# A Hierarchical Control System for Autonomous Driving towards Urban Challenges
## 2 Hierarchical Control System
### Vehicle Control Strategy
#### 2.3.2 Adaptive-Pure Pursuit Algorithm Based-Lateral Controller
In Figure 10, the PW runs a deep learning node using YOLO v3 [40] and 3D LiDARs for ODAT with IMM-UKF-JPDAF algorithm [19]. The CSW handles the localization by applying the sensor fusion technique of GPS and IMU [39]. The control system includes global path planning based on an HD map node, local path planning node, and controller node. We notice that LiDAR object detection and LiDAR localization must work in one computer because of latency transportation of LiDAR data through the Ethernet. ### The Robustness of the Path Tracking Controller

Firstly, we implement path-tracking algorithm based on adaptive-PPC in Section 2.3.2. Then, the working performances in a proving ground are analyzed. The results show that the algorithm works efficiently and performs missions successfully in the test. The tracking results are visualized in

Figure 10: Software and hardware architecture. The left computer manages the perception using a stereo camera and 3D LiDAR fusion. The right computer performs the localization with multiple sensor fusion of GPS and IMU and the control system. The software architecture in Robot Operating System (ROS) middle-ware arrangement is joined between the two workstations. Rviz as shown in Figure 11. The outcomes indicate that the lateral controller obtains the stabilization and robustness to disturbances such as terrain, rolling resistance, and aerodynamic effect. In the common areas with small curvature such as regions 1, 2, 3, and 4 handle well with the low slip respect to the reference trajectory. Although Region 6 and 7 have convex curvatures, the lateral controller also performs well. Figure 12 presents the path tracking results in structured environments. The data is recorded with a bag file, then processing in MATLAB-Robotics System Toolbox. Figure 12b-d are cropped from Figure 1 working at high-curvatures. The path tracking algorithm operates well with small tracking errors in this trial. The hardest task is shown in zone 5 with a concave curve, and the vehicle performs comfortably while the vehicle speed is around 12 kph. It should be remarked that, the adaptive-PPC effortlessly tracks the center of the road while the human is troublesome to conduct this challenge. Figure 11: The visualization of the path tracking algorithm in different routes, where the red line is the actual path and the green line is the ground-truth path. Roughly speaking, the adaptive-PPC can outperform humans in this test.To check the performance of adaptive-PPC, we define the root square error of the path tracking algorithm as follows

\[\centering\xi_{x}=\frac{\sqrt{\sum\limits_{i=1}^{N}\delta_{x}^{2}}}{N}=\frac{ \sqrt{\sum\limits_{i=1}^{N}\left(P_{x}-P_{x}^{ref}\right)^{2}}}{N};\centering\xi_ {y}=\frac{\sqrt{\sum\limits_{i=1}^{N}\delta_{y}^{2}}}{N}=\frac{\sqrt{\sum \limits_{i=1}^{N}\left(P_{y}-P_{y}^{ref}\right)^{2}}}{N};\centering\xi=\frac{ \xi_{x}+\xi_{y}}{2},\@add@centering \tag{23}\]

where \(\centering\xi_{x}\) and \(\centering\xi_{y}\) are the Root Mean Square Error (RMSE) of the path tracking in x and y-axis, and \(\centering\xi\) represents the average error in both x and y-axis. Furthermore, \(\centering\delta_{x}\) and \(\centering\delta_{y}\) denote the error of measured and ground-truth point at each time step. \(P_{x}\) and \(P_{x}^{ref}\) are x coordinate of each position and reference point at each measured time step, respectively. \(P_{y}\) and \(P_{y}^{ref}\) are similar for y coordinate. The results of path tracking error in the structured environment in Figure 12 shown in Figure 8:0

The overall error of the tracking algorithm is around 6 mm per waypoint. The errors at high-curvature approximately are 10 to 25 mm per waypoints. We also demonstrate the error in terms of the histogram as shown in Figure 8:1