臺灣博碩士論文加值系統

本篇研究重點為單輪機器人之運動方程式推導及運動狀態分析。單輪機器人運動方程式的推導包含定義座標系統和凱恩法 (Kane’s Method) ，根據推導出的運動方程式建立數值模擬程式。另外車體上有驅動輪和飛輪，分別用來控制車體俯仰角 (pitch) 及滾動角 (roll) 平衡，使用數值模擬程式進行模擬及驗證，驅動輪和飛輪之力矩對於車體的影響。
接著使用Linear-quadratic regulator（LQR）方法，設計回授控制器。根據模擬數值選用馬達、電池等元件，並透過融合濾波器等演算法設計，撰寫機器人內部程式，完成實體機器人，接著透過實驗量得馬達相關參數，利用回歸分析，計算得馬達特性平面，將回授控制器力矩轉換成輸出電壓，推動驅動馬達。最後透過人機介面，快速調整、驗證機器人各項參數與平衡狀態。

The purpose of this thesis aims to derive equations of motion and to perform analysis of motion for a single-wheel robot. In order to derive equations of motion, coordinate systems are defined and Kane's method is applied. Then, a numerical simulation is established based on the equations of motion and with MATLAB/Simulink. In addition, the robot is equipped with one driving wheel and one flywheel, which are used to control the pitch angle and the roll angle of the robot body, respectively. Finally, verification is conducted by using numerical simulation program. The influence and impact on the robot body due to driving torque and flywheel torque are studied and discussed.
Feedback controller is designed by using LQR method. According to simulation results, motor, battery and components are selected to design robot. Moreover, algorithms are applied here to complete the design of the robot. The motor-related parameters are measured by experiments. Regression analysis is utilized to find the motor characteristic plane, by which the output torque command from feedback controller is converted into voltage signal to drive the motor.
Finally, the human machine interface is designed, which allows user to adjust the parameters easily and to verify balance condition efficiently.

誌　謝 i
摘　要 ii
Abstract iii
目　錄 iv
圖目錄 vi
表目錄 viii
第一章 序論 1
1.1. 前言 1
1.2. 文獻探討 2
1.3. 論文導覽 5
第二章 單輪機器人運動方程式 6
2.1. 座標系統 6
2.2. 座標轉換 7
2.3. 動力系統 9
2.4. 慣性張量 10
2.5. 運動方程式 11
2.5.1. 廣義速度、廣義加速度 11
2.5.2. 廣義主動力、廣義慣性力 16
2.6. 開迴路模擬 19
2.6.1. 等速前進 19
2.6.2. 飛輪等速旋轉 21
2.6.3. 左右擺盪 22
2.6.4. 飛輪加速旋轉 23
第三章 機體控制 24
3.1. 一階擾動技術 24
3.2. 狀態方程式 25
3.3. 可控規範形式 28
3.4. 控制器設計 31
3.4.1. 前饋控制器 32
3.4.2. 回授控制器 33
3.4.3. 權重矩陣自動最佳化程式 35
3.5. 控制器模擬 37
3.5.1. 一階回授控制器模擬 37
3.5.2. 閉迴路模擬 40
第四章 機器人設計 44
4.1. 系統架構圖 44
4.2. 零件選配 45
4.2.1. 單晶片與馬達驅動器 45
4.2.2. 感測器 46
4.2.3. 減速馬達 47
4.2.4. 系統電源 49
4.3. 零件測試 51
4.3.1. 機器人控制程式 51
4.3.2. 馬達、旋轉編碼器 51
4.3.3. 六軸感測器 52
4.4. 結構設計 54
第五章 演算法與程式設計 55
5.1. 角度、角速度轉換 55
5.2. 融合濾波器 59
5.3. 馬達輸出轉換 61
5.3.1. 量測馬達扭力 61
5.3.2. 馬達特性平面 62
第六章 實際測試與成果 65
6.1. 人機介面 65
6.2. 機器人平衡測試 68
第七章 結論與未來展望 71
7.1. 結論 71
7.2. 未來展望 72
參考文獻 73
附錄、機器人運動方程式 75

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