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研究生： 林岑璋
Lin, Tsen-Chang
論文名稱： 基於最大似然估計之直接學習覆蓋控制
Direct Learning Coverage Control Based on Maximum Likelihood Estimation
指導教授： 劉彥辰
Liu, Yen-Chen
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2017
畢業學年度： 105
語文別： 中文
論文頁數： 192
中文關鍵詞： 多機器人系統 、無線感測器與機器人網路 、覆蓋控制 、最大似然估計 、期望最大演算法
外文關鍵詞： multi-robot control system, wireless sensor and robot network, coverage control, maximum likelihood estimation, expectation maximization
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    • 本論文基於最大似然估計提出在階層式無線感測器與機器人網路架構下的直接學習覆蓋控制方法。此架構中有兩種感測器，高階感測器僅配置在機器人上，提供特定範圍的感測資訊；低階感測器僅能提供特定位置的感測資訊，除了配置在機器人上，也在環境中預先置放靜態感測器以確保系統獲得充足的資訊。環境中感測資訊的分布稱為感測密度函數，而本研究之目的乃藉由此架構中低階感測器回授的資訊建構估測密度函數以學習感測密度函數，並利用覆蓋控制方法找到多機器人系統的最佳分布，使搭載高階感測器的移動型機器人之感測資訊量最大化。
    本論文分別分析感測密度學習的相似性和覆蓋任務的性能函數與似然函數最佳化的一致關係，依此關係利用期望最大演算法完成最大似然估計，提出移動基底函數中心位置之感測密度學習方法，以及考慮感測模型之覆蓋控制器的設計方法。此外，若選擇感測模型為感測密度學習的基底函數，則相似性與性能函數會同時達到最大化，進而得以感測密度學習所求得的參數設計直接學習覆蓋控制器。
    直接學習覆蓋控制方法不但在感測密度學習中有良好的強健性與學習效果，同時也具有極佳的運算效能，也能利用複雜的感測模型完成覆蓋。本論文以理論分析、數值模擬以及實驗驗證此控制架構之最佳化與穩定性，也就模擬與實驗結果的不同，討論其造成原因並提出可能之解決辦法。

    This thesis proposes a direct learning coverage controller in wireless sensor and robot network(WSRN) structure based on the concept of maximum likelihood estimation. There are two kinds of sensors under WSRN. High-level sensors are embedded on mobile robots to sense information within indoor environment. On the other hand, low-level sensors also embedded on mobile robots, in addition, some of them are stationary sensors pre-deployed in the environment. Sensing density function represents the distribution of information of low-level sensor. The objective of this thesis is to utilize the information collected by low-level sensors to construct estimated density in order to learn sensing density and maximize the information quantity of high-level sensors.
    Based on equivalence between optimization problem of similarity in learning task, performance function in coverage task, and likelihood function. The expectation maximization algorithm can be utilized to find an optimal solution of maximum likelihood estimation. This thesis introduces a sensing density function learning method by tuning the center of basis function and derives a general solution for complicated sensor model such as Gaussian function. Moreover, if the basis function in sensing density learning is chosen as sensor model, similarity and performance function are optimized simultaneously so that direct learning coverage controller can be derived.
    The direct learning coverage control has robust performance in sensing density learning and high computational efficiency, which also takes sensor model into account. Moreover, this thesis provides theoretical analysis, numerical simulation and experiment to validate the optimization and stability of controller.

    圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii 表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi 第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 研究動機與問題定義. . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 研究目標及貢獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 第二章基礎理論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 非線性系統穩定性理論. . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.1 非線性系統. . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2 系統穩定性. . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.3 Lyapunov穩定性分析. . . . . . . . . . . . . . . . . . . . . . 13 2.2 凸函數最佳化. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 凸函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 延森不等式. . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 機率理論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.1 高斯混合模型. . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.2 最大似然估計. . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 期望最大演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 餘弦相似性. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 第三章環境感測密度函數學習. . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1 群組機器人覆蓋問題. . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Lloyd控制器設計. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 感測密度學習. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.1 中心學習方法. . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.3.2 權重學習方法[5] . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.3 中心權重學習方法. . . . . . . . . . . . . . . . . . . . . . . 38 3.4 模擬結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 第四章考慮感測模型之覆蓋控制. . . . . . . . . . . . . . . . . . . . . . . 63 4.1 複雜感測模型之群組機器人覆蓋問題. . . . . . . . . . . . . . . . . 63 4.2 隱函數轉換. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.1 EM控制器設計. . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.2 避障控制器設計[11] . . . . . . . . . . . . . . . . . . . . . . 70 4.2.3 加入責任區域分割之覆蓋問題[12] . . . . . . . . . . . . . . 70 4.3 模擬結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.1 感測模型-高斯函數. . . . . . . . . . . . . . . . . . . . . . . 76 4.3.2 感測模型-半球型函數. . . . . . . . . . . . . . . . . . . . . . 76 第五章直接學習覆蓋控制. . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.1 性能函數與估測相似性之關係. . . . . . . . . . . . . . . . . . . . . 81 5.2 直接性覆蓋控制器設計. . . . . . . . . . . . . . . . . . . . . . . . . 84 5.3 模擬結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 第六章實驗結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.1 實驗平台架設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.1.1 群組機器人系統. . . . . . . . . . . . . . . . . . . . . . . . . 99 6.1.2 室內定位系統. . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2 實驗參數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.3 感測密度學習. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.4 隱函數轉換. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.5 直接感測密度學習覆蓋控制. . . . . . . . . . . . . . . . . . . . . . 116 6.6 討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 第七章結論與未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.1.1 環境感測密度函數學習. . . . . . . . . . . . . . . . . . . . . 125 7.1.2 考慮感測模型之覆蓋控制. . . . . . . . . . . . . . . . . . . 126 7.1.3 直接學習覆蓋控制. . . . . . . . . . . . . . . . . . . . . . . 127 7.2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Appendix - Experimet Codes . . . . . . . . . . . . . . . . . . . . . . . . . . 135 A.1 Localization and Orientation Detection . . . . . . . . . . . . . . . . 135 A.2 Learning and Control . . . . . . . . . . . . . . . . . . . . . . . . . . 160 A.3 Bluetooth Communication . . . . . . . . . . . . . . . . . . . . . . . . 189

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