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系統識別號 U0002-1308200911265600
中文論文名稱 人型機器人腳之彈性接觸分析
英文論文名稱 Elastic Contact Analysis of a Humanoid Robot Foot
校院名稱 淡江大學
系所名稱(中) 機械與機電工程學系碩士班
系所名稱(英) Department of Mechanical and Electro-Mechanical Engineering
學年度 97
學期 2
出版年 98
研究生中文姓名 杜俊霖
研究生英文姓名 Chun-Lin Tu
學號 696370971
學位類別 碩士
語文別 中文
口試日期 2009-07-16
論文頁數 55頁
口試委員 指導教授-劉昭華
委員-陳正光
委員-王銀添
中文關鍵字 雙足機器人  穩定條件  接觸應力  完全滑動 
英文關鍵字 Biped robots  stability conditions  contact stress  gross sliding 
學科別分類 學科別應用科學機械工程
中文摘要 本論文分析機器人腳與地面的彈性接觸,探討可能造成雙足機器人行走時發生傾倒及滑動的外力大小。若機器人腳所受外力矩較大,可能使腳與地面的接觸面積僅剩最後微小的區域,這就是發生傾倒不穩定的臨界狀態;而機器人在運動過程中,亦可能同時在地面上發生滑動。本研究針對滑動不穩定狀態進行分析,找出所有造成滑動臨界狀態的力及力矩(Fx, Fy, Mz)組合,並且亦找出數個造成傾倒臨界狀態的力及力矩組合(Mx, My, Fz)。分析的方法分成兩部分,第一部分是進行接觸分析,求出外力(矩)作用之下接觸面積及壓力分布。此部分結果可找出造成傾倒臨界狀態之(Mx, My, Fz)組合。第二部分是在接觸區域及正向壓力求出之後,利用平面運動之瞬時中心的觀念,找出滑動臨界狀態之(Fx, Fy, Mz)組合。
英文摘要 In this thesis the elastic contact between a robot foot and ground is analyzed to investigate the forces to cause falling or sliding of a biped robot in walking. In cases with large applied moments, the foot-to-ground contact area may reduce to a very small region, and this is the critical condition for falling. Gross sliding may also occur during robot walking, which is also a state of instability. In this thesis the size of foot-to contact region and pressure distribution in the region is determined first, from which the tangential stress distribution may also be found by using the technique of instantaneous center of zero velocity. With these stress distributions the resultant moments in gross sliding or falling may be determined. In this thesis we show all combinations of forces (moments) (Fx, Fy, Mz) to cause sliding, and a few combinations of forces (Mx, My, Fz) to cause falling. These forces are compared with results obtained by treating the foot as a rigid body.
論文目次 目 錄
中文摘要 I
英文摘要 II
目錄 III
圖目錄 Ⅳ
表目錄 Ⅶ
第一章 緒論 1
1.1前言及研究動機 1
1.2 文獻回顧 1
1.3 雙足機器人腳之模型 3
第二章 雙足機器人之穩定性分析 4
2.1簡介 4
2.2邊界積分方程式 5
2.3穩定性分析 9
第三章 數值分析 12
3.1導角上任一點高度 12
3.2接觸區域網格化 14
第四章 結果與討論 17
第五章 結論及未來研究 23
參考文獻 24
附錄A f(x,y,s,t)的積分 26

圖目錄
圖1 雙足機器人之示意圖...................................30
圖2 機器人腳及受力狀態...................................31
圖3 機器人腳對地面之相對位移圖...........................32
圖4 接觸區域及網格,虛線是腳的原始接觸區域...............33
圖5 機器人腳尺寸參數圖...................................34
圖6 將腳形劃分區域,針對不同區域導角上的點分別分析.......35
圖7 (a) 腳前方圓弧導角上某點P之xy面圖,(b)C1P之截面......36
圖8 腳左、右側之xz面圖...................................37
圖9 腳與地面的接觸區域網格化(a)沿y方向分割n個strip,再把每個strip分割成有限個網格(cell),(b)第i個網格示意圖.........38
圖10 將腳形變為圓柱體後與赫氏應力分佈之比較...............39
圖11 theta_x=theta_y=0時delta與Fz之關係.................. 40
圖12 delta=0.002,theta_x=theta_y=0,在y/K=0.1390的應力分佈........................................................41
圖13 fz=0.0033時,theta_x與Fz和theta_y與Fz之關係..........42
圖14 fz=0.0033時,theta_x與Mx之關係.......................43
圖15 fz=0.0033時,theta_y與My之關係.......................44
圖16 fz=0.0033時,theta_x與對Q之力矩的關係............... 45
圖17 delta=0.002、theta_x=0、theta_y=0時mpz之等高線圖.....46
圖18 delta=0.002、theta_x=0.003、theta_y=0.005時mpz之等高線圖........................................................47
圖19 delta=0.002、theta_x=0、theta_y=0時,腳與地面之接觸區域
..........................................................48
圖20 delta=-0.77、theta_x=-0.0024、theta_y=-1.5時,腳與地面之接觸區域................................................49
圖21 delta=-0.77、theta_x=-0.0024、theta_y=-1.5時mpz之等高線圖........................................................50
圖22 delta=-0.77、theta_x=-0.0024、theta_y=-1.5時,Tz沿y方向之分佈....................................................51
圖23 機器人腳與地面接觸區域僅剩腳前方圓弧的頂端時之臨界數值;直線為最近似之線性解..................................52
圖24 機器人腳與地面接觸區域僅剩腳後端直線時之臨界數值;直線為最近似之線性解..........................................53
圖25 機器人腳為剛體且與地面接觸區域僅剩腳前方圓弧之頂端時,腳上之受力狀態................ ...........................54
圖26 機器人腳為剛體且與地面接觸區域僅剩腳後側一直線時,腳上之受力狀態................................................55

