# Trajectory Tracking of Autonomous Vehicle Using Clothoid Curve
## 3 Tracking Control Method Using Clothoid Curve
### Preview Point Selection
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 can be seen that the steering wheel angle control commands given by the pure pursuit method still suffer a drastic oscillation when leaving the right-angle turn. Fourth row: yaw angle deviation from the reference path point. The obvious direction deviation generated by the pure pursuit tracking method when leaving the right-angle turn also appears as expected. Last row: lateral deviation from the reference path. The performance of the method proposed in this paper is obviously better than the pure pursuit tracking method when passing through right-angle curves, but the accuracy is slightly lower when passing through S curves with a small curvature. The analysis of the three groups of comparative test results shows that the performance of the method proposed in this paper is generally better than the pure pursuit tracking method. In particular, the yaw deviation is improved by more than 50%. Under different speeds, both methods can control the lateral tracking deviation and yaw deviation within 5 cm on the straight track. The maximum lateral deviation and yaw deviation of both control methods occurred at the first right turn. The reason is that the maximum curvature of this turn curve is 0.168, which almost reaches the limit of the turning radius of the vehicle. The value of the steering wheel target angle output by the method proposed in this paper in this curve reaches about 94%. When the vehicle passed this curve at the speed limit of 10 km/h, due to the relatively low entry speed, the lateral deviation and heading deviation obtained at 10 km/h is less than those at the speed limits of 15 km/h and 20 km/h. During the 15 km/h and 20 km/h speed limit tests of the pure tracking method, there is a large jitter after every right turn, which leads to a large deviation in yaw. A small curvature S curve and a lane-changing scene are designed in the route. In the 10 km/h speed limit test, the performance of the method proposed in this paper is better than that of the pure pursuit tracking method. In the speed limit 15 km/h and 20 km/h tests, the tracking result of the pure tracking method is better than that of the method proposed in this paper, but the method proposed in this paper still controls the lateral tracking deviation within 5 cm. The reason for the analysis is that the preview distance of the pure pursuit tracking method is close at low speed and oscillates when tracking small curvature paths. As the speed increases, the preview distance also increases, which can better adapt to small curvature paths. However, the parameter adjustment of the method proposed in this paper requires that the speed is low enough to show better tracking performance when passing curves. During the test, the control frequency is set to 100 HZ. Although it may require multiple calculations to solve the optimal clothoid curve in one control cycle, the method provided in Reference [18] is very efficient in solving the clothoid curve and can reach a delicate level, so the average calculation efficiency of the system can meet the real-time requirements. The system transplantation would take some work. In addition to the basic parameters of the vehicle geometric model, such as the wheelbase and the steering ratio, it is also necessary to adapt the communication delay of the control system and the response lag time parameters of the vehicle steering servo system. In general, the system has good real-time performance. ## 5 Conclusions

The trajectory tracking control method using a clothoid curve is proposed in this paper. First, the vehicle motion control model is constructed; then, based on the current state of the vehicle, the control system communication delay time is used to predict the vehicle state, which is the starting point of the clothoid curve.