## 5 Conclusions and Future Directions  
This article proposed a new PP method based on CPS and an ESWG to enable a UAV's safe navigation in 3D urban environments. The main objectives of the proposed PP method are to lower the time complexity in both task modeling and pathfinding without degrading the path quality for UAVs operating at lower elevations in urban environments with fixed, convex obstacles. The main contributions of this article are listed as follows:  
Figure 11: (**Left**) Graph/tree nodes: proposed method versus the ApVL algorithm and the RRT*-AB algorithm; (**Right**) path nodes: proposed method versus the ApVL algorithm and the RRT*-AB algorithm.  
* We propose a new PP method based on CPS and an ESWG that has the potential to find an optimal/quasi-optimal path with considerably reduced time complexity.
* We propose a new space reduction method that abstracts the full map into a 3D constrained polygonal space that guarantees a path for the UAV's mission.
* We analyze the effectiveness of CPS for low-cost paths considering six complexity parameters, including the ratio of free space, obstacle density in distinct regions of the CPS, the complexity in the options for avoiding obstacles, deviation in the length from the optimal path, the ratio of connected obstacles to pertinent obstacles, and obstacle tendencies in the CPS.
* The proposed method enlarges the CPS to the next level/space by including obstacles that are in close proximity to the first CPS if the first CPS fails to provide an opportunity for low-cost solutions owing to a higher complexity from obstacles in it.
* The proposed method generates an ESWG from the CPS, leveraging the principles of maximum distance reachability, having only a few nodes and edges, and direction guidance, and it computes an abstract path that is further improved with the assistance of more nodes and edges around it.
* This initial work makes use of obstacle information from an underlying environment in order to lower the computing overhead for pathfinding without compromising path quality in 3D urban environments.  
The proposed method performance is substantiated through extensive tests, and, in most cases, it performs consistently better than prior PP methods. It lowers pathfinding time complexity considerably by restricting path exploration solely in the highest priority CPS that has the greatest chance of providing an optimal/sub-optimal path. While conducting the tests, we considered numerous parameters related to the underlying operating environment's complexity and UAV's safety. Meanwhile, during the PP at lower elevations in urban environments, we may need to consider hanged/thin obstacles (e.g., electrical wires and poles in the streets). Another group of evaluation parameters can be the wind/gust and wind/crosswind (e.g., wind's direction and speed), especially when passing through buildings. Hence, further testing with these parameters is yet to be investigated in future work. Finally, we intend to analyze the fidelity of our proposed PP method with other task modeling methods (e.g., Voronoi diagrams, grids, and navigation meshes, etc.).  
All authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2B5B01002145).  
Not applicable.  
The data used in the experimental evaluation of this study are available within this article.  
The authors declare no conflict of interest regarding the publication of this manuscript.