臺灣博碩士論文加值系統

本研究同時考慮雙腳支撐和單腳支撐階段，以 ZMP 預觀控制法自動產生雙足機器人的步態序列。先由 D-H 法定義機器人連桿座標系統，求得正向運動學數學式與反向運動學解析式，再推導三質點模型之 ZMP 方程式，作為預觀控制器受控系統的輸出方程式。於步態規劃時，引入雙腳支撐階段與單腳支撐階段，規劃 x 與y 方向的期望 ZMP 軌跡，以及利用多項式內插法規劃遊動腳腳踝與腳底板期望軌跡。基於預觀控制的步態產生器，於選用適當的性能指標權重矩陣後，可由代數黎卡提方程式求解性能最佳的回授控制增益矩陣與預觀控制矩陣，以自動產生雙足機器人步行時的基底座標原點運動軌跡，再由反向運動學計算步行時所需的關節角度時間序列。本文先將步態規劃以及步態產生器進行電腦模擬，再將步態產生器自動生成的關節角度轉換為實際機器人的角度 輸入實際機器人的控制介面，，以驗證步態規劃和預觀控制器的有效性。

In this thesis, three-mass model based preview control of ZMP (zero moment point) is considered for automatically generating the walking pattern sequence for a biped robot. First, the DH method is adopted to define the robot link coordinate systems, and analytic forward kinematics and inverse kinematics are derived. Then a simplified three-mass model for the biped robot is used for deriving the ZMP equation, and discrete-time preview control of ZMP is derived. In order to obtain better walking performance, double support phase is introduced in the gait planning. Simple desired ZMP trajectories in the x- and y-direction are considered, and polynomial interpolation method is adopted for planning the swing leg ankle point trajectory and foot board inclining angle trajectory. By selecting appropriate weight matrices of the performance index, better preview control gain matrices can be obtained by solving the algebraic Riccati equation. Based on the preview control of ZMP, the motion trajectory of the origin of the base link frame can be generated, then the joint angle sequences of the two legs can be computed using the inverse kinematics equations. Finally, computer simulation and real experiment on the HUNO biped robot are used to demonstrate the effectiveness of the suggested walking pattern generating method.

誌謝 .........i
摘要 .........ii
Abstract .........iii
目錄 .........iv
圖目錄 .........vi
表目錄 .........viii
符號說明 .........ix
第一章緒論 .........1
1.1 研究動機 .........1
1.2 文獻回顧 .........2
1.3 論文大綱 .........4
第二章 雙足機器人運動學模式與三質點模型 .........5
ZMP 方程式推導.........5
2.1 雙足機器人正向運動學 .........5
2.1.1 雙足機器人構造 .........5
2.1.2 座標系統定義.........6
2.2 雙足機器人反向運動學.........11
2.2.1 θ1 解析式推導......... 11
2.2.2 兩腳 θ 2 , θ3 , θ 4 解析式推導 .........14
2.3 關節角度關係式.........19
2.4 基於三質點模型之 ZMP 方程式推導.........23
2.4.1 雙足機器人三質點模型之座標系統定義 .........23
2.4.2 三質點模型之 ZMP (Zero Moment Point)方程式推導.........27
第三章 雙足機器人步態規劃與.........32
預觀控制器設計 .........32
3.1 雙足機器人步態規劃 .........32
3.1.1 雙足機器人 ZMP 期望軌跡規劃 .........32
3.1.2 雙足機器人遊動腳規劃.........42
3.2 預觀(preview)控制器設計.........52
3.2.1 離散時間控制系統推導 .........52
3.2.2 預觀(preview)控制律 .........55
第四章 電腦模擬結果與步行實驗 .........59
4.1 雙足機器人參數選定 .........59
4.2 控制器參數選定.........60
4.3 雙足機器人步態參數及模擬 .........62
4.3.1 ZMP 期望軌跡參數選定.........62
4.3.2 電腦模擬結果.........64
4.4 雙足機器人步行實驗 .........70
第五章 結論與建議 .........75
參考文獻 .........77
附錄 .........79
A.1 右腳為支撐腳時，支撐腳各連桿質心相對於支撐腳座標系 .........79
A.2 右腳為支撐腳時，遊動腳各連桿質心相對於遊動腳座標系 .........87
A.3 左腳為支撐腳時，支撐腳各連桿質心相對於支撐腳座標系 ......... 93
A.4 左腳為支撐腳時，遊動腳各連桿質心相對於遊動腳座標系 .........100

[1] S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, and H.Hirukawa,“Biped Walking Pattern Generation by Using Preview Control of Zero-Moment Point,” in Proc. IEEE Int. Conf. Robot. Autom.,Vol. 2, pp. 1620-1626, 2003.
[2] K. Harada, S. Kajita, K. Kaneko, and H. Hirukawa, “An Analyical Method on Real-time Gait Planning for a Humanoid Robot,” Int. J. Humanoid Robotics,Vol. 3, No. 1, pp. 1-19, 2006.
[3] T. Sato, S. Sakaino, and K. Ohnishi, “Real-Time Walking Trajectory Generation Method at Constant Body Height in Single Support Phase for Three-Dimensional Biped Robot,” in Proc. IEEE Int. Conf. on Industrial Technology, pp. 1-6, 10-13 Feb., 2009.
[4] T. Sato, S. Sakaino, and K. Ohnishi, “Real-Time Walking Trajectory Generation Method with Three-Mass Models at Constant Body Height for Three- Dimensional Biped Robots,” IEEE Trans. on Industrial Electronics, pp. 376-383, Feb. 2011.
[5] S. Shimmyo, T. Sato, and K. Ohnishi, “Biped Walking Pattern Generation by Using Preview Control Based on Three-Mass Model,” IEEE Trans. on Industrial Electronics, Vol. 60, No. 11, pp. 5137-5147, 2013.
[6] K. Nishiwaki and S. Kagami, “High Frequency Walking Pattern Generation Based on Preview Control of ZMP,” IEEE Int. Conf. on Robotics and Automation, pp. 2668-2670, 2006.
[7] T. Katayama, T. Ohki, T. Inoue, and T. Kato, “Design of an Optimal Controller for a Discrete-Time System Subject to Previewable Demand,” Int. J. Control, Vol. 41, No. 3, pp. 677-699, 1985.
[8] 王泊翔, “仿被動式步行之雙足機器人步態規劃與實現”, 國立中興大學機械工 程學系碩士論文, 2012。
[9] 楊昀諭, “七連桿平面雙足機器人之系統建模與步行控制”, 國立中興大學機械 工程學系碩士論文, 2012。
[10] HUNO robot platform, RoboBuilder Co., Ltd.
[11] 梶田秀司 編著, 管貽生 譯,仿人機器人, 清華大學出版社, 北京, 2007。
[12] J. J. Craig, Introduction to Robotics : Mechanics and Control, 3rd Ed., Addison Wesley, 2005.
[13] P. Corke, Robotics, Vision and Control : Fundamental Algorithms in MATLAB, Springer Verlag, 2011.
[14] H. Kwakernaak, Linear Optimal Control Systems, New York , 1972.