A Spatial Redundant Robotic Manipulator’s Chaotic Self-motion
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摘要: 建立了空间自由飘浮冗余度机器人的模型和运动学方程, 分析了其Jacobian矩阵, 得出相应的运动学逆解, 通过仿真验证了空间自由飘浮冗余度机器人自运动中存在混沌运动, 利用混沌分析的直接观察法、时间历程法、相图法和poincare映射法, 对一个空间3R刚性冗余度机器人, 采用PD控制器控制其末端执行器重复跟踪工作空间内一平面路径时连杆的自运动进行了研究. 结果表明, 该机器人的自运动存在混沌运动.
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关键词:
- 空间冗余度机器人 /
- Jacobian矩阵 /
- 自运动 /
- 逆运动学 /
- 混沌
Abstract: The model and kinematics equations of a floating redundant spatial robotic manipulator are established. The Jacobian matrices are analyzed, and the inverse kinematics is obtained. Chaotic motions which existed in the floating spatial redundant robotic manipulator's self-motions are proved by simulation. At last, a spatial 3R redundant robotic manipulator is taken as an example, and the links' self-motion has been studied when the end-effector tracking a plane path repeatedly in its workspace for PD controlling by analysis of direct observation, time history method, phase diagram method, and poincare mapping method. Results show that there exist chaotic motions in the self-motion of the floating spatial redundant robotic manipulator when solving the floating redundant robotic manipulator's inverse kinematics based on pseudo-inverse Jacobian matrix.-
Key words:
- Spatial redundant robot /
- Jacobian matrix /
- Self-motion /
- Inverse kinematics /
- Chaos
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[1] Lu Zhen. Principle and Application of Redundant Degrees of Freedom Robot[M]. Beijing: Mechanic Industry Press, 2007. In Chinese (陆震. 冗余自由度机器人原理及应用[M]. 北京: 机械工业出版社, 2007) [2] Zhang Dengcai, Li Li. Chaotic Motion and its control in self-motion of redundant robot[J]. Robot, 2004, 26(2):166-169. In Chinese (张登才, 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) [3] Klein A, Huang C H. Review of pseudoinverse control for use with kinematically redundant manipulators[J]. IEEE Trans. SMC, 1983, 13(3):245-250 [4] Shrinivas L, Ghosal A. Possible chaotic motions in a feedback controlled 2R robot[C]//Proceeding of the International Conference on Robot and Automation. Washington DC: IEEE, 1996. 241-1246 [5] Ravishallkar A S, Ghosal A. Nonlinear dynamics and chaotic motions in feedback controlled two-and three-degree-of-freedom robots[J]. Int. J. Robots Res., 1999, 18(1):93-108 [6] Li Kaifu, Li Li, Chen Yong. Chaotic motion phenomenon in planar 2R robot[J]. Mech. Sci. Tech., 2002, 29(l):6-8. In Chinese (李开富, 李立, 陈永. 平面2R机器人中的混沌运动现象[J]. 机械科学技术, 2002, 29(l):6-8) [7] Varghese M, Fuehs A. Zero dynamics in kinematically redundant robots[C]//Proceedings of the 2nd IEEE International Conference on Systems Engineering. Pittsburgh, PA: IEEE, 1990. 66-69 [8] Varghese M, Fuehs A. Chaotic zero dynamics in kinematically redundant robots[J]. IEEE Trans. Aerosp. Elec. Syst., 1991, 27(5):784-796 [9] Liu Zhaohui, Zhang Dengcai, Li Li. Chaotic self-motion of a spatial 4R redundant robot[J]. Mech. Sci. Technol., 2005, 24(3):307-309. In Chinese (刘朝晖, 张登才, 李立. 空间4R冗余度机器人的混沌自运动研究[J]. 机 械科学与技术, 2005, 24(3):307-309) [10] Liu Zhaohui, Zhang Dengcai, Li Li. Chaotic motion in planar redundant robot based on resolved motion control[J]. Mach. Design Res., 2004, 20(3):38-41. In Chinese (刘朝晖, 张登才, 李立. 基于分解运动控制的平面冗余度机器人中的混沌运动[J]. 机械设计与研究, 2004, 20(3):38-41) [11] Li Li, Li Kaifu, Chen Yong. On the chaotic motion of planar serial kinematically redundant robot[J]. China Mech. Eng., 2003, 14(17):1512-1515. In Chinese (李立, 李开富, 陈永. 平面串联型冗余度机器人的混沌运动研究[J]. 中国机械工程, 2003, 14(17):1512-1515) [12] Li Li, Zhang Dengcai. Delayed feedback control method for chaotic control of spatial rigid redundant robot[J]. Chin. J. Mech. Eng., 2005, 41(9):122-127. In Chinese (李立, 张登才. 空间刚性冗余度机器人混沌运动控制的延迟反馈控制法[J]. 机械工程学报, 2005, 41(9):122-127) [13] Vakakis A F, Burdiek J W. An "Interesting" Strange Attractor in the Dynamics of a Hopping Robot[J]. J. Robot. Res., 1991, 10(6):606-618 [14] Vakakis A F, Burdick J W. Chaotic motions of a hopping robot[C]//Proceedings of the IEEE International Conference on Robotics and Automation. Cincinnati, Ohio: IEEE, 1990. 14-18 [15] Hong Bingrong, Liu Changan, Wang Hongpeng, et al. Recommendations on Chinese development of free-flying space robot[J]. Robot, 2000, 22(2):66-71. In Chinese (洪炳熔, 柳长安, 王鸿鹏, 等. 关于我国发展自由飞行空间机器人的建议[J]. 机器人, 2000, 22(2):66-71) [16] Danevit J, Hartenberg R S. A kinematic notation for lower-pair mechanisms based on matrices[J]. Trans. ASME J. Appl. Mech., 1995, 22:215-221 [17] Craig J J. Introduction to Robotics: Mechanics and Control[M]. Addison-Wesley, Reading, MA, 1986
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