Research on Dynamic Coupling Characteristic of Rootless Underactuated Redundant Robots

doi:10.3901/JME.2016.09.049

Abstract

Abstract: The general characteristic of rootless multi-body system and underactuated redundant robots is essentially dynamic systems with second-order nonholonomic constraints. The configuration space constraints equations can not realize the control request, which is generally based on dynamic equation. The constraints of these systems are mainly on velocity and acceleration and in general not integral. Therefore, the research on the characteristic of coupling motion of this kind of robots system is the basis of the controllability analysis. Based on dynamic nominal mechanism method and the differential and variation theory of nonholonomic system, the dynamic model of rootless underactuated redundant system is built, from which the second-order nonholonomic constraint equations of the system and the acceleration expressions of passive joints are derived based on the decoupling of nominal mechanism, active and passive joints. According to the defined performance indices for describing the coupling motion of passive joint, the influence of the active joints’ position on controllability of the robot are simulated. The beneficial conclusion for controllability performance advance of rootless underactuted redundant robot are obtained, which provides reference for actual input control of robots.

Key words: dynamic coupling, redundant robots, rootless multi-body systems, second-order nonholonomic constraints, underactuated

CLC Number:

TH31

LI Na¹, ZHAO Tieshi², JIANG Haiyong¹, WANG Jiazhong¹. Research on Dynamic Coupling Characteristic of Rootless Underactuated Redundant Robots[J]. Journal of Mechanical Engineering, 2016, 52(9): 49-55.

References

[1] DAACHI B,BENALLEGUE A. A neural network adaptive controller for end-effector tracking of redundant robot manipulators[J]. Journal of Intelligent and Robotic Systems,2006,46(3)：245-262.
[2] 葛新锋,赵东标. 7 自由度自动铺丝机器人参数化的自运动流形[J]. 机械工程学报, 2012, 48(13)：27-31.
GE Xinfeng,ZHAO Dongbiao. Parameterized self-motion manifold of 7-DOF automatic fiber placement robotic manipulator[J]. Journal of Mechanical Engineering,2012,48(13)：27-31.
[3] ZHAO Jing,FENG Dengdian. Comprehensive evaluation of fault-tolerant properties of redundant robots[J]. Chinese Journal of Mechanical Engineering,2008,21(4)：22-26.
[4] 邵君奕,张传清,陈雁,等. 用于空间内曲面喷涂的冗余机器人轨迹规划方法[J]. 清华大学学报,2014,54(6)：799-804.
SHAO Junyi,ZHANG Chuanqing,CHEN Yan, et al. Trajectory planning for redundant robots for internal surface spraying[J]. Journal of Tsinghua Unieversity,2014,54(6)：799-804.
[5] BIRGLEN L,GOSSELIN C M. Grasp-state plane analysis of two-phalanx underactuated fingers[J]. Mechanism and Machine Theory,2006,41(7)：807- 822.
[6] 张文增,陈强,孙振国,等. 具有形状自适应的欠驱动拟人机器人手指[J]. 机械工程学报,2004,40(10) ：115-118.
ZHANG Wenzeng, CHEN Qiang, SUN Zhenguo, et al. Under-actuated humanoid robot finger with shape adaptation[J]. Journal of Mechanical Engineering,2004,40(10)：115-118.
[7] 万磊, 崔士鹏, 张国成,等. 欠驱动水下机器人航迹跟踪控制[J]. 电机与控制学报,2013,17(2)：103-111.
WANG Lei,CUI Shipeng,ZHANG Guocheng,et al. Path following control of underactuated autonomous underwater vehicles[J]. Electric Machines and Control,2013,17(2)：103-111.
[8] NAKAMURA Y,CHUNG W,SORDALEN O J. Design and control of the nonholonomic manipulator[J]. IEEE Transactions on Robotics Automation,2001,17(1)：48-59.
[9] BISHOP B E. Formation control of underactuated autonomous surface vessels using redundant manipulator analogs[C]//IEEE International Conference on Robotics and Automation(ICRA), May 14-18, 2012, Saint Paul, MN. IEEE,2012：4892-4897.
[10] HUSSEIN I. BLOCH A M. Optimal control of underactuated nonholonomic mechanical systems[J]. IEEE Transactions on Automatic Control,2008,53(3)：668-682.
[11] ROBERTS R G. The dexterity and singularities of an underactuated robot[J]. Journal of Robotic System,2001,18(4)：159-169.
[12] HE Guangping,GENG Zhiyong. Optimal motion planning for differentially flat underactuated mechanical systems[J]. Chinese Journal of Mechanical Engineering,2009,22(3),347-353.
[13] FANG Yongchun,MA Bojun,WANG Pengcheng,etc. A motion planning-based adaptive control method for an underactuated crane system[J]. IEEE Transactions on Control Systems Technology,2012,20(1)：241-248.
[14] XIN Xin,LIU Yannian. Reduced-order stable controllers for two-link underactuated planar robots[J]. Automatica,2013,49(7)：2176-2183.
[15] LI Jing, GUO Xi,LI Zhijun,et al. Stochastic adaptive optimal control of under-actuated robots using neural networks[J]. Neurocomputing,2014,42(22)：190-200.
[16] HIROHISA K,SHOKO I,SHINYA K. Frequency-tuning input-shaped manifold-based switching control for underactuated space robot equipped with flexible appendages[J]. Astronautica,2014,101：42-54.
[17] 张劲松,秦卫阳. 高等动力学[M]. 北京：科学出版社, 2004.
ZHANG Jinsong, QIN Weiyang. Advanced Dynamics[M]. Beijing：Science Press,2004.
[18] BUSLMELL LG,TILBURY D,SASTRY S. Steering three-input chained form nonholonomic systems using sinusoids：The fire truck example[C]//Proceedings of the European Control Conference,1993,Cambridge,UK,1993：1432-1437.
[19] 赵铁石,李娜. 蛇形机器人动力建模的虚设机构法[J]. 机械工程学报,2007,43(8)：66-71.
ZHAO Tieshi,LI Na. Nominal Mechanism method of dynamic modeling for snak-like robots[J]. Journal of Mechanical Engineering,2007,43(8)：66-71.
[20] 梅凤翔. 非完整系统力学基础[M]. 北京：北京工业学院出版社,1985.
MEI Fengxiang. Nonholonomic system mechanics basis[M]. Beijing：Beijing Industrial College Press,1985.