# Trajectory Tracking of Autonomous Vehicle Using Clothoid Curve
## 3 Tracking Control Method Using Clothoid Curve
### Preview Point Selection
\right., \tag{14}\]

where \(\omega\) is the target angular velocity of the steering wheel, \(\delta_{v}\) is the current angle of the front wheel, \(angle_{v}\) is the current steering wheel angle, and \(angle\) is the target steering angle. The meaning of the other characters in Formula (14) is consistent with that in Formula (7). The steering system response hysteresis time \(t_{2}\) has some differences due to the different step values of the actual target angle. If \(t_{2}\) is too large, the target angle may be reached in advance, resulting in tracking deviation; on the other hand, if the selection of \(t_{2}\) is too small, it may cause the steering response to be too slow and delay reaching the target steering angle, thus resulting in tracking deviation. ## 4 Test Results and Analysis

### Test Method

#### 4.1.1 Test Platform

In order to verify the effectiveness of the trajectory tracking control method using the clothoid curve proposed in this paper, an intelligent vehicle modified based on Wey VV6 (as shown in Figure 5) was used for the field test. The intelligent driving software architecture used in the vehicle is shown in Figure 6, which mainly consists of a sensor system, data preprocessing module, perception module, prediction module, planning and decision-making module, positioning module, map and navigation module, control module, system service and log, simulation analysis tools, and other modules. Communication protocol interfaces are defined between modules, and data communication is carried out using the ROS platform. The platform is equipped with two Nuvo-7160 GC industrial control computers, one of which is used in this experiment. #### 4.1.2 Test Path Design

In order to avoid the interference of misidentification and detection on the test, only differential GPS and IMU sensors were used to collect the position information in the test. The driver drove the vehicle along the set route to collect and record the positioning information of the route. Because of the differential GPS positioning system, the accuracy of the recorded path position information is \(\pm\)0.02 m. When the vehicle ran in automatic mode, the decision-making module extracted the path ahead of the vehicle, calculated the position, distance, direction angle, and curvature of each path point, and sent the data to the control module in the form of a path point array. The control module used this path as the reference path to follow and calculated the control command. The control module then sent the generated control command to the drive module and forwarded it to the servo execution system via CAN messages to drive the steering wheel to execute corresponding actions. The test path is shown as Figure 7.

Figure 5: Test platform. Figure 6: Software architecture. #### 4.1.3 Comparison Method

The most popular geometric controllers are the pure pursuit tracking controller and the Stanley controller. Because the pure pursuit tracking controller has few parameters and is insensitive to sudden changes in the path, it is widely used in autonomous vehicles. In recent years, its optimization is mainly focused on the selection of preview points. This paper uses the pure tracking controller for comparative tests. The selection strategy of preview points adopts the method proposed in Reference [9], as shown in Formula (15). The calculation method of the front wheel target angle of the pure pursuit tracking method is shown in Equation (16) [9]. \[l_{d}= \begin{cases}5&v_{cur}<10\;\text{kph},\\ 0.5*v_{cur}&10\;\text{kph}\;\leq\;v_{cur}<50\;\text{kph},\\ 25&50\;\text{kph}\;\leq\;v_{cur}.\end{cases}  \tag{15}\]

where \(l_{d}\) is the preview distance, and \(v_{cur}\) is the current vehicle speed. \[\delta_{l_{d}}(t)=\tan^{-1}\biggl{(}\frac{2L\text{sin}(\alpha(t))}{l_{d}} \biggr{)}, \tag{16}\]

where \(\delta_{l_{d}}(t)\) is the desired steering wheel angle, \(l_{d}\) is the preview distance, \(L\) is the wheel-base, and \(\alpha\) represents the angle between the heading angle of the vehicle and the look-ahead vector.