# Trajectory Tracking of Autonomous Vehicle Using Clothoid Curve
## 1 Introduction  
Accurate and smooth motion control is a key technology to ensure the safety and comfort of autonomous vehicles. Vehicle motion control can be further divided into longitudinal speed control and lateral trajectory tracking. Trajectory tracking of autonomous driving has been widely studied in industry and academia alike [1; 2; 3; 4]. This problem can be summarized into two major research contents: the control model and the control method. Control models mainly include geometric models, kinematic models, dynamic models, etc. Control methods include geometric methods, feedforward and feedback control methods [5], Lyapunov direct methods [6], robust control methods [7], intelligent control methods [8], etc. Thanks to properties such as low model complexity, few parameters, and low computation consumption, the geometric model and the control method have been widely used. The pure pursuit tracking method is the most popular geometric control method that has been studied and applied the most in recent years [9; 10; 11]. However, its planned control curve is an arc segment and does not consider the constraint of the actual vehicle control on the continuity of the path curvature. In addition, the algorithm uses a certain preview distance selection strategy that has poor adaptability to paths with different curvatures.  
This paper introduces a method that constructs a vehicle motion model with a continuous curvature path and provides a new control law that uses a G2 continuous clothoid curve to improve the tracking accuracy and ride comfort experience for the trajectory tracking task of an autonomous vehicle. The overall flow of the algorithm is shown in Figure 1. First, the vehicle state is predicted by the communication delay of the control system, and then the starting and ending points of the clothoid curve are determined according to thevehicle state and the parameters of the reference path. The clothoid curve is calculated using the method given in Reference [12]. This method is reliable and quick and can reach the microsecond level. The parameters of the clothoid curves are checked for feasibility constraints, and the optimal control curve is obtained. Then, the response hysteresis of the steering system that is controlled through the CAN bus is taken into consideration; finally, the preview control method based on the clothoid curve is proposed. The correctness of the approach proposed in this paper can be checked by simulation and experiment. The simulation verification can adopt the concept of model-based testing [13; 14]. In this paper, we directly use field experiments to check the correctness of the approach. The field experiment consists of comparative tests in various curved-road environments in a park. The experimental results show that the trajectory tracking control method based on the clothoid curve proposed in this paper greatly improved the tracking accuracy at different speeds compared with the pure pursuit method.  
The rest of this paper is organized as follows. In Section 2, the related literature on the geometric vehicle model, control curve, and control system delay are discussed. Section 3 details the steps taken to calculate the steering wheel angle based on the clothoid control curve. Section 4 details the experiments conducted on an actual vehicle and analyzes the accuracy and advantages of the method proposed in this paper. The last section concludes the work and discusses further research.