张登材, 李立. 冗余度机器人自运动中的混沌运动及其控制[J]. 机器人, 2004, 26(2): 166-169,175..
ZHANG Dengcai, LI Li. Chaotic Motion and Its Control in Self-motion of Redundant Robot. ROBOT, 2004, 26(2): 166-169,175..
Abstract:In this paper,the possible chaotic motion in the self-motion of a planar 3R redundant robot is discussed under the PD controller when the end-effector traces a closed-path repeatedly in the workspace,by the numerical simulation,phase plot and the largest Lyapunov exponent. The numerical results show that the self-motion is chaotic based on the pseudoinverse of the Jacobian method for solving the inverse kinematics of the redundant robot. The delayed feedback control method is used to control the discovered chaotic motion for the first time. It is shown that the chaotic motion can be turned into regular motion with some appropriate parameters.
[1] Matthew V,Andreas F.Zero dynamics in kinematical redundant robots[A].Proceedings of the 2nd IEEE International Conference on Systems Engineering[C].Pittsburgh,PA:1990.66-69. [2] Matthew V,Andreas F.Chaotic zero dynamics in kinematical redundant robots[J].IEEE Transaction on Aerospace and Electronic Systems,1991,27(5):784-796. [3] 李立,李开富,陈永.平面4R冗余度机器人自运动中的混沌现象[J].机械传动,2003,27(2):1-4. [4] Ott E,Grebogi C,Yorke J A.Control chaos[J].Physical Review Letters,1990,64(6):1196-1199. [5] Pyragas K.Continuous control of chaos by self-controlling feedback[J].Physical Letters A,1992,170(6):421-428. [6] 王光瑞,于熙龄,陈式刚.混沌的控制、同步与利用[M].北京:国防工业出版社,2001. [7] 熊有伦,丁汉,刘恩沧.机器人学[M].北京:机械工业出版社,1993. [8] 陈士华,陆君安.混沌动力学初步[M].武汉:武汉水利电力大学出版社,1998. [9] 姜万录,张淑清,王益群.混沌运动特征的数值试验分析[J].机械工程学报,2000,36(10):13-17. [10] 徐缤昌,阙志宏.机器人控制工程[M].西安:西北工业大学出版社,1991.