臺灣博碩士論文加值系統

本論文進行五連桿二足機器人於平面週期步行的分析與設計。五連桿二足機器人的步行運動是複雜的，為了簡化分析本文只考慮機器人在側視平面的運動。二足機器人的步行過程可分解成單腳支撐相和雙腳支撐相。二足機器人的混合動力方程式是非線性而且高維度的，運用零動力理論與虛擬限制的概念，機器人可表示為一維二階的零動力方程式。依據機器人的機械及幾何參數，本文可以解出機器人週期性步行的動態行為，並由機器人性能優化模式來決定機器人的運動參數。首先設定代表二足機器人性能的優化函數和特性的限制條件，以優化工具解出機器人的運動參數，最後模擬二足機器人各種步行模式的週期性動態行為。

This thesis studies on the analysis and design of a five-link bipedal robot that can walk periodically. The analysis of the walking behavior of a five-link bipedal robot is very complicated. In order to simplify the analysis, only the walking motion of the bipedal robot in sagittal plane is considered. The biped's walking motion consists of successive phases of single support and double support, and its hybrid mathematical model of walking is non-linear and high dimensional. Using concepts of zero dynamics and virtual constraints, the dynamical equation of the bipedal robot can be treated as an one-dimensional first-order equation. Given a set of robot's parameters and from an optimization program, one can obtain a dynamic periodic walking of the bipedal robot. By setting an optimization function and various constraints, and then using the tool of optimization, one can simulate the periodically dynamical behavior of bipedal robot in various walking motion.

目錄……………………………………………………………………i
誌謝……………………………………………………………………v
中文摘要………………………………………………………………ix
英文摘要………………………………………………………………x
圖表索引………………………………………………………………xi
第一章　緒論…………………………………………………………1
1.1 前言………………………………………………………1
1.2 研究回顧…………………………………………………2
1.3 研究動機與目的…………………………………………5
1.4 論文架構…………………………………………………6
第二章　步態模型與動力方程式……………………………………8
2.1 二足機器人模型…………………………………………9
2.2 二足機器人步行狀態……………………………………11
2.3 二足機器人數學模型……………………………………14
2.3.1 直接運動學方程式…………………………………16
2.3.2 反運動學方程式……………………………………18
2.3.3 機器人系統重心位置向量…………………………19
2.3.4 機器人連桿重心速度向量…………………………20
2.4 二足機器人步行的動力方程式…………………………21
2.4.1 系統動能計算………………………………………22
2.4.2 系統位能計算………………………………………23
2.4.3 系統動力方程式……………………………………24
2.4.4 單腳支撐相動力方程式……………………………24
2.4.5 雙腳支撐相動力方程式……………………………25
2.4.6 換腳模式……………………………………………28
2.4.7 混合動力方程式……………………………………28
第三章 零動力方程式及軌跡規劃…………………………………31
3.1 零動力理論簡介…………………………………………31
3.2 虛擬限制簡介……………………………………………33
3.3 零動力方程式……………………………………………34
3.4 Bezier曲線設計 ………………………………………40
3.4.1合成曲線介紹………………………………………40
3.4.2 Bezier曲線設定 …………………………………45
第四章　步行模式優化設計及步行程式流程………………………50
4.1 步行模式優化設計………………………………………50
4.1.1 優化函數設定………………………………………51
4.1.2 限制條件設定………………………………………52
4.2 fmincon函數 ……………………………………………54
4.3 ode函數 …………………………………………………56
4.3.1 ode函數基本用法 …………………………………56
4.3.2 ode函數選項 ………………………………………57
4.4 模擬步行程式流程 ………………………………………57
4.4.1 步行週期動態行為的程式流程 ……………………58
4.4.2 步行週期輸入力矩的程式流程 ……………………64
第五章 模擬結果 ……………………………………………………66
5.1 二足機器人模型參數 ……………………………………66
5.2 性能優化的參數設定 ……………………………………67
5.3 模擬結果 …………………………………………………67
5.3.1 模擬結果一 …………………………………………68
5.3.2 模擬結果二 …………………………………………72
5.3.3 模擬結果三 …………………………………………77
5.3.4 模擬結果四 …………………………………………81
5.3.5 模擬結果五 …………………………………………86
5.4 模擬結果說明 ……………………………………………90
第六章 結論與建議 …………………………………………………93
6.1 結論 ………………………………………………………93
6.2 建議………………………………………………………94
參考文獻………………………………………………………………95

