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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/84269

    Title: 3D Map Exploration and Search using Topological Fourier Sparse Set
    Authors: 呂秉憲;Lu, Bing-Xian
    Contributors: 數學系
    Keywords: 3D 地圖勘探;壓縮感測;物件搜尋;3D map exploration;Compressed sensing;Object search
    Date: 2020-07-17
    Issue Date: 2020-09-02 18:45:12 (UTC+8)
    Publisher: 國立中央大學
    Abstract: 3D地圖探索是機器人技術中的關鍵技術之一。
    此外,該演算法顯示了探索問題的持續同調性。;3D map exploration is one of key technologies in robotics.
    However, nding an optimal exploration path is a challenge due to unknown environments.
    This research proposed the Topological Fourier Sparse Set (TFSS) algorithm to enable an unmanned aerial vehicle (UAV) to explore 3D environments with theoretical guarantees.
    The algorithm consists of the Rips complex and Fourier sparse set.
    The Rips complex is to expand subgoals for map exploration while the Fourier sparse set is to learn submodular functions for subgoal selection.
    Since the objective function of spatial exploration is reformulated as a maximizing submodular function with path constraints,
    greedy algorithms can achieve (1/2)(1-e^(-1)) of the optimum.
    Experiments conducted with this algorithm demonstrates that the UAV can explore the environments more than the benchmark approaches.
    Furthermore, the algorithm shows the persistence homology of exploration problems.
    Appears in Collections:[數學研究所] 博碩士論文

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