## 6 Discussion and Conclusions  
In this study, we developed a method for calculating the travel time of a UAV along a path defined by two nodes, considering the complexity of factors such as UAV speed, payload, wind conditions, and geometric aspects of the path. By treating this calculation as a 'black box' we have addressed the nonlinearity and interdependencies of these factors, which would otherwise make explicit modeling challenging. To enhance computational efficiency and accuracy, we introduced a neural network model capable of estimating the time required to traverse individual path segments. This modular approach allows for real-time estimation across various trajectories, even in dynamic and complex environments. The network was trained using simulated data and validated with real-world conditions, demonstrating the system's ability to learn complex patterns and generalize across new scenarios. The iterative training process further refined the model's predictions, reducing discrepancies between estimated and real travel times. Our model's ability to account for travel time uncertainty through stochastic modeling represents a significant advancement in practical UAV route planning. By classifying edges based on destination node characteristics and employing lognormal distributions with a moderate variability level (\(\lambda=0.3\)) to model travel time uncertainty, we have created a framework that balances computational efficiency with realistic representation of operational  
Figure 12: Route optimization under northerly wind conditions. uncertainties. The simulation results show that solutions optimized without considering uncertainty can significantly underperform when deployed in real-world conditions. This study fills an important gap in the literature on the team orienteering problem in environments with physical obstacles and dynamic environmental factors, conditions that are rarely considered in traditional TOP research. By combining A* path-finding with neural network-based travel time prediction, our approach introduces a flexible, data-driven framework capable of handling complex routing scenarios in realistic UAV applications. The proposed methodology also has relevant implications for Robotic Engineering, particularly in the design of autonomous navigation and control systems. By integrating classical path planning (A*) with data-driven travel time prediction through neural networks, the approach supports more informed and adaptive navigation in dynamic and constrained environments. This hybrid model enables robots or UAVs to make route decisions based not only on geometry but also on external conditions such as wind or payload effects, which are often critical in real-world deployment. Still, the proposed methodology has several practical limitations. Combining the A* algorithm with neural network predictions increases both memory usage and computational demands. The memory required by the A* algorithm can become excessive in large or detailed grid environments, while performance on a \(30~{}\times~{}30\) km grid with moderate obstacles was acceptable, scaling to larger or denser environments would require further memory optimizations. Additionally, training the neural network demands significant processing power, especially in early iterations. Another limitation is the dependency of prediction accuracy on the volume and variety of training data. In the initial stages, with limited data, the model's travel time estimates can be inaccurate, leading to less optimal routing. Future work will focus on enhancing the model's adaptability and accuracy by incorporating real-time data integration, such as live environmental factors, weather, and traffic conditions. This would improve the system's ability to make dynamic adjustments during operation. Additionally, expanding the framework to accommodate multi-UAV collaboration could optimize route efficiency across several UAVs, considering communication and coordination constraints.