Map Explorations via Dynamic Tree-Structured Graph

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謝瑞煦(Rei-Shu Shieh) 查詢紙本館藏

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數學系

論文名稱

(Map Explorations via Dynamic Tree-Structured Graph)

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至系統瀏覽論文 (2025-8-1以後開放)

摘要(中)

在未知環境中進行地圖探勘是具有挑戰性的，因為最大化覆蓋率
是個NP-hard的問題，這項研究提出了基於動態更新樹狀結構路徑而
最大化覆蓋率之邊際效益的方法。由於缺少環境資訊，樹狀結構路徑
需於不同時間段進行更新。因此，此項研究證明出每個時間段的理論
保證值。實驗結果說明此項研究提出的方法效能更勝於其他方法。

摘要(英)

Map exploration in unknown environments is challenging since finding the optimal solution to maximize the environmental coverage is NPhard. This research proposes a method that maximizes the dynamic marginal gain of the coverage with the tree-Structured routing. Since the map is unknown, the tree-structured routing is dynamically updated at each time step. Thus, the theoretical guarantees at each time step are proved. The experiments show that the proposed method outperforms benchmark methods.

關鍵字(中)

★ 次模性
★ 3D地圖探勘
★ 最大覆蓋問題

關鍵字(英)

★ Submodularity
★ 3D map exploration
★ Maximal coverage problem

論文目次

摘要 .................................................................................................... i
Abstract.............................................................................................. ii
Contents ............................................................................................. iii
Figures................................................................................................ iv
Table...................................................................................................vii
1 INTRODUCTION.............................................................. 1
2 RELATED WORK............................................................. 4
2.1 Map exploration problems . . . . . . . . . . . . . . . 4
2.2 Submodular maximization problems . . . . . . . . . 5
2.3 Traveling salesman problems . . . . . . . . . . . . . 6
2.4 Information Path Planning (IPP) . . . . . . . . . . . 7
3 BACKGROUND ................................................................ 8
3.1 Submodularity . . . . . . . . . . . . . . . . . . . . . 8
4 PROBLEM FORMULATION............................................ 11
4.1 Objective Functions . . . . . . . . . . . . . . . . . . 11
4.2 Theoretical Guarantees . . . . . . . . . . . . . . . . 12
5 PROPOSED ALGORITHM............................................... 15
6 EXPERIMENTS ................................................................ 18
6.1 Experiment Setup . . . . . . . . . . . . . . . . . . . 18
6.2 EX1: Map Exploration . . . . . . . . . . . . . . . . 20
6.3 EX2: 2D Simulations of Total Curvatures . . . . . . 22
7 CONCLUSION AND FUTURE WORK............................ 28
Reference ............................................................................................ 30

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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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