[1] K. Hirai, M. Hirose, Y. Haikawa, and T. Takenaka, “The Development of Honda Humanoid Robot,” IEEE International Conference on Robotics and Automation, pp. 1321-1326, 1998.
[2] S. Napoleon, Nakaura, and M. Sampel, “Balance Control Analysis of Humanoid Robot Based on ZMP Feedback Cobtrol,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2437-2442, 2002.
[3] T. Sugihara, Y. Nakamura, and H. Inoue, “Realtime Humanoid Motion Generation Through ZMP Manipulation Based on Inverted Pendulum Cobtrol,” Proceedings of the 2002 International Conference on on Robotics and Automation, pp. 1404-1409, 2002.
[4] J. Furusho, and A. Sano, “Sensor-Based-Control of a Nine Link Biped,” International Journal of Robotics Research, Vol. 9, No.2 pp.83-98, April 1990.
[5] F. Miyazaki, and S. Arimoto, “A Control Theoretic Study on Dynamical Biped Locomotion,” ASME Journal of Dynamic Systems, Measurement, and Control,Vol. 102, pp. 233-239, December 1990.
[6] H.K. Lum, M. Zribi, and Y.C. Soh, “Planning and Control of The Development of Honda Humanoid Robot,” IEEE International Conference on Robotics and Automation, pp. 1321-1326, 1998.
[7] W. Blajer, and W. Schiehlen, “Walking Without Impacts as a Motion/ Force Control Prolem,” ASME Journal of Dynamic systems, Measurement, and Control,Vol. 114, pp. 660-665, December 1992.
[8] C.L. Golliday, and H. Hemami, “An Approach Analyzing Biped Locomotion Dynamics and Designing Robot Locomotion Control,” IEEE Transactions on Automation Control, Vol. 22, No. 6, pp. 963-972, 1977.
[9] T. Mcgeer, “Passive Dynamic Walking,” International Journal of Robotics Research, Vol. 9, No.2, pp.62-82, April 1990.
[10] J.H. Park, and H. Chung, “Hybrid Control for Biped Robots Using Impedance Control and Computed-Torque Cobtrol,” Proceedings of the 1999 International Conference on Robotics and Automation, pp. 1365-1370, 1999.
[11] H. Lim, S. Setiawan, and A. Takanishi, “Balance and Impedance Control for Biped Humanoid Robot Locomotion,” Proceedings of the 2001IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 494-499, 2001.
[12] Q. Li, A. Takanishi, and I. Kato, “A Biped Walking Robot Having a ZMP Measurement System Using Universal Force-Moment Sensors,” IEEE/RSJ International Workshop on Intelligent Robots and Systems IROS’91, Osaka, Japan, Nov. 3-5, pp. 1568-1573, 1991.
[13] M. Vukobratovic, A. Frank, and D. Juricic, “On the Stability of Biped Locomotion,” IEEE Transactions on Bio-Medical Engineering, Vol. BME-17, No. 1, pp. 25-36, 1970.
[14] H.P. Jong, and H. Chung, “ZMP Compensation by On-Line Trajectory Generation for Biped Robots,” Proceedings of IEEE Conference on Systems, Vol. 3, pp. 960-965, 1999.
[15] C.L. Shin, Y.Z. Li, S. Churng, T.T. Lee, and W.A. Gruver, “Trajectory Synthesis and Physical Admissibility for a Biped Robot During the Single-Support Phase,” Proceedings of IEEE International Conference on Robotics and Automation 3, pp. 1646-1652, 1992.
[16] P.H. Channon, S.H. Hopkins, and D.T. Pham, “Derivation of Optimal Walking Motions for a Bipedal Walking Robot,” Robotica,Vol. 10, pp. 165-172, 1992.
[17] A.A. Grishin, A.M. Formal, A.V. Lensky, and S.V. Zhitomirsky, “Dynamic Walking of a Vehicle with Two Telescopic Legs Controlled by Two Drives,” the International Journal of Robotics Research, Vol. 13, No. 2, April 1984.
[18] Shuuji Kajita, and Kazuo Tani, “Adaptive Gait Control of a Biped Robot Based on Realtime Sensing of the Ground Profile,” Proceedings of the 1996 IEEE International Conference on Robotics and Automation Minneapolis, Minnesota-April6, pp. 570-577, 1996
[19] S.H. Collins, M. Wisse, and A. Rulna, “A Three-Dimensional Passive-Dynamic Walking Robot with two Legs and Knees,” Int. J. Robot. Res, Vol. 20, No. 7, pp. 607-615, July 2001.
[20] J.W. Grizzle, G. Abba, and F. Plestan, “Asymptotically Stable Walking for Biped Robots：Analysis via Systems with Impulse Effects,” IEEE Transactions on Automatic Control, Vol. 46, pp. 51-64, January 2001.
[21] F. Plestan, J.W. Grizzle, E.R. Westervelt, and G. Abba, “Stable Walking of a 7-DOF Biped Robot,” IEEE Transactions on Robotics and Automation, Vol. 19, pp. 653-668, Aug. 2003.
[22] C. Chevallereau, G. Abba, Y. Aoustin, F. Plestan, E.R. Westervelt, C. Canudas-De-Wit, and J.W. Grizzle,“RABBIT: a Testbed for Advanced Control Theory,” IEEE on Control Systems Magazine, Vol. 23, pp. 57-79, Oct. 2003.
[23] E.R. Westervelt, J.W. Grizzle, and D.E. Koditschek, “Hybrid Zero Dynamics of Planar Biped Walkers,” IEEE Transactions on Automatic Control, Vol. 48, pp. 42-56, Jan. 2003.
[24] J.W. Grizzle, “An Analytical Approach to Asymptotically Stable Walking in Planar Biped Robots,”, SuperMechano Systems Symposium, Tokyo, Japan, November 19-20 2001.
[25] E.R. Westervelt, and J.W. Grizzle, “Design of Asymptotically Stable Walking for a 5-link Planar Biped Walker via Optimization,” Proceedings of IEEE International Conference on Robotics and Automation, Vol. 3, pp. 3117-3122, 2002.
[26] J.W. Grizzle, “Remarks on Event-Based Stabilization of Periodic Orbits in Systems with Impulse Effects,”, Second International Symposium on Communication, Control and Signal Processing, March 2006, Marrakech Morocco.