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 本文是以影像處理為基礎來偵測環境中障礙物之分佈模型，以環境模型為基礎，建構一條連接起始點到終點之B-spline平滑軌跡。除了滿足車輛轉彎時最小曲率半徑的限制以及起始點與終點之運動約束外，並可成功地避開障礙物。在障礙物影像偵測方面，提出了邊點序向排列法，將所有物體的邊點座標進行有序排列，除了決定每個邊點之間的鏈結關係外，並且將影像中的物體作個別分類。配合向量內積圓形偵測法以及轉折點偵測法來決定圓形物體中心點、半徑及其外切正六邊形以及多邊形物體的頂點座標，以建立障礙物的分佈模型。並透過Dijkstra’s最短路徑搜尋法，以障礙物的頂點即轉折點為網路節點，最短路徑為代價函數，完成避障路徑設計。在最短路徑搜尋中，我們提出兩種禁行路徑偵測法來判別兩頂點間的連通性，分別為幾何偵測法與影像偵測法兩種。前者是利用直線與凸邊形的特性，後者則運用影像二值化及邊緣之訊息，來決定偵測點是否座落在障礙物範圍內。最後本文推導分段型B-spline曲線來取代傳統的遞迴表示式，採用B-spline解析函數作為平滑路徑的設計，有效地整合約束最佳化之演算法，將曲率限制以及運動約束引入最小路徑的代價函數中，將軌跡規劃的問題轉換成求解約束最佳化求解控制點的問題。為了驗證本文架構的可行性，我們以Matlab程式語言的GUI介面，完成B-spline軌跡規劃模擬軟體。由模擬得知，利用約束最佳化求解B-spline避障軌跡不僅具有可行性，並可獲至良好的效果。
 In this thesis, the problem of path planning for autonomous vehicles or mobile robots moving in the exploration of hazardous or complex areas is solved. The purpose is to generate a feasible path with the initial posture and the final one so that no collisions with obstacles would occur and various constraints are satisfied. First, an obstacle distribution model is established in a modeled-based environment by image processing techniques. As for the obstacle detection, the boundary sequence method arranges boundary coordinates for each object in order as well as determines the link relation of each boundary such that the objects are detected and classified. Applying the geometric characteristics of the circumferential angle, the inner product detection is developed to determine whether there are round objects in the image. By adopting the corner detection algorithm, we compare the angles of bordered vector in order to determine the location of corners of each object. Using the corner points of each obstacle object as nodes to create a network, Dijkstra’s method is adopted to search the shortest path. To determine the connectivity between two nodes, geometric detection and image detection are evolved respectively to determine the forbidden paths. The former applies geometric characteristics of straight lines and convex hull, and the latter adopts the information of image binary threshold to judge whether the detecting point is allocated within the range of obstacle area. Finally, the matrix form of divided B-spline curve is derived, which makes it possible to realize the constrained optimization programming. The proposed algorithm is an integrated application of the constrained optimization method and B-spline basis function to generate the control points and to characterize the optimized B-spline curve that the kinematic constraints and curvature restrictions are satisfied. By using Matlab GUI toolbox, simulation results show that the design of B-spline obstacle avoidance trajectory which is based on image detection is applicable and it shows a better result.
 中文摘要………………………………………………………………………………i英文摘要 ……………………………………………………………………………ii目次…………………………………………………………………………………iii表目錄……………………………………………………………………………… vi圖目錄………………………………………………………………………………vii符號表 ………………………………………………………………………………xii第一章 緒論…………………………………………………………………………1 第一節 研究動機…………………………………………………………………1 第二節 文獻回顧…………………………………………………………………2 第三節 內容概述與論文架構……………………………………………………7第二章 圓形偵測與轉折點偵測影像處理演算法………………………………10 第一節 影像處理基本概念……………………………………………………10 壹 灰階轉換…………………………………………………………………10 貳 影像二值化………………………………………………………………10 参 邊緣偵測…………………………………………………………………12 肆 邊點序向排列……………………………………………………………13 第二節 向量內積圓偵測法……………………………………………………16 壹 圓的幾何性質……………………………………………………………16 貳 向量內積圓偵測法………………………………………………………17 參 圓周角門檻值的計算……………………………………………………20 第三節 轉折點偵測……………………………………………………………22 壹 轉折點偵測概念…………………………………………………………22 第四節 模擬結果……………………………………………………………25 壹 向量內積圓偵測法………………………………………………………25貳 轉折點偵測………………………………………………………………29第三章 Dijkstra's最短路徑搜尋法………………………………………………32第一節 環境資訊………………………………………………………………32壹 環境資訊的定義…………………………………………………………32貳 凸邊形障礙物模型………………………………………………………33第二節 禁行路徑判斷…………………………………………………………35壹 幾何禁行路徑偵測步驟…………………………………………………35貳 影像禁行路徑之偵測……………………………………………………38參 邊緣門檻值設定…………………………………………………………39第¬三節 Dijkstra's最短路徑搜尋法流程………………………………………40第四節 模擬結果………………………………………………………………43第四章 B-spline分段曲線之路徑規劃…………………………………………49第一節 B-spline曲線及其特性………………………………………………49壹 B-spline曲線 ……………………………………………………………49貳 曲線特性………………………………………………………………53第¬二節 分段 B-spline曲線……………………………………………………56第三節 問題描述………………………………………………………………60第四節 分段B-spline曲線位置、速度、加速度與控制點的關係…………63第五節 具有約束條件之B-spline曲線最佳化演算法………………………66第六節 模擬結果………………………………………………………………70壹 淚滴線曲線測試…………………………………………………………70貳 外擺曲線測試……………………………………………………………75第五章 模擬結果與討論…………………………………………………………80第一節 B-spline避障軌跡圖形介面…………………………………………80第二節 向量內積圓形偵測模擬………………………………………………84第三節 轉折點偵測法偵測模擬………………………………………………85第四節 Dijkstra’s最短路徑搜尋法模擬………………………………………87第五節 B-spline分段曲線之路徑規劃………………………………………88第六節 特殊曲線繪製…………………………………………………………90壹 繪製淚滴線曲線…………………………………………………………90貳 繪製外擺曲線……………………………………………………………91參 繪製心臟線………………………………………………………………92第七節 討論……………………………………………………………………95第六章 結論與未來研究方向……………………………………………………96壹 結論………………………………………………………………………96貳 未來研究方向……………………………………………………………97參 結語………………………………………………………………………97附錄…………………………………………………………………………………98參考文獻…………………………………………………………………………111
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 1 自走車避障與導航性能之分析與設計 2 應用模糊控制於自走車路徑導引避障之整合設計 3 車牌辨識系統之研究 4 一個應用托勒密定理的隨機圓形偵測演算法 5 交通號誌辨識 6 使用K曲率法則於二維物體的分斷點偵測之研究 7 模糊理論在機器人即時避障的應用 8 基於B-Spline曲線之六軸機械手臂繪圖系統 9 使用多感測器之自主式行動輔助及導航機器人設計與實現 10 擴增實境輔助感覺統合訓練之研究 11 利用影像處理技術進行硬幣辨識之研究 12 無人車之B-樣條曲線路徑規劃與控制 13 多軸運動控制器軌跡規劃之研究 14 非完整約束輪型機器人之建模與控制 15 結合基因演算法與B樣條曲線於平滑避障路徑規劃之研究

