## 2 Method
### Autonomous Vehicle Pipeline and Vehicle Setup  
The considered vehicle is a fully electric all-wheel drive racing prototype with four on-wheel electric motor coupled with a highly efficient planetary transmission system concentrically mounted on each wheel hub. The vehicle has an integral carbon fiber chassis built with honeycomb panels, double wishbone push-rod suspensions, and a custom aerodynamic package. The vehicle can reach a maximum speed equal to 120 km/h with longitudinal acceleration peaks reaching up to 1.6 g. The main specifications of the racecar are listed in Table 1.  
The vehicle senses the surrounding environment featuring a custom perception pipeline composed of a LiDAR-based sensor with an integrated high-performance Graphic Processing Unit (GPU) and a stereocamera. The former sensor is mounted in the middle of the front wing of the vehicle at a height of about 0.1 m from the ground. The latter instead is placed on the main roll hoop, above the driver's seat. Both the sensors are interfaced with a properly designed Robotic Operating System (ROS) environment that can handle the measurements during vehicle's motion and fuse them in order to provide real-time estimation about the position and type of surrounding obstacles. Specifically, the racing environment is structured with multiple traffic cones of different colors, as illustrated in Figure 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Mass & \(m\) & 190 & [kg] \\ Moment of Inertia about \(z\)-axis & \(I_{z}\) & 95.81 & [kgm\({}^{2}\)] \\ Vehicle wheelbase & \(l\) & 1.525 & [m] \\ Overall length & \(L\) & 2.873 & [m] \\ Front axle distance to CoG & \(a\) & 0.839 & [m] \\ Rear axle distance to CoG & \(b\) & 0.686 & [m] \\ Vehicle rack width & \(t\) & 1.4 & [m] \\ Overall width & \(W\) & 1.38 & [m] \\ Height of CoG & \(h_{CG}\) & 0.242 & [m] \\ Wheel radius & \(R_{W}\) & 0.241 & [m] \\ Longitudinal drag area & \(A_{f}\) & 2 & [m\({}^{2}\)] \\ Longitudinal drag coefficient & \(C_{d}\) & 0.3 & - \\ Longitudinal lift & \(C_{l}\) & 0.1 & - \\ Longitudinal drag pitch moment & \(C_{pm}\) & 0.1 & - \\ Maximum power & & & \\ (total vehicle) & \(P_{max}\) & 80 & [kW] \\ Motors peak torque & \(T_{max}\) & 84 & [Nm] \\ Steering transmission ratio & \(\tau\) & 4.23 & [-] \\ Maximum energy stored & \(E_{bp}\) & 6.29 & [kWh] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Technical specifications of the racing prototype. CoG is the vehicle’s Center of gravity.  
Figure 1: (**a**) Racing vehicle in the structured environment; (**b**) Vehicle dimensions and perception hardware location: 1. Velodyne VLP-16 LiDAR; 2. Stereolabs ZED stereocamera; 3. nVIDIA Jetson Xavier high-performance computational unit with embedded GPU.  
Information coming from the perception pipeline is then exploited for building a local map that enables the path planning method based on a modified version of RRT algorithm using Dubins curves.  
Once the optimal path has been identified with respect to the goal position in each sensed local map, the investigated control strategy based on MPC assesses the vehicle dynamics control during motion. The vehicle is controlled via longitudinal acceleration and steering angle commands that are computed with respect to the planned path, while minimizing the tracking errors defined in terms of relative yaw angle and lateral deviation, as defined in [16; 18; 19].  
The proposed PIL architecture is developed by deploying the planning and control methods into the retained real-time target platforms: a high-performance Speedgoat Baseline platform and low-cost Raspberry Pi 4B board. Both these target machines have been connected via UDP protocol to a host personal computer in which the retained vehicle model is accordingly defined. Figure 2 illustrates the retained autonomous pipeline and PIL architecture.