# Trajectory Tracking of Autonomous Vehicle Using Clothoid Curve
## 3 Tracking Control Method Using Clothoid Curve
### Preview Point Selection
### Test Results and Analysis

The performance of the trajectory tracking controller is compared and evaluated by the lateral position deviation and yaw deviation. The calculation method is as follows [22]. Maximum lateral deviation:

\[\varepsilon_{d,\;max}=\max_{i\in[1..N]}\left|\varepsilon_{d,\;i}\right| \tag{17}\]

Maximum yaw deviation:

\[\varepsilon_{\theta,\;max}=\max_{i\in[1..N]}\left|\varepsilon_{\theta,\;i}\right| \tag{18}\]

Average lateral deviation:

\[\varepsilon_{d,rms}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\varepsilon_{d,i}{}^{2}}, \tag{19}\]

Figure 7: Test path. Average yaw deviation:

\[\varepsilon_{\theta,rms}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\varepsilon_{\theta,j}{}^{2}}, \tag{20}\]

The pure pursuit method and the method proposed in this paper were tested on the designed route with speed limits of 10 km/h, 15 km/h. and 20 km/h respectively, as shown in Figures 8-10. The statistics of maximum lateral deviation, maximum yaw deviation, average lateral deviation, and average yaw deviation are shown in Table 1.

Figure 8: Speed limit 10 km/h trajectory tracking. Top first row: the curvatures along the field test road. Second row: actual speed of the vehicle during the trajectory tracking experiment under the speed limit of 10 km/h. It can be seen that the vehicle will slow down according to the curvature of the road ahead before entering the curve. Third row: steering wheel angle commands the comparison between the pure pursuit method and the method proposed in this paper. When tracking the curve, the method proposed in this paper increases the steering wheel angle control command later when entering the curve, and decreases the steering wheel angle control command in advance when leaving the curve, and the control amount given in the curve is also larger. It is because of this that the “cutting corner” problem suffered by the pure pursuit method is avoided. Fourth row: yaw angle deviation from the reference path point. The method proposed in this paper reduces the angle deviation to a large extent and avoids the problem of directional oscillation when turning, so as to improve the driving stability and riding comfort of the vehicle. Last row: lateral deviation from the reference path. The method proposed in this paper greatly reduces the reference path tracking error and improves the accuracy of vehicle path tracking control. Figure 9: Speed limit 15 km/h trajectory tracking. Top first row: the curvatures along the field test road. Second row: actual speed of the vehicle during the trajectory tracking experiment under the speed limit of 15 km/h. It can be seen that the vehicle will slow down according to the curvature of the road ahead before entering the curve. Third row: steering wheel angle commands the comparison between the pure pursuit method and the method proposed in this paper. It is noted that the steering wheel angle control commands given by the pure pursuit method suffer a drastic oscillation when leaving the right-angle turn, which does not occur in the previous test with a speed limit of 10 km/h. This problem might be caused by the improper selection of the preview distance. Fourth row: yaw angle deviation from the reference path point. The direction deviation generated by the pure pursuit tracking method when leaving the right-angle turn is actually caused by the violent oscillation of the steering wheel angle control command. Last row: lateral deviation from the reference path. Compared with the 10 km/h speed limit test, the tracking deviation of the method proposed in this paper in the first right-angle turn increased, which indicates a limitation that the trajectory tracking accuracy of the method proposed in this paper is sensitive to speed changes when passing the curve with a large curvature. Figure 10: Speed limit 20 km/h trajectory tracking. Top first row: the curvatures along the field test road. Second row: actual speed of the vehicle during the trajectory tracking experiment under the speed limit of 20 km/h.