Robust Servo Constrained Control of Parallel Robots Based on the Udwadia-Kalaba Method

HAN Jiang; WANG Peng; DONG Fangfang; XIA Lian; ZHAO Xiaomin

doi:10.21656/1000-0887.410197

Volume 42 Issue 3

Mar. 2021

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Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(3): 264-274

HAN Jiang, WANG Peng, DONG Fangfang, XIA Lian, ZHAO Xiaomin. Robust Servo Constrained Control of Parallel Robots Based on the Udwadia-Kalaba Method[J]. Applied Mathematics and Mechanics, 2021, 42(3): 264-274. doi: 10.21656/1000-0887.410197

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Robust Servo Constrained Control of Parallel Robots Based on the Udwadia-Kalaba Method

doi: 10.21656/1000-0887.410197

¹School of Mechanical Engineering, Hefei University of Technology, Hefei 230009, P.R.China
²School of Automobile and Transportation Engineering, Hefei University of Technology, Hefei 230009, P.R.China

Funds: The National Natural Science Foundation of China（51905140）

Received Date: 2020-07-01
Rev Recd Date: 2021-01-14
Publish Date: 2021-03-01

Abstract

Abstract

For the trajectory tracking control problems of 2-DOF redundant drive parallel robots, a robust servo control method based on the Udwadia-Kalaba equation was proposed. Under the influences of load, external interference and manufacturing errors, it is impossible to obtain the accurate and complete motion model for the robot, and the control performance of the robot is poor. To solve the impacts of this type of uncertainty, a robust control method was proposed to enable the system to accurately track the ideal trajectory, and ensure the uniform boundedness and the uniform ultimate boundedness of the overall system. In addition, the Udwadia-Kalaba equation was used to solve the constraint force required by the system to meet the ideal constraint in the control process. The Udwadia-Kalaba equation does not require auxiliary variables such as Lagrangian multipliers or pseudo-generalized velocities, and can handle both complete and incomplete constraints, with analytical solutions of constraint forces satisfying the trajectory obtained. The stability of this robust control method was proved theoretically with the Lyapunov function. Simulation experiments show that, the proposed robust control method can achieve high-precision tracking control along a given trajectory under non-ideal conditions.
- Udwadia-Kalaba method,
- robust control,
- uncertainty,
- parallel robot,
- constrained control

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References(15)

References

[1]	孟瞾. 基于模型的机器人控制系统集成仿真验证平台[D]. 硕士学位论文. 广州: 华南理工大学, 2015.(MENG Zhao. Model-based integrated simulation and verification platform for robot control system[D]. Master Thesis. Guangzhou: South China University of Technology, 2015.(in Chinese))
[2]	郭盛, 梁艺瀚, 王志群, 等. 基于虚拟仿真的并联构型手控器动力学建模与力反馈控制[J]. 机器人, 2015,37(2): 224-230.(GUO Sheng, LIANG Yihan, WANG Zhiqun, et al. Dynamic modeling and force-feedback control of haptic device with parallel structure based on virtual simulation[J].Robot,2015,37(2): 224-230.(in Chinese))
[3]	苏玉鑫, 段宝岩, 张永芳, 等. 并联机器人的非线性PID控制[J]. 控制与决策, 2003,18(4): 490-493.(SU Yuxing, DUAN Baoyan, ZHANG Yongfang, et al. Nonlinear PID control of a parallel manipulator[J]. Control and Decision,2003,18(4): 490-493.(in Chinese))
[4]	常青, 韩宝玲, 乔志霞, 等. 四足机器人斜坡运动的自适应控制算法[J]. 北京理工大学学报, 2019,39(9): 900-906.(CHANG Qing, HAN Baoling, QIAO Zhixia, et al. An adaptive control algorithm for quadruped robot trotting on a slope[J]. Transaction of Beijing Institute of Technology,2019,39(9): 900-906.(in Chinese))
[5]	郭伟斌, 陈勇. 基于模糊控制的除草机器人自主导航[J]. 机器人, 2010,32(2): 204-209.(GUO Weibin, CHEN Yong. Fuzzy control based autonomous navigation for a weeding robot[J]. Robot,2010,32(2): 204-209.(in Chinese))
[6]	孔令文, 李鹏永, 杜巧玲. 基于模糊神经网络的六足机器人自主导航闭环控制系统设计[J]. 机器人, 2018,40(1): 16-23.(KONG Lingwen, LI Pengyong, DU Qiaoling. The closed-loop control system design of hexapod robot autonomous navigation based on fuzzy neural network[J]. Robot,2018,40(1): 16-23.(in Chinese))
[7]	YU R R, ZHAO H, ZHEN S C, et al. A novel approach for 2-degrees of freedom redundant parallel manipulator dynamics[J]. Advances in Mechanical Engineering,2017,9(6): 371-386.
[8]	彭慧莲, 郭易圆, 王琪. 用第一类Lagrange方程求解平面多体系统约束力的方法[J]. 工程力学, 2008,〖STHZ〗 25(12): 65-71.(PENG Huilian, GUO Yiyuan, WANG Qi. A method for solving constrained force of planar multibody system via the first kind of Lagrange’s equations[J]. Engineering Mechanics,2008,25(12): 65-71.(in Chinese))
[9]	冯志友, 张燕, 杨廷力, 等. 基于牛顿欧拉法的2UPS-2RPS并联机构逆动力学分析[J]. 农业机械学报, 2009,40(4): 193-197.(FENG Zhiyou, ZHANG Yan, YANG Tingli, et al. Inverse dynamics of a 2UPS-2RPS parallel mechanism by Newton-Euler formulation[J]. Transactions of the Chinese Society for Agricultural Machinery,2009,40(4): 193-197.(in Chinese))
[10]	UDWADIA F E, KALABA R E. Analytical Dynamics: a New Approach [M]. New York: Cambridge University Press, 1996.
[11]	张新荣, CHEN Yehwa, 平昭琪. 基于Udwadia和Kalaba方程的机械臂轨迹跟踪控制[J]. 长安大学学报(自然科学版), 2014,34(1): 115-119.(ZHANG Xinrong, CHEN Yehwa, PING Zhaoqi. Mechanical manipulator tracking control based on Udwadia and Kalaba equation[J]. Journal of Chang’an University(Natural Science Edition),2014,34(1): 115-119.(in Chinese))
[12]	ROSENBERG R. Analytical Dynamics of Discrete Systems [M]. New York: Plenum Press, 1977.
[13]	CORLESS M J, LEITMANN G. Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems[J]. IEEE Transactions on Automatic Control,1981,26(5): 1139-1144.
[14]	CHENG H, YIU Y K, LI Z X. Dynamics and control of redundantly actuated parallel manipulators[J]. IEEE/ASME Transactions on Mechatronics,2003,8(4): 483-491.
[15]	HUI J Z, PAN M X, ZHAO R Y, et al. The closed-form motion equation of redundant actuation parallel robot with joint friction: an application of the Udwadia-Kalaba approach[J]. Nonlinear Dynamics, 2018,93: 689-703.