1.Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China；
2. Zhejiang Provincial Key Lab of Part Rolling Technology, Ningbo, 315211, China)
3. Institute of Manufacture Engineering, Zhejiang University, Hangzhou310027, China
Abstract：In this paper, an optimal trajectory planning method of a flexible manipulator for vibration suppression is proposed, which is combined of genetic algorithm and polynomial functions interpolation. The dynamic equations of the manipulator are derived using the extended Hamilton’s principle and the assumed modes method. Then, the trajectory planning mechanism for vibration suppression is elaborated. For trajectory planning, the quintic polynomials are employed as basic functions to interpolate the discrete trajectory, and the floating values of the discrete joint angles are considered as optimal parameters to be determined. After applying the constraint conditions of the initial and final conditions, the optimal trajectory with minimum vibration energy is conducted using the genetic algorithm. Numerical calculations and experiments are performed to verify the applicability and effectiveness of the proposed trajectory planning method. Compared with the results tracking the quintic polynomials function, experimental results show that the amplitude of the residual link vibration tracking the optimal trajectory reduces about 10 times, and the damping time of the link reduced to 4.5s from 12s. Consequently, the position precision and operating efficiency of the system are improved.
[1] 娄军强, 魏燕定, 杨依领, 等. 空间柔性机械臂弯扭耦合振动的主动控制研究[J]. 振动工程学报. 2014(03): 400-407.
Lou Junqiang, Wei Yanding, Yang Yiling, et al. Active control of bending torsion coupled vibration of a space flexible manipulator[J]. Journal of Vibration Engineering, 2014(03):400-407. (In Chinese)
[2] Choi S, Seong M, Ha S H. Accurate position control of a flexible arm using a piezoactuator associated with a hysteresis compensator[J]. Smart Materials and Structures. 2013, 22 (0450094).
[3] Abe A. Trajectory planning for flexible Cartesian robot manipulator by using artificial neural network: numerical simulation and experimental verification[J]. Robotica. 2011, 29(5): 797-804.
[4] Qiu Zhicheng, Wang Bin, Zhang Xianmin, et al. Direct adaptive fuzzy control of a translating piezoelectric flexible manipulator driven by a pneumatic rodless cylinder[J]. Mechanical Systems and Signal Processing. 2013, 36(2): 290-316.
[5] Park K, Park Y. Fourier-based optimal-design of a flexible manipulator path to reduce residual vibration of the end-point[J]. Robotica. 1993, 11(3): 263-272.
[6] Abe A. Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation[J]. Mechanism and Machine Theory. 2009, 44(9): 1627-1639.
[7] Korayem M H, Nikoobin A, Azimirad V. Trajectory optimization of flexible link manipulators in point to point motion[J]. Robotica. 2009, 27: 825-840.
[8] 吴立成, 孙富春, 孙增圻, 等. 柔性空间机器人振动抑制轨迹规划算法[J]. 机器人. 2003(03): 250-254.
Wu Licheng, Sun Fuchun, Sun Zengqi, et al. Optimal trajectory planning of flexible space robot for vibration reducing[J]. Robot. 2003(03): 250-254. (In Chinese)
[9] 邵君奕，张传清，刘召，等. 考虑振动抑制的多冗余度特种操作机器人轨迹优化方法[J]. 机械工程学报. 2012(01): 13-18.
Shao Junyi, Zhang Chuanqing, Liu Zhao, et al. Trajectory optimization method of special operation redundant robot for vibration suppression[J]. Journal of Mechanical Engineering. 2012(01): 13-18. (In Chinese)
[10] 徐文福，徐超，孟得山. 基于粒子群优化的刚柔混合机械臂振动抑制规划[J]. 控制与决策. 2014(04): 632-638.
Xu Wenfu, Xu Chao, Meng Deshan. Trajectory planning of vibration suppression for rigid flexible hybrid manipulator based on PSO algorithm[J]. Control and Decision. 2014(04): 632-638. (In Chinese)
[11] Chu Ming, Chen Gang, Jia Qingxuan, et al. Simultaneous positioning and non-minimum phase vibration suppression of slewing flexible-link manipulator using only joint actuator[J]. Journal of Vibration and Control. 2014, 20(10): 1488-1497.
[12] Springer K, Gattringer H, Staufer P. On time-optimal trajectory planning for a flexible link robot[J]. Journal of Systems and Control Engineering. 2013, 227(10): 752-763.
[13] 巩敦卫. 交互式遗传算法原理及其应用[M]. 北京: 国防工业出版社, 2007.
