為了展現機械手腕之靈活性，本研究以桌球運動觀點，提供一套靈巧機器手腕與影像回授控制設計。選擇球板系統(Ball and Plate)作為首要開發的目標，吾人製作具兩個自由度的機器手腕系統，末端是一只壓克力板，網路攝影機擷取影像回授至個人電腦上，撰寫程式取得球位置，並設計線性二次調節器(Linear Quadratic Regulator, LQR)決策平板傾斜角度，能使球到達平板上的特定位置。經實驗驗證，對於靈巧手開發已有初步的成果，可供未來進一步改良或是開發相關研究主題。

This thesis presents a skillful robotic wrist system using a visual servo control technique to demonstrate dexterity of the mechanical wrist from the viewpoint of the table tennis. A ball and plate system is chosen as the first stage of this long-term project. A two degrees-of-freedom robotic wrist with an acrylic plate attached as the end effector is developed. A visual feedback
control system is implemented with a web cam and a personal computer to acquire the ball's position. In order to implement decision making for changing
orientation of the plate, a Linear Quadratic Regulator (LQR) is designed. As a result, the ball can be balanced at specific positions. Experimental results
exhibit preliminary and promising achievement. Based on this progress, further improvement and deeper exploration can be carried on in the future.

目錄............................................................................................................. i
圖目錄....................................................................................................... iii
表目錄....................................................................................................... iv
摘要.............................................................................................................v
Abstract ..................................................................................................... vi
第1 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............................................................................................ 2
1.4 本文架構............................................................................................ 3
第2 章 數學模型建立.............................................................................4
2.1 系統座標定義.................................................................................... 4
2.2 平板旋轉角與球速度之關係............................................................ 6
第3 章 實驗設備規劃與製作...............................................................10
3.1 硬體設備.......................................................................................... 10
3.1.1 動力輸入.................................................................................. 10
3.1.2 平板.......................................................................................... 12
3.1.3 球.............................................................................................. 13
3.1.4 球位置感測器.......................................................................... 14
3.1.5 主控系統.................................................................................. 14
3.2 軟體系統.......................................................................................... 16
第4 章 影像伺服與控制.......................................................................17
4.1 視覺系統.......................................................................................... 18
4.1.1 平板四邊角搜尋...................................................................... 18
4.1.2 球位置搜尋.............................................................................. 19
4.1.3 投影映射轉換(Projective Transformation)............................. 20
4.2 控制器設計...................................................................................... 23
4.2.1 動態方程式.............................................................................. 23
4.2.2 線性二次調節器(Linear Quadratic Regulator, LQR)............. 24
4.3 系統整合與實驗結果...................................................................... 26
4.3.1 定位控制模擬與實驗.............................................................. 26
4.3.2 軌跡追循實驗.......................................................................... 29
第5 章 結論與建議...............................................................................31

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