ZHAO Zhi-gang, WANG Yan-lin, SU Cheng, LI Jin-song, JI Gang. Analysis and Optimization on Inverse Kinematics for Multi-Robot Parallel Lifting Systems[J]. Applied Mathematics and Mechanics, 2017, 38(6): 643-651. doi: 10.21656/1000-0887.370147
 Citation: ZHAO Zhi-gang, WANG Yan-lin, SU Cheng, LI Jin-song, JI Gang. Analysis and Optimization on Inverse Kinematics for Multi-Robot Parallel Lifting Systems[J]. Applied Mathematics and Mechanics, 2017, 38(6): 643-651.

# Analysis and Optimization on Inverse Kinematics for Multi-Robot Parallel Lifting Systems

##### doi: 10.21656/1000-0887.370147
Funds:  The National Natural Science Foundation of China（51265021）
• Rev Recd Date: 2016-07-18
• Publish Date: 2017-06-15
• The inverse kinematics problem of close-coupling multi-robot parallel lifting systems was discussed. Firstly, the kinematic and dynamic models for the system were established by means of geometrical relations and wrench balance equations. Secondly, the inverse kinematics for the system, which was divided into two cases of fixed lengths and variable lengths of cables, was analyzed. Subsequently, the ways to solve the problems were given when the inverse kinematics had infinite solutions, multiple solutions or no solution at one moment, respectively. Then the optimization goal for finding the optimum solution was given in the case of multiple solutions. Finally, the numerical experiment platform for the parallel lifting system was established based on software UG/ADAMS/MATLAB, and the parameters of a real system were given for simulation. The simulation results show that, the proposed method effectively solves the multi-solution problem, and provides a foundation for further research on dynamical stability, cable tension optimization and control algorithm design for the system.
•  [1] 王砚麟, 赵志刚, 石广田. 多机器人协调吊运系统控制优化仿真[J]. 计算机仿真, 2015,32(10): 404-408.(WANG Yan-lin, ZHAO Zhi-gang, SHI Guang-tian. Analysis of kinematics and control simulation for multi-robot collaboratively towing system[J]. Computer Simulation,2015,32(10): 404-408.(in Chinese)) [2] 赵泽, 仇原鹰. 大射电望远镜AB轴机构指点运动与误差分析[J]. 机械科学与技术, 2016,35(4): 584-588.(ZHAO Ze， QIU Yuan-ying. Motion and pointing error of AB-axis mechanism for large radio telescope[J]. Mechanical Science and Technology for Aerospace Engineering,2016,35(4): 584-588.(in Chinese)) [3] Michael N, Fink J, Kumar V. Cooperative manipulation and transportation with aerial robots[J]. Autonomous Robot,2011,30(1): 73-86. [4] Barnett E, Gosselin C. Large-scale 3D printing with a cable-suspended robot[J]. Additive Manufacturing,2015,7: 27-44. [5] Maza I, Kondak K, Bernard M, et al. Multi-UAV cooperation and control for load transportation and deployment[J]. Journal of Intelligent and Robotic Systems,2010,57(1): 417-449. [6] Bosscher P, Ebert I. A stability measure for underconstrained cable-driven robots[C]//Proceedings of 2004 IEEE International Conference on Robotics & Automation.New Orleans, LA, 2004. [7] ZHENG Ya-qing, LIN Qi, WU Jian-po, et al. Analysis of inverse kinematics and dynamics of a novel 6-degree-of-freedom wire-driven parallel gantry crane robot[C]// IEEE/ASME International Conference on Advanced Intelligent Mechatronics.Singapore: Suntec Convention and Exhibition Center, 2009: 1786-1792. [8] YU Lan, ZHENG Ya-qing. Configuration design and analysis of generalized inverse pose kinematic problem of 6-DOF wire-driven gantry crane robots[C]// International Conference on Automatic Control and Artificial Intelligence.Xiamen, 2012: 676-680. [9] ZI Bin, QIAN Sen, DING Hua-feng, et al. Design and analysis of cooperative cable parallel manipulators for multiple mobile cranes[J]. International Journal of Advanced Robotic Systems,2012,9(5): 207. doi: 10.5772/53670. [10] QIAN Sen, ZI Bin, ZHANG Dan, et al. Kinematics and error analysis of cooperative cable parallel manipulators for multiple mobile cranes[J]. International Journal of Mechanics and Materials in Design,2014,10(4): 395-409. [11] 赵志刚, 腾富军, 石广田, 等. 多机器人联合吊运系统可行域分析与求解[J]. 上海交通大学学报, 2015,49(8): 1174-1180.(ZHAO Zhi-gang, TENG Fu-jun, SHI Guang-tian, et al. Analysis and calculation of feasible region of multi-robot combined lifting system[J]. Joural of Shanghai Jiaotong University,2015,49(8): 1174-1180.(in Chinese)) [12] 赵志刚, 腾富军, 石广田, 等. 紧耦合多机器人联合吊运系统逆运动学求解[J]. 哈尔滨工程大学学报, 2016,37(2): 254-260.(ZHAO Zhi-gang, TENG Fu-jun, SHI Guang-tian, et al. The inverse kinematics analysis of multi-robot combined lifting system[J]. Journal of Harbin Engineering University,2016,37(2): 254-260.(in Chinese)) [13] LI Wei, ZHAO Zhi-gang, SHI Guang-tian, et al. Inverse dynamics analysis and simulation of a class of under-constrained cable-driven parallel system[J]. UPB Scientific Bulletin, Series D: Mechanical Engineering,2016,78(1): 87-98.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

/