本研究藉由腳踏車的動態分析，探討機器人騎腳踏車的控制問題。動態分析假設腳踏車的前後輪擁有各自的自由度存在於空間座標系中，在考慮車身總長、前後輪側傾角及方向角的關係等限制條件後組裝成為一台腳踏車，之後利用Euler-Lagrange equations得到腳踏車的二階側方向動態方程式。此方程式經線性化後發現系統為側方向不穩定，且當輪速加快時，龍頭轉角控制輸入的可控性可以被提高。此外從動態分析我們發現龍頭轉角直接影響方位角速度。利用所推導的動態方程式可設計平衡與轉向控制器，控制器的模擬中得知：藉由全狀態回授可維持車體側向平衡及轉向，系統為開迴路不穩定且控制模擬呈現低射的非極小相位現象。我們將把控制系統實作在機器人騎乘腳踏車上，以驗證動態分析的特性與控制的性能，並探討其結果。

This thesis investigates the issue of the bicycle-riding robot via dynamic analysis of the bicycle. Assumed that the rear wheel and the front wheel of the bicycle with their own degree of freedom in the space coordinate. After considering the length of the bicycle, the relationship of the roll and yaw angle between the rear and front wheel and other restrictions, a bicycle model has been resembled. Using the Euler-Lagrange equation derives the dynamic equation and finds that it is unstable on the roll direction after linearization; however, when the bicycle speeds up, the controllability of the steering angle can be improved. Moreover, we find that the yaw rate is influenced by the steering angle directly. A balance controller and a steering controller are designed using the linear model. Simulations show that the bicycle-riding robot can keep balance and turn around by the state feedback control. Because the system is unstable in the open-loop and there is a non-minimum phase phenomenon, we implement the controller on the bicycle-riding robot and verify the performances and the characteristics of the dynamic analysis and discuss the results.

目錄
摘要 i
Abstract ii
致謝 iii
表目錄 x
符號一覽表 xi
第一章 緒論 1
1.1. 研究動機與目的 1
1.1. 文獻回顧 2
第二章 動態模型分析 5
2.1. 座標軸與變數定義 5
2.2. 系統模型 9
2.2.1. 能量 10
2.2.2. 動態方程式 13
2.2.3. 方程式線性化 14
第三章 系統分析與控制策略 16
3.1. 系統分析 16
3.2. 平衡控制器設計 18
3.2.1. LQR Controller Design 19
3.2.2. Pole Placement Method 20
3.3. 轉彎平衡控制器設計 22
3.3.1. LQR Controller Design 23
3.3.2. Pole Placement Method 24
3.4. 模擬結果 25
第四章 騎乘腳踏車機器人之實作 30
4.1. 硬體介紹 30
4.1.1. 機器人 30
4.1.2. 腳踏車 33
4.1.3. Raspberry Pi Camera 34
4.1.4. 六軸加速規陀螺儀 35
4.1.5. 控制板 36
4.2. 感測器校正 36
4.2.1. 相機模型 36
4.3. 軌跡規畫 41
4.3.1. 手部逆向運動學 41
4.3.2. 腳部逆向運動學 44
4.4. 實驗結果 46
4.4.1. 平衡控制 46
4.4.2. 轉彎平衡控制 47
第五章 結論與未來工作 50
5.1. 結論 50
5.2. 未來工作 51
參考資料 52
附錄 54

參考資料
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