本研究針對倒單擺系統，提出創新的姿態估測與控制方法，使人型輪式倒單擺機器人在縱向移動上具防打滑與一定的追跡能力。在姿態估測上，藉由重力向量恆定的特性以估測姿態，配合訊號融合技術與運動分析，達成此估測器的收斂性與性能。在控制器設計上，由分析倒單擺載具的動態，推導線性矩陣不等式(LMI)，一證明引入積分的防滑插值控制器的收斂性與設計方法，再以卡爾曼濾波器估測打滑狀況以獲得插值控制的插值指標，二證明無插值之強健線性控制器之收斂性與設計方法。最後以模擬與實作人型倒單擺機器人驗證理論的可行性。

This research investigates robust balancing and tracking control issues associated with a humanoid wheeled-inverted-pendulum(WIP) robot. Particularly, a method to estimate the attitude of WIP vehicle and an anti-slip interpolating controller with integral action are proposed. In the attitude estimating method, dynamics and the sensor fusion technique are applied to realize the gravity estimator. The convergence rate of the estimator is also studied. In the controller design, the dynamics of the typical WIP vehicle is analyzed and is further applied with an integral control. A set of linear matrix inequalities (LMI’s) is derived to prove the controller convergence rate. Finally, simulations are conducted and a humanoid WIP robot is constructed to validate the performance of the estimation method and the control system.

摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 VII
表目錄 X
1. 第一章 緒論 1
1.1. 研究動機與目的 1
1.2. 文獻回顧 4
1.3. 論文簡介 8
2. 第二章 系統分析 10
2.1. 運動學定義與定理 10
2.1.1. 座標與向量定義 10
2.1.2. 倒單擺機器人模型定義 12
2.1.3. 三維運動學定理 13
2.1.3.1. 三維運動學方程式 13
2.1.3.2. 座標系統的轉換 15
2.2. 姿態量測分析 16
2.2.1. 倒單擺系統量測加速度分析 17
2.2.2. 重力估測器設計：IMU訊號融合 19
2.2.3. 重力估測器穩定性證明 21
2.3. 倒單擺機器人動態系統推導 23
2.3.1. Lagrange動力學定義 23
2.3.2. 控制模型推導 25
3. 第三章 防滑追跡控制器設計 27
3.1. 打滑辨識 27
3.2. 縱向防滑插值控制器 28
3.2.1. 追跡控制與系統積分擴階 29
3.2.2. 打滑系統方程式 30
3.2.3. 適應性插值回授控制設計 32
3.3. 牽引力估測 33
3.3.1. 干擾估測器 33
3.3.2. 卡爾曼濾波器估測滑差比 34
3.4. 替代滑差比之防滑控制器 36
4. 第四章 模擬結果 38
4.1. 姿態估測模擬 38
4.2. 機器人防滑控制模擬 40
5. 第五章 實作結果 46
5.1. 硬體介紹 46
5.1.1. 倒單擺機器人外觀 46
5.1.2. 內部電子設備 47
5.2. 重力估測器實作 49
5.3. 三相馬達驅動 51
5.3.1. 馬達簡化控制模型 51
5.3.2. 弦波近似：SPWM 52
5.3.3. 電流控制結果 53
5.4. 倒單擺機器人控制實作 54
5.4.1. 控制架構 54
5.4.2. 平衡控制 55
5.4.3. 防滑控制 57
6. 第六章 結論與未來規劃 62
6.1. 結論 62
6.2. 未來規劃 63
7. 附錄 64
7.1. 倒單擺載具系統矩陣 64
7.2. 機構幾何改變對IMU量測之校正 66
7.2.1. 角度偏差補償 66
7.2.2. 角速度偏差補償 69
7.2.3. 加速度偏差補償 70
8. 參考資料 72

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