## 5 Discussion and Conclusions  
The scope of this work lies in bringing the formally ensured safety of set-based methods for trajectory planning into artificial intelligence-based ones, with the aim being to exploit the effectiveness of performing the complex tasks that characterize the latter.  
By combining a graph-based trajectory planning technique used in robotics with an artificial intelligence-based hybrid \(A^{*}\), the technique can improve the performance of the baseline set-based method in terms of the time needed to find a first solution (regardless of its optimality) and the time needed to find the optimal solution.  
Namely, the SVM-based planning showed up to a 28% reduction in computation effort with respect to the classical \"Euclidean\" \(A^{*}\) planning (i.e., the \(A^{*}\) planning). Furthermore, it has been shown that higher accuracy is tied with the performance outcomes of the algorithm but also that the false negative rate can significantly hamper the performances.  
Furthermore, the possibility to enhance planning through the use of a long-short term memory has been evaluated: although it can improve the efficiency of the algorithm while exploring the environment, its higher computational cost exceeds this benefit. It is interesting to note that the highest accuracy of the LSTM can be reached with just five hidden layers. This result could probably be linked to the fact that the kynodynamic feasibility of a trajectory depends, from a physical point of view, on a part of the trajectory that has been already crossed, and further investigation could exploit this result for improving planning performances.  
The results obtained in this work contribute to validating a methodological approach that, while focused on trajectory planning for autonomous vehicles, offers insights and potential for future applications in various scientific and technological contexts. Its possible use in autonomous driving could deal with the local planning of trajectories, not only from the autonomous driving perspective but also in terms of traffic management. In particular, starting from SAE J016 level 2 features, AVSes require kynodynamically feasible trajectories.  
Further deployments will look forward in embedding incremental learning features in the planning framework, without hampering computational efficiency.  
Conceptualization, V.A.N., M.L. and V.S.; Methodology, V.A.N. and M.L.; Software, V.A.N.; Validation, V.A.N.; Formal analysis, V.A.N., F.R. and V.S.; Investigation, V.A.N. and M.L.; Data curation, V.A.N.; Writing--original draft, V.A.N. and M.L.; Writing--review & editing, V.A.N., M.L. and F.R.; Visualization, V.A.N. and F.R.; Supervision, V.S. All authors have read and agreed to the published version of the manuscript.  
This study was partially carried out within the MOST--Sustainable Mobility National Research Center--and received funding from the European Union Next-GenerationEU (PIANO NAZIORALE DI RIPRESA E RESILIENZA (PNRR)--MISSIONe 4 COMPONENTE 2, INVESTI-MENTO 1.4--D.D. 1033 17/06/2022, CN00000023). This manuscript only reflects the authors' views and opinions; neither the European Union nor the European Commission can be considered responsible for them. This work was partially funded by the Next Generation EU Italian NRRP Mission 4, Component 2, Investment 1.5, call for the creation and strengthening of 'Innovation Ecosystems', building 'Territorial R&D Leaders' (Directional Decree n. 2021/3277)--project Tech4 You--technologies for climate change adaptation and quality of life improvement, n. ECS0000009.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** The authors declare no conflicts of interest.