LQR control of parallel robot based on genetic algorithms
WANG Linjun1,2，SHI Baozhou1,2，ZHANG Dong2，DING Shihao1,2，LIU Jianming1,2
1. Department of Electrical and Mechanical Engineering, Lanzhou University of Technology, Lanzhou 730050, China;
2. Western China Energy and Environment Research Center, Lanzhou University of Technology, Lanzhou 730050, China
Parallel mechanism is difficult to be controlled, because of its strong nonlinearity and complex control process, and its accuracy can not meet the working requirements. This work took a three-degree-of-freedom rigid-flexible coupled parallel robot as the research object, established a simplified space structure model of a robot and the tree model of a multi-body system, used the transfer matrix method of the multi-body system to study the Kinetics and the state space of the robot, and used the Hankel model reduction for the state space. The LQR control and the genetic algorithm (GA)-optimized LQR control were designed, and the working conditions of the robot were simulated and compared. The results show that the LQR control robot based on genetic algorithms (GA) only needs 1 second to enter the steady state. In a steady state, after optimization compared with that before optimization, the maximum displacement of the robot moving platform x, y and z decreased by 24.34%, 13.51% and 1.03% respectively; and the maximum acceleration on the three legs decreased by 26.92%, 33.96% and 35.71% respectively; the maximum control force of each leg decreased by 8.96%, 7.37% and 9.01% respectively. It can be seen that under the optimal control method, the robot has the advantages of fast response, high precision and good stability. Thus the rationality and superiority of the method are fully proved, which provides a theoretical basis for further study of Kinetics performance and control methods of Parallel robots.
王林军1,2，史宝周1,2，张东2，丁仕豪1,2，刘建明1,2. 基于GA优化的LQR控制对并联机器人的控制研究[J]. 振动与冲击, 2020, 39(20): 82-90.
WANG Linjun1,2，SHI Baozhou1,2，ZHANG Dong2，DING Shihao1,2，LIU Jianming1,2. LQR control of parallel robot based on genetic algorithms. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(20): 82-90.
[1] Nguyen D Q , Gouttefarde M , Company O , et al. On the Simplifications of Cable Model in Static Analysis of Large-Dimension Cable-Driven Parallel Robots[C]// IEEE/RSJ International Conference on Intelligent Robots & Systems. IEEE, 2013: 928-934．
[2] Olarra A, Axinte D, Uriarte L, et al. Machining with the WalkingHex: A walking parallel kinematic machine tool for in situ operations[J]. CIRP Annals, 2017, 66(1)：361-364.
[3] 刘凉,赵新华,周海波,等.空间刚柔耦合并联机器人动力学求解策略[J].农业机械学报,2018,49(02): 376-384.
Liu Liang, Zhao Xinhua, Zhou Haibo, Wang Jiabin. Dynamics Solution Strategy of Space Rigid-Flexible Coupled Parallel Robot [J]. Journal of Agricultural Machinery, 2018, 49 (02): 376-384.
[4] Yang Jianfeng, Xu Zhenbang, Wu Qingwen, et al. Dynamic modeling and control of a 6-DOF micro-vibration simulator[J]. Mechanism & Machine Theory, 2016, 104: 350-369.
[5] Babaghasabha R , Khosravi M A , Taghirad H D . Adaptive robust control of fully-constrained cable driven parallel robots[J]. Mechatronics, 2015, 25:27-36.
[6] 刘晓飞,姚建涛,赵永生.基于模型的冗余驱动并联机构神经网络同步协调控制[J].农业机械学报,2018,49(02):367-375.
Li Xiaofei, Yao Jiantao, Zhao Yongsheng. Model-based Synchronous Control of Redundantly Actuated Parallel Manipulator with Neural Network[J]. Transactions of the Chinese Society for Agricultural Machinery, 2018, 49(02): 367-375.
[7] 陶晗,曲智勇,丛大成.液压并联机器人力/位混合控制策略研究[J].农业机械学报,2018,49(09): 361-366+405.
Tao Han, Qu Zhiyong, Cong Dacheng. Research on Hydraulic Parallel Robot Force/Position Hybrid Control Strategy [J]. Journal of Agricultural Machinery, 2018,49 (09): 361-366+405.
[8] Gu Junjie, Rui Xiaoting, Zhang Jianshu. Riccati Transfer Matrix Method for Linear Tree Multibody Systems[J]. Journal of Applied Mechanics, 2017, 84(1): 1-7.
[9] Rui Xiaoting, Wang Guoping, Lu Yuqi, et al. Transfer matrix method for linear multibody system[J]. Multibody System Dynamics, 2008, 19(3):179-207.
[10] Ferhatoglu Erhan Cigeroglu Ender , Özgüven H. Nevzat. A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes[J]. Mechanical Systems and Signal Processing, 2018, 107:317-342.
[11] Zhang Shuai, Hao Yingshuai, Wang Meng, et al. Multichannel Hankel Matrix Completion Through Nonconvex Optimization[J]. IEEE Journal of Selected Topics in Signal Processing, 2018, 12(4):617-632.
[12] Khosravi M A, Taghirad H D. Dynamic Modeling and Control of Parallel Robots With Elastic Cables: Singular Perturbation Approach[J]. IEEE Transactions on Robotics, 2017, 30(3):694-704.
[13] Bordalba R , Porta J M , Ros L. A Singularity-Robust LQR Controller for Parallel Robots[C]// 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2018：5048-5054.
[14] Wu Lingyu, Wang Xiaodong, Wu Jiande. Research on LQR optimal control of robot based on ant colony algorithm[J]. Transducer & Microsystem Technologies, 2018,37(01):56-59.
[15] 刘乃军, 牛军川. 2-PRC-PR(C)并联机构减振平台及其动力学特性[J]. 中南大学学报(自然科学版)，2017, 48(4):
925-935.
Liu Naijun, Niu Junchuan. 2-PRC-PR(C) Parallel Mechanism Damping Platform and Its Dynamic Characteristics [J]. Journal of Central South University (Natural Science Edition), 2017, 48 (4): 925-935.
[16] 张进秋,彭虎,张建，等. 车辆悬挂LQR主动控制权矩阵权重参数优化[J].振动与冲击, 2018, 37(22): 214-219.
Zhang Jinqiu, Peng Hu, Zhang Jian, et al. Weight parameter optimization of LQR active control matrix for vehicle suspension [J]. Vibration and impact, 2018, 37(22): 214-219.
[17] 佚名. 基于多目标遗传算法的双机器人协调焊接路径规划[J]. 中国机械工程, 2018, 29(16):1984-1989.
Yi Ming. Coordination of welding path planning for two robots based on multi-objective genetic algorithm [J]. China Mechanical Engineering, 2018, 29 (16): 1984-1989.
[18] Afzalirad M , Shafipour M . Design of an efficient genetic algorithm for resource-constrained unrelated parallel machine scheduling problem with machine eligibility restrictions[J]. Journal of Intelligent Manufacturing, 2018，29（2）: 423-437.