 1 邱文彬、林美珍(1999)，大學生發展成熟的人際關係中親密性能力的發展：自我揭露與自主性之年級與性別差異的探討，教育心理學報，31(1)，37-62。 2 周文賢、魏諦芊、王馨葦(2004)，壽險業顧客關係品質模式之建立與實證分析，國立台北大學企業管理研究所，管理與系統，11(2)，199-220。 3 周建亨、陳津美、曾郁雯(2004)，服務接觸人員行為量表之建立及其與服務互動品質關係之研究，文大商管學報，9(2)，67-84。 4 李旻陽(1998)，團體諮商中領導者的自我揭露，輔導季刊，34(2)，21。 5 邱文彬、萬金生(2005)，網路性話題的自我揭露初探：性別差異和去個人化及話題親密性的影響，國立高雄餐旅學院通識教育中心，國立政治大學教育與心理研究，28(3)，495-525。 6 吳秀碧、許育光、李俊良(2003)，諮商團隊歷程中成員自我揭露頻率與深度之初探，彰化師大輔導學報，25(2)，24。

 1 整合機械手臂之輪型機器人路徑追蹤控制 2 結合CCD與INS之輪型機器人在滾球追蹤之實現 3 影像式避障系統 4 運動控制軌跡規劃 5 結合基因演算法與B樣條曲線於平滑避障路徑規劃之研究 6 具搜尋與避障之自動跟隨機器人 7 視覺伺服應用於自走車追蹤避障之實現 8 移動機器人影像處理及其在避障之應用 9 結合影像及紅外線感測於自動導航車避障策略之設計 10 結合類神經網路與LabVIEW實現PC-based自走車控制避障之研究 11 基於即時影像之智慧型自走車避障與動態追蹤控制 12 輪式移動型機器人之避障控制 13 基於B樣條曲線之掌形辨識 14 B-spline曲線的knotsequence的探討 15 應用B-spline計算無交叉補償路徑方法之研究

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