# Trajectory Tracking of Autonomous Vehicle Using Clothoid Curve
## 3 Tracking Control Method Using Clothoid Curve
### Preview Point Selection
On the reference path, the optimal selection interval of the end point of the clothoid curve is selected, and finally, the optimal clothoid planned control path that satisfies the non-integrity constraints and safety conditions of vehicle driving is obtained. Based on the response hysteresis parameters of the steering system, the curvatures of points are previewed on the clothoid curve to further calculate the target angle of the output steering wheel control. A test path, including a straight lane, a right-angle turn, a curve, and lane-change scenarios, is designed in a park environment, and comparative tests are conducted against the pure pursuit tracking algorithm under

\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Limited Speed** & \(\epsilon_{d,max}\) **(m)** & \(\epsilon_{\theta,max}\) **(rad)** & \(\epsilon_{d,rms}\) **(m)** & \(\epsilon_{\theta,rms}\) **(rad)** \\ \cline{2-7}
**(km/h)** & **Clothoid** & **PP** & **Clothoid** & **PP** & **Clothoid** & **PP** \\ \hline
10 & 0.109 & 0.381 & 0.0557 & 0.1390 & 0.0157 & 0.1225 & 0.0071 & 0.03148 \\
15 & 0.227 & 0.378 & 0.0934 & 0.1753 & 0.0365 & 0.1218 & 0.0134 & 0.03662 \\
20 & 0.232 & 0.368 & 0.0864 & 0.1727 & 0.0393 & 0 the speed limits of 10 km/h, 15 km/h, and 20 km/h. The results show that the trajectory tracking control method using the clothoid curve proposed in this paper outperforms the pure pursuit tracking algorithm in terms of lateral deviation and yaw deviation indicators. In this study, we adopted a geometric vehicle model based on Ackermann steering, so the method proposed in this paper is not applicable to the vehicle platform of other steering models, such as differential steering. At the same time, because the geometric vehicle model is used, the dynamic characteristics of the vehicle, such as the slip of the vehicle caused by the tire sideslip, are not considered. Therefore, the vehicle speed must be strictly controlled according to the curvature of the curve when turning to ensure the path tracking accuracy. In future work, we will use a different platform to test and verify the effectiveness of the method proposed in this paper and future improve the trajectory tracking performance of the method when passing curves with a small curvature. Conceptualization, [PERSON] ([PERSON]) and Y.X. ; methodology, [PERSON] ([PERSON]) and Y.X. ; software, J.L. ([PERSON]) and S.P. ; validation, [PERSON] ([PERSON]), S.P. and Y.L. ; formal analysis, Y.L. and J.L. ([PERSON]); investigation, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); resources, Y.X. ; data curation, [PERSON] ([PERSON]) and [PERSON]; writing--original draft preparation, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); writing--review and editing, Y.X., [PERSON] ([PERSON]) and [PERSON]; supervision, Y.X. All authors have read and agreed to the published version of the manuscript. This Research was funded by the military pre-research project [ZW040202]. And the APC was funded by military pre-research project. Not applicable. The data used to support the findings of this study are available from the corresponding author upon request. The authors would like to thank the handling editor and the anonymous reviewers for their valuable comments and suggestions. The authors declare no conflict of interest. ## References

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