臺灣博碩士論文加值系統

本論文針對七連桿平面雙足機器人，利用Lagrange方程式推導出雙腳支撐階段(double support phase)與單腳支撐階段(single support phase)之動力學方程式，再利用角動量守恆原理推導換腳碰撞(impact)前後的角速度轉換方程式。步態軌跡規劃方面，以包含一準備階段、二完整步伐，以及一結束階段為例，將單腳支撐階段的支撐腳視為倒單擺直接規劃其關節角度軌跡，遊動腳則以多項式內插法進行規劃，再以幾何法推導逆向運動學方程式以求得各連桿之期望軌跡。在控制器設計方面，則分別針對雙腳支撐階段與單腳支撐階段設計其公稱控制器，以及考慮實際系統不確定性之適應控制器，穩定適應控制器中包含輻射基底類神經網路函數近似器，以補償系統之不確定性。最後並以電腦模擬，驗證控制器之有效性。

In this thesis, modeling and control of a seven-link planar biped robot are considered. The dynamics models including the double support phase and single support phase motion equations are first derived using the Lagrange’s equations. And then based on conservation of angular momentum, the impact’s angular velocity transformation equations are derived. A gait pattern consisted of a preparation phase, two complete paces, and one ending phase, is synthesized by considering the support leg as a single inverted pendulum and the swing leg’s trajectories are planned via polynomial interpolation. Inverse kinematics equations are derived using geometric methods for calculating the joint trajectories of the swing leg. Furthermore, based on Lyapunov stability, stable adaptive controls for the double support and single support phase are respectively derived. In the stable adaptive controllers, radial basis neural network (RBNN) function approximators are included to compensate for the model uncertainty. Finally, computer simulations are presented to illustrate the effectiveness of the suggested control strategy.

誌謝 i
中文摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
符號說明 ix
第一章　緒論 1
1.1　研究動機 1
1.2　文獻回顧 1
1.3　論文大綱 3
第二章　七連桿平面雙足機器人之系統模式 5
2.1　機器人模型參數定義 6
2.2　主動式機器人系統模式推導 8
2.2.1　雙腳支撐階段之系統模式 9
2.2.2　單腳支撐階段之系統模式 14
2.2.3　碰撞前後角速度變換方程式推導 19
第三章　平面雙足機器人之步態軌跡規劃 29
3.1　雙足機器人運動軌跡規劃 30
3.1.1　起始雙腳支撐階段之步態規劃 31
3.1.2　起始單腳支撐階段之步態規劃 37
3.1.3　完整步伐之雙腳支撐階段之步態規劃 43
3.1.4　完整步伐單腳支撐階段之步態規劃 52
3.1.5　結束階段單腳支撐時之步態規劃 58
3.1.6　結束階段雙腳支撐時之步態規劃 64
第四章　平面雙足機器人主動式控制器設計 69
4.1　雙腳支撐階段之公稱控制與直接式適應控制設計 69
4.1.1　系統公稱控制律推導 70
4.1.2　考慮不確定性影響之適應控制律推導 73
4.1.3　輻射基底類神經網路函數近似器設計 74
4.1.4　考慮不確定性影響之穩定控制律推導 77
4.2　單腳支撐階段之公稱控制與直接式適應控制設計 80
4.2.1　系統公稱控制律推導 81
4.2.2　考慮不確定性影響之適應控制律推導 84
4.2.3　輻射基底類神經網路函數近似器設計 86
4.2.4　考慮不確定性影響之穩定控制律推導 87
第五章 電腦模擬與結果討論 91
5.1　雙足機器人參數之選定 91
5.2　公稱控制律電腦模擬結果 94
5.2.1　步行運動過程之控制器參數選定 94
5.2.2　電腦模擬結果與討論 97
5.3　適應控制律電腦模擬結果 105
5.3.1　步行運動過程之控制器參數選定 105
5.3.2　電腦模擬結果與討論 120
第六章　結論與建議 135
參考文獻 137
附錄 139
A.1. 雙腳支撐階段之系統模式推導 139
A.2. 單腳支撐階段之系統模式推導 153
A.3. 平面雙足機器人碰撞之角速度轉換方程式推導 168
作者簡歷 201

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