使用成本效益生成樹的資訊軌跡規劃

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邱韋翔(Wei-Hsiang Chiu) 查詢紙本館藏

畢業系所

數學系

論文名稱

使用成本效益生成樹的資訊軌跡規劃
(Informative path planning via cost-benefit spanning tree)

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至系統瀏覽論文 (2025-7-25以後開放)

摘要(中)

資訊軌跡規劃 (IPP) 是無人機的關鍵應用之一。它可以重新定義為在軌跡限制下的次模性最大化問題。然而，尋找最佳搜索軌跡包括兩個NP-hard問題，即最大覆蓋問題和最小路徑問題。此研究提出成本效益生成樹(CBST) ，以提高IPP 的效能。理論說明樹的總曲率影響了理論保證值。實驗表明，所提出的 CBST 演算法的效能比其他演算法的效能更好。

摘要(英)

Informative path planning (IPP) is one of key applications for unmanned aerial vehicles (UAVs). It can be formulated as the submodular maximization problem with routing constraints. However, finding an optimal search path includes two NP-hard problems, the covering problem and routing problem. In this research, the proposed algorithm generates the cost-benefit spanning tree (CBST) to boost the IPP performance. The proofs show the theoretical guarantees depends on the total curvatures of the trees. The experiments demonstrate that the proposed method outperforms the benchmark approaches.

關鍵字(中)

★ 機率搜尋
★ 次模性
★ 普林-戴克斯特拉演算法
★ 資訊軌跡規劃
★ 空中機器人
★ 貪婪演算法

關鍵字(英)

論文目次

摘要...................................................... i
Abstract................................................. ii
Acknowledgements........................................ iii
Contents................................................. iv
Figures.................................................. vi
Tables................................................... ix
1 Introduction............................................ 1
2 Related work............................................ 4
2.1 Probabilistic search . . . . . . . . . . . . . . . . 4
2.2 Informative path planning (IPP) . . . . . . . . . . 4
2.3 Submodular maximization problems . . . . . . . . . . 5
2.4 Prim-Dijkstra algorithm . . . . . . . . . . . . . . 6
3 Background knowledge.................................... 7
3.1 Submodularity . . . . . . . . . . . . . . . . . . . 7
3.2 Lower bound of GCB . . . . . . . . . . . . . . . . . 7
3.3 Prim and Dijkstra (PD) algorithm . . . . . . . . . . 8
3.4 Extended probability of detection (EPD) . . . . . . 9
4 Problem formulation.................................... 12
4.1 Cost-benefit spanning tree (CBST) . . . . . . . . . 12
4.2 Theoretical bound of CBST . . . . . . . . . . . . . 13
5 Proposed algorithms.................................... 23
6 Experiments............................................ 25
6.1 Experiment setup . . . . . . . . . . . . . . . . . 25
6.2 EX1: EPD maximization . . . . . . . . . . . . . . . 28
6.3 EX2: Search experiment . . . . . . . . . . . . . . 30
6.3.1 Simulation . . . . . . . . . . . . . . . . . . 30
6.3.2 Real world . . . . . . . . . . . . . . . . . . 35
6.4 EX3: α tuning . . . . . . . . . . . . . . . . . . 35
7 Conclusions and future work ........................... 41
References............................................... 42

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指導教授

曾國師(Kuo-Shih Tseng)

審核日期

2023-7-25

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