediction methods. An example of making a right turn at the intersection from the data acquisition experiments is shown in Figure 5. This figure contains four subfigures: Figure 5a shows a bird's-eye view of the intersection; Figure 5b shows point cloud data and the observed driver's path in the experiment; Figure 5c,d shows the recorded results of observed velocity and steering wheel angle in the experiment, respectively. On the point cloud data in Figure 5b, a white line indicates the path that the experiment vehicle took. White boxes on the point cloud data indicate the positions of the ego vehicle. The boxes are plotted every 5 m on the right turning maneuver. The distance values by the white boxes show the travel distances of the vehicle at each box. From the acquired driving data, the prediction performance was evaluated as follows. First, from the point cloud data, the position of the escaping road and the relative angle from the ego vehicle to the escaping road \(\theta\) were derived. Second, from the recorded vehicle data, given the trajectory prediction parameters and the intersection information, geometrical trajectories of each method, including the proposed Triclothoidal curve, were sequentially calculated in every time frame. Finally, comparing the recorded actual path of the ego vehicle and the predicted trajectories, the effectiveness of the prediction performance of each prediction method was evaluated. Figure 6 shows the point clouds data from turning right at the intersection, the observed trajectory, and the predicted trajectories from each trajectory prediction method: (a) a circular arc with a constant radius; (b) a circular arc considering the steering angle; (c) Biarc curve; (d) a clothoidal curve; and (e) Triclothoidal curve. In Figure 6, a white broken line indicates the path that the experiment vehicle took. White boxes on the point cloud data indicate the positions of the ego vehicle. The boxes are plotted every 5 m of the turning right maneuver. Green lines indicate the predicted trajectories. Green lines are also plotted every 5 m of the turning right maneuver. Figure 7 shows the comparison of the curvatures of the observed driving data and the predicted trajectories for each trajectory prediction method. A black, bold solid line shows the curvature from the observed data and the colored fine solid lines show the curvature of the predicted trajectories. The predicted curvatures are plotted every 5 m of the turning right maneuver. The colors of the predicted trajectories correspond to the positions of the vehicle. The left-side tip of each colored line corresponds to each position of the vehicle that was represented in Figure 6 as white boxes. Note that, in the experiments, the parameters such as turning radius for (a) the circular arc with a constant radius, and distance parameters \(d_{pre}\) to define the terminal point positions for (c) Biarc, (d) clothoidal curve, and (e) the Triclothoidal curve, were optimized by minimizing the prediction error between the predicted trajectory and the actual driving path from the experiment data.