本篇論文研究了在多個限制區域內啟用無人機的監視任務，旨在確定最佳的無人機飛行路徑，以最大限度地減少任務的總完成時間。由於政府法規或對抗性問題，無人機被禁止飛入限制區域，因此只能在這些區域的邊界收集資訊。只要滿足每個區域所需的監視時間，就能完成整個監視任務。我們觀察到，在滿足所需的監視持續時間的同時，無人機無需停留在固定位置，而是可以沿著限制區域的邊界移動，一旦完成了本地監視任務，就可以減少到下一個區域的距離。為了利用這一優勢，我們提出了一個最小完成時間（MinTime）演算法，該演算法首先通過旅行商問題（TSP）的近似解來確定區域的拜訪順序，然後使用動態規劃在限制區域序列上優化無人機的飛行路徑。在存在障礙物的情況下，我們進一步提出障礙物感知的最小完成時間（OA-MinTime）演算法，該演算法將每個障礙物視為監視時間為零的額外限制區域，使無人機能夠更有效地避開障礙物。此外，考慮到每個興趣點間在路徑上繞過障礙物所需的額外距離，我們還提出了一個修正的TSP解決方案。模擬結果表明，與傳統的最小距離方法相比，提出的MinTime和OA-MinTime演算法皆可以顯著減少總完成時間。

This work examines a UAV-enabled surveillance mission over multiple restricted regions and aims to determine the optimal UAV trajectory that minimizes the overall completion time of the mission. The UAV is prohibited from entering the restricted regions due to government regulations or adversarial concerns, and, thus, can only gather information at the boundaries of these regions. The surveillance mission is completed by satisfying the required surveillance duration for every region. We observe that, while fulfilling the required surveillance duration, the UAV need not stay at a fixed position but can instead move along the boundary of the restricted region to reduce its distance to the next region once the local surveillance task is completed. To exploit this advantage, we propose a minimum completion time (MinTime) algorithm that first determines the visiting order of the regions by employing an approximate solution to the traveling salesman problem (TSP) and then optimizes the UAV trajectory over the sequence of restricted regions using dynamic programming. In the presence of obstacles, we further propose an obstacle-aware MinTime (OA-MinTime) algorithm that treats each obstacle as an additional restricted region with zero surveillance duration, allowing the UAV to avoid the obstacles in a more efficient manner. A modified TSP solution is also proposed by taking into consideration the additional distance required to circumvent the obstacles on each inter-POI path. Simulation results show that the proposed MinTime and OA-MinTime algorithms can significantly reduce the total completion time compared to the conventional minimum distance approaches.

1. Introduction ................................................................ 1
2. Related Work ................................................................ 4
3. System Model and Problem Formulation ........................................ 9
3.1 System Model ............................................................... 9
3.2 Problem Formulation ........................................................ 12
4. Minimum Completion Time Trajectory Optimization via Dynamic Programming ..... 13
5. Extension of the MinTime Algorithm to the Case with Obstacles ............... 18
6. Simulation Results .......................................................... 23
6.1 Simulation Setting ......................................................... 23
6.2 Simulation Results ......................................................... 25
6.2.1 Total Completion Time versus the Number of POIs .......................... 25
6.2.2 Total Completion Time versus Surveillance Time ........................... 27
6.2.3 Total Completion Time versus the Mean Radius of the Restricted Regions ... 29
6.2.4 Total Completion Time versus the Number of Obstacles ..................... 30
7. Conclusion .................................................................. 32
References ..................................................................... 33

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