為了展現影像伺服控制系統之性能，本文選擇球板系統做為首要開發
目標，並於平板上設計障礙物形成迷宮，增加環境之變化性與狀況之多樣
性。以具有兩個自由度的機器手腕之末端銜上一壓克力平板作為球板機構，
透過網路攝影機擷取影像回授至個人電腦上，使用影像處理相關技巧取得
球位置，並設計模糊控制器決策平板傾斜角度，完成一套影像伺服控制系
統。另引入距離轉換法之路徑規劃方式，能夠視球之位置找出通往目標點
之最短路徑，並配合同樣以距離轉換為基礎之障礙物擴張法，提供更適合
實際之球移動的鬆弛路徑。
經由模擬與實驗的驗證，本系統對球之動態控制已有初步之成果，能
有效的進行定位控制與軌跡追尋，並可達成使球穿過迷宮到達目標終點之
任務，可供未來進一步改良或是開發相關研究主題。

This thesis presents a visual servo control scheme for a ball-and-plate
system with a maze. The maze built on the plate forms obstacles for the ball
and increases variety and complexity of its environment. The ball-and-plate
system is a two degrees-of-freedom robotic wrist with an acrylic plate attached
as the end effector. By using image processing techniques, the ball’s position is
acquired from the visual feedback, which was implemented with a webcam and
a personal computer. A fuzzy controller, which provides dexterity of the robotic
wrist, is designed to decide the slope angles of the plate to guide the ball to a
designated target spot. Using the method of distance transform, the path
planning based on the current position of the ball is conducted to find the
shortest path toward the target spot. Besides, a relaxed path, appears to be more
suitable for actual applications, is provided by the obstacle’s expansion
approach.
Experimental results show that the presented control framework
successfully leads the ball to pass through the maze and arrive at target spot.
The visual servo control scheme works effectively in both stabilization and
tracking control. Based on this preliminary achievement, further improvement
and deeper exploration on related research topics can be carried on in the
future.

目錄 ........................................................................................................... i
圖目錄 ..................................................................................................... iii
表目錄 ...................................................................................................... v
摘要 ......................................................................................................... vi
Abstract ....................................................................................................vii
第一章 緒論 ......................................................................................... 1
1.1 研究動機與目的 ..................................................................... 1
1.2 研究方法與步驟 ..................................................................... 1
1.3 文獻回顧 ................................................................................. 3
1.4 本文架構 ................................................................................. 4
第二章 系統架構與數學模型 .............................................................. 5
2.1 硬體設備 ................................................................................. 5
2.1.1 致動器 ........................................................................... 7
2.1.2 平板 ............................................................................... 8
2.1.3 球 ................................................................................. 11
2.1.4 攝影機 ......................................................................... 11
2.1.5 控制板 ......................................................................... 12
2.1.6 主控系統 ..................................................................... 12
2.2 軟體系統 ............................................................................... 12
2.3 數學模型建立 ....................................................................... 13
2.3.1 座標系統定義 ............................................................. 13
2.3.2 座標轉換 ..................................................................... 15
2.3.3 運動方程式 ................................................................. 16
第三章 模糊理論及控制 ................................................................... 20
3.1 模糊集合 ............................................................................... 20
3.2 模糊關係 ............................................................................... 22
3.3 模糊推論 ............................................................................... 23
3.4 模糊化及解模糊化................................................................ 25
3.5 模糊控制 ............................................................................... 28
第四章 影像處理相關理論................................................................ 30
4.1 RGB 與灰階 ............................................................................ 30
4.2 影像二值化 ........................................................................... 31
4.3 影像標籤化 ........................................................................... 33
4.4 距離轉換 ............................................................................... 35
第五章 影像伺服與控制 ................................................................... 38
5.1 視覺系統 ............................................................................... 39
5.1.1 平板四邊角搜尋 ......................................................... 39
5.1.2 球位置搜尋 ................................................................. 40
5.2 路徑規劃 ............................................................................... 41
5.3 控制器設計 ........................................................................... 44
第六章 模擬與實驗結果 ................................................................... 50
6.1 定位控制模擬與實驗 ............................................................ 52
6.2 軌跡追尋實驗 ....................................................................... 55
6.3 路徑規劃模擬與實驗 ............................................................ 59
第七章 結論與建議 ........................................................................... 62
參考文獻 ................................................................................................ 64

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