表目錄
表1 機器人腳與地面接觸區域僅剩腳前方圓弧的頂端時之臨界數值........................................................28
表2 機器人腳與地面接觸區域僅剩腳後端直線時之臨界數值........................................................28
表3 機器人腳與地面接觸區域僅剩腳左側直線時之臨界數值........................................................29
參考文獻 [1] Vukobratvoić, M., and Juričić, D., Contribution to the synthesis of biped gait, IEEE Transactions of Biomedical Engineering, 16 (1), 1969.

[2] Vukobratvoić, M., and Borovac, B., Zero-Moment point- thirty five years of its life, International Journal of Humanoid Robotics, 1 (1), 2004, pp. 157-173.

[3] Hatano, M. and Obara, H., Stability evaluation for mobile manipulators using criteria based on reaction, SICE 2003 Annual Conference, 2, 2003, pp. 2050-2055.

[4] Saida, T., Yokokohji, Y. and Yoshikawa, T., FSW (Feasible Solution of Wrench) for multi-legged robots, IEEE International Conference on Robotics and Automation 3, 2003, pp. 3815-3820.

[5] Hirukawa, H., Hattori, S., Harada, K., Kajita, S., Kaneko, K., Kanehiro F., Fujiwara, K., and Morisawa, M., A universal stability criterion of the foot contact of legged robots-adios ZMP, IEEE, Int. Conf. on Robotics and Automation, 2006, pp. 1976–1983.

[6] Goswami, A., and Kallem, V., Rate of change of angular momentum and balance maintenance of biped robots, Proceedings of the 2004 IEEE, Int. Conf. on Robotics and Automation, 2004, pp. 3785-3790.

[7] Popovic, M., Hofmann, A., and Herr, H., Angular momentum regulation during human walking: biomechanics and control, Proceedings of the 2004 IEEE, International Conference on Robotics and Automation, 2004, pp. 2405-2411.

[8] Popovic, M., and Englehart, A., Angular momentum primitives for human walking: biomechanics and control, Proceedings of the 2004 IEEE, International Conference on Robotics and Automation, 2004, pp. 1685-1691.

[9] Goswami, A., Postural stability of biped robot and the Foot-Rotation indicator (FRI) point, International Journal of Robotics Research, 18 (6), 1999, pp. 523–533.

[10] Peng, Z., Fu, Y., Tang, Z. and Huang, Q., Motion planning for humanoid robot based on a new stability evaluation technique, IEEE International Conference on Information Acquisition, art. no. 4097743, 2006, pp. 689-694.

[11] Johnson, K. L., Contact Mechanics, Cambridge University Press, UK, 1985.

[12] Timoshenko, S. P., and Goodier, J. N., Theory of Elasticity, McGraw-Hill, 1970.

[13] Vijayakar, S., Busby, H., and Wilcox, L., Finite element analysis of three-dimensional conformal contact with friction, Computers and Structures, 33(1), 1989, pp. 49-61.

[14] Fagan, M. J., and McConnachie, J., A review and detailed examination of non-layered conformal contact by finite element analysis, Journal of Strain Analysis for Engineering Design, 36(2), 2001, pp. 177-195.

[15] Paul, B., and Hashemi, J., Contact Pressure on Closely Conforming Elastic Bodies, ASME Journal of Applied Mechanics, 48 (3), 1981, pp.543-548.

[16] Ghaderi-Panah, A., and Fenner, R.T., General boundary element method approach to the solution of three-dimensional frictionless contact problems, Engineering Analysis with Boundary Elements, 21 (4), 1998, pp. 305-316.

[17] Liu, C, and Paul, B., Fully developed sliding of rough surfaces, ASME Journal of Tribology, 111 (3), 1989, pp. 445-451.
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