A Method for Multi-objective Optimization of Redundant Manipulator' s Trajectory
-
摘要: 针对冗余机械臂在轨迹规划过程中构型不唯一的特点，对冗余机械臂轨迹的多目标优化方法进行了研究，建立了以减小机械臂动作幅度、能量消耗和关节运动冲击为指标的多目标优化模型。通过改进的双模式混合差分进化算法（DHDE），对机械臂运动轨迹进行优化以获得逆运动学解的数值解。DHDE算法将DE/current-to-best/1/bin策略中的F因子改进为互补因子K，并利用天牛须算法原理进行优化，同时结合DE/rand/1/bin策略，改进后算法具有求解精度高、收敛速度快和鲁棒性强等特点。仿真表明所提方法能有效优化关节轨迹，理论定位精度可达到10−5 mm。最后实验验证了该方法的合理性和正确性。Abstract: To understand the characteristics of the configurationnon-uniqueness in the course of trajectory planning, this paper systemically studied the multi-objective trajectory optimization of a redundant manipulator and established a multi-objectiveoptimization model so as to reduce its motion amplitude, energy consumption and joint motion impact. With the double-mode hybrid differential evolution algorithm (DHDE), the trajectory of the manipulator is optimized, and the numerical solution of inverse kinematics is obtained. The DHDE algorithm uses the principles of the beetle antennae search algorithm to optimize the factor K in the DE/current-to-best/1/bin mode, and the DE/rand/1/bin modeis used as the secondary mode. It has the characteristics of high accuracy, less evolutionary algebra and strong robustness. Simulation and experimental results verify the correctness and practicability of the proposed method.
-
表 1 冗余机械臂DH参数表
θ d a α 0-1 θ1 0 0 90° 1-2 θ2 0 0 90° 2-3 θ3 d1 0 90° 3-4 θ4 0 0 90° 4-5 θ5 d2 0 90° 5-6 θ6 0 0 90° 6-H θ7 0 0 0° 
下载: 导出CSV
表 2 算法测试函数集
函数 表达式 最优点 Rastrigr ${f_1}({x_i}) = \displaystyle\sum\limits_{i = 1}^D {\left[x_i^2 - 10\cos (2{\text{π}} {x_i}) + 10\right]}$ x=[0,0,…,0] Griewank ${f_2}({x_i}) = \displaystyle\sum\limits_{i = 1}^D {\dfrac{ {x_i^2} }{ {4\;000} } - \prod\limits_{i = 1}^D {\cos \left(\dfrac{ { {x_i} } }{ {\sqrt i } }\right)} + 1}$ x=[0,0,…,0] Rosenbrock ${f_3}({x_i}) = \displaystyle\sum\limits_{i = 1}^{D - 1} {\left[100{ {(x_i^2 - {x_{i + 1} })}^2} + { {({x_i} - 1)}^2}\right]}$ x=[0,0,…,0] Sphere ${f_4}({x_i}) = \displaystyle\sum\limits_{i = 1}^D {x_i^2}$ x=[0,0,…,0]
下载: 导出CSV
表 3 冗余机械臂PTP任务的定位误差
mm 起点 目标点 最大值 最小值 平均值 方差 (86.7,−81.2,−2.31) (39.9,−89.3,−67.4) 2.58E-05 1.83E-14 2.54E-06 5.95E-06 (89.6,17.4,76.0) (48.3,−17.3, 84.1) 4.79E-05 4.44E-16 3.71E-06 1.01E-05 (−18.5,34.0,90.5) (−30.2,55.5,87.6) 1.68E-05 1.25E-15 9.87E-07 3.54E-06 (41.4,−24.6,96.7) (56.6,1.53,98.2) 8.63E-06 0 8.46E-07 2.17E-06 (50.4,61.4,80.8) (41.3,75.2,74.1) 3.48E-05 1.98E-15 2.40E-06 6.89E-06 (107.8,35.0,−18.6) (117.8,13.2,7.90) 5.59E-05 8.88E-16 3.45E-06 1.22E-05 (2.91, −118.5,7.91) (−24.5,−85.8,10.5) 5.13E-05 0 4.44E-06 1.11E-05 (94.1,−78.4,22.1) (63.5,−105.9,69.4) 3.82E-05 0 2.21E-06 7.05E-06
下载: 导出CSV
-
[1] Assal S F M, Watanabe K, Izumi K. Neural network-based kinematic inversion of industrial redundant robots using cooperative fuzzy hint for the joint limits avoidance[J]. IEEE/ASME Transactions on Mechatronics, 2006, 11(5): 593-603 [2] Daachi B, Madani T, Benallegue A. Adaptive neural controller for redundant robot manipulators and collision avoidance with mobile obstacles[J]. Neurocomputing, 2012, 79: 50-60 [3] 曹海蕊, 顾晓勤, 梁瑞仕. 冗余机械臂的加权广义逆避障算法研究[J]. 