## 4 Numerical Results and Discussion
### Training and Scenario  
The planning considered the motion of the vehicle in a 250 m long road segment of a two-lane road that is 7.1 m wide. Following common procedures in the literature [18; 19; 20], fixed and moving obstacles (traffic flow) were assumed to be represented by rectangular no-go areas (red boxes in Figure 4). The operational scenario is covered with a grid of 1836 points (graph nodes) and a maximum length of trajectory segments of 10 m, resulting in arcs.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Unit** & **Uncertainty (\%)** \\ \hline Vehicle A & & & \\ \hline Vehicle mass & 1550 & kg & 8 \\ Yaw-axis moment of inertia of the vehicle & 1260 & kg/m\({}^{2}\) & 10 \\ Rear axle tires stiffness & 43,300 & N/rad & 15 \\ Front axle tires stiffness & 63,700 & N/rad & 15 \\ Forward velocity & 25 & m/s & 10 \\ \hline Vehicle B & & & \\ \hline Vehicle mass & 1800 & kg & 8 \\ Yaw-axis moment of inertia of the vehicle & 1500 & kg/m\({}^{2}\) & 10 \\ Rear axle tires stiffness & 43,300 & N/rad & 15 \\ Front axle tires stiffness & 63,700 & N/rad & 15 \\ Forward velocity & 20 & m/s & 10 \\ \hline Vehicle C & & & \\ \hline Vehicle mass & 1550 & kg & 8 \\ Yaw-axis moment of inertia of the vehicle & 1260 & kg/m\({}^{2}\) & 10 \\ Rear axle tires stiffness & 40,000 & N/rad & 15 \\ Front axle tires stiffness & 60,000 & N/rad & 15 \\ Forward velocity & 20 & m/s & 10 \\ \hline Vehicle D & & & \\ \hline Vehicle mass & 1300 & kg & 8 \\ Yaw-axis moment of inertia of the vehicle & 1056 & kg/m\({}^{2}\) & 10 \\ Rear axle tires stiffness & 43,300 & N/rad & 15 \\ Front axle tires stiffness & 63,700 & N/rad & 15 \\ Forward velocity & 25 & m/s & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 1: System parameters values (vehicle A is taken from [58]) for tests.  
Figure 4: Two planned trajectories: the SVM-enhanced one (green line) and the non-SVM-enhanced one (blue line). The trajectories start from the circles on the right. The two red boxes denote two forbidden areas (vehicle A and target A).  
The training for the AIs used a dataset consisting of approximately 17,000 instances of the feasible/unfeasible trajectory classes. The dataset was obtained by setting different start and target points with the proper kinds of vehicles and collecting data from the planning procedure using the Euclidean (nonhybrid) \(A^{*}\). The collected dataset consists of partial trajectories (i.e., the trajectory from the starting point to a candidate segment) in terms of the following:  
* The change in pose (angle and tracking error) associated with each segment of the trajectory;
* The length of each trajectory segment;
* The feasible/unfeasible label for the trajectory followed by a candidate segment.  
The SVM training was performed considering just the last segment of a partial trajectory, while the LSTM was trained on the whole sequences from the starting point.  
It should be noted that uncertainties regarding the vehicle model and road conditions were taken into account by the feasibility check; thus, they were not explicitly changed while creating the dataset, i.e., for a certain vehicle, if a certain uncertain parameter is considered during modeling, the feasibility of a trajectory is guaranteed (and thus it is not influenced) for any allowable value of the parameter in question.  
The data were split into 90% for training and 10% for testing for any trained classifier. For the LSTM, the network was trained using the Adam optimizer for a maximum of 200 epochs, with a learning rate of 0.001, gradient clipping at a threshold of 1, and the cross-entropy loss function. The data were not shuffled during training, and accuracy was used as the evaluation metric. For the SVM, feature scaling ensured normalization using the mean and standard deviation. The model utilized 64 support vectors to define the decision boundary.