机械科学与技术, 2018, 37(9): 1313-1318Cao H R, Gu X Q, Liang R S. A weighted generalized inverse obstacle avoidance algorithm for redundant manipulator[J]. Mechanical Science and Technology for Aerospace Engineering, 2018, 37(9): 1313-1318 (in Chinese) [4] 高涵, 张明路, 张小俊, 等. 冗余机器人的任务优先级轨迹规划方法[J]. 机械科学与技术, 2018, 37(1): 24-29Gao Han, Zhang Minglu, Zhang Xiaojun, et al. An approach for task priority trajectory planning of redundant robots[J]. Mechanical Science and Technology for Aerospace Engineering, 2018, 37(1): 24-29 (in Chinese) [5] Wu J, Wu H P, Song Y T, et al. Genetic algorithm trajectory plan optimization for EAMA: EAST Articulated Maintenance Arm[J]. Fusion Engineering and Design, 2016, 109-111: 700-706 [6] 黄沛天, 黄文, 胡利云. 关于变加速动力学及其应用[J]. 力学与实践, 2004, 26(1): 67-68 doi: 10.3969/j.issn.1000-0879.2004.01.021Huang P T, Huang W, Hu L Y. On jerk dynamics and its applications[J]. Mechanics in Engineering, 2004, 26(1): 67-68 (in Chinese) doi: 10.3969/j.issn.1000-0879.2004.01.021 [7] 李岩汀, 徐绩青, 许锡宾, 等. 结构动力响应中急动度的计算[J]. 应用数学和力学, 2017, 38(8): 922-931Li Y T, Xu J Q, Xu X B, et al. A numerical method for calculation of structural jerk responses[J]. Applied Mathematics and Mechanics, 2017, 38(8): 922-931 (in Chinese) [8] Cao H X, Sun S Q, Zhang K J, et al. Visualized trajectory planning of flexible redundant robotic arm using a novel hybrid algorithm[J]. Optik, 2016, 127(20): 9974-9983 [9] Guigue A, Ahmadi M, Langlois R, et al. Pareto Optimality and multiobjective trajectory planning for a 7-DOF redundant manipulator[J]. IEEE Transactions on Robotics, 2010, 26(6): 1094-1099 [10] Menasri R, Nakib A, Daachi B, et al. A trajectory planning of redundant manipulators based on bilevel optimization[J]. Applied Mathematics and Computation, 2015, 250: 934-947 [11] 王安琪, 魏延辉, 韩寒, 等. 基于构形平面的冗余机械臂轨迹规划方法[J]. 北京航空航天大学学报, 2018, 44(9): 1991-1997Wang A Q, Wei Y H, Han H, et al. Trajectory planning method for redundant manipulator based on configuration plane[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(9): 1991-1997 (in Chinese) [12] 王俊龙, 张国良, 羊帆, 等. 改进人工势场法的机械臂避障路径规划[J]. 计算机工程与应用, 2013, 49(21): 266-270 doi: 10.3778/j.issn.1002-8331.1201-0360Wang J L, Zhang G L, Yang F, et al. Improved artificial field method on obstacle avoidance path planning for manipulator[J]. Computer Engineering and Applications, 2013, 49(21): 266-270 (in Chinese) doi: 10.3778/j.issn.1002-8331.1201-0360 [13] Wu G H, Shen X, Li H F, et al. Ensemble of differential evolution variants[J]. Information Sciences, 2018, 423: 172-186 [14] Opara K R, Arabas J. Differential evolution: a survey of theoretical analyses[J]. Swarm and Evolutionary Computation, 2019, 44: 546-558 [15] 邵良杉, 韩瑞达. 基于天牛须搜索的花朵授粉算法[J]. 计算机工程与应用, 2018, 54(18): 188-194 doi: 10.3778/j.issn.1002-8331.1805-0152Shao L S, Han R D. Beetle antenna search flower pollination algorithm[J]. Computer Engineering and Applications, 2018, 54(18): 188-194 (in Chinese) doi: 10.3778/j.issn.1002-8331.1805-0152 [16] Wu Q, Shen X D, Jin Y Z, et al. Intelligent beetle antennae search for UAV sensing and avoidance of obstacles[J]. Sensors, 2019, 19(8): 1758 -
点击查看大图
图(9) / 表(3)
计量
- 文章访问数: 471
- HTML全文浏览量: 51
- PDF下载量: 50
- 被引次数: 0
