Trajectory Optimization of Robotic Arm Based on Improved Simulated Annealing Genetic Algorithm

doi:10.16182/j.issn1004731x.joss.23-1148

Abstract

Abstract:

To optimize the working trajectory of the robotic arm, a modified simulated annealing genetic algorithm is proposed. Comprehensively considering the operating requirements and performance characteristics of the robotic arm, the five-order polynomial interpolation method is used to plan a smooth motion trajectory in the joint space. The penalty function method is used to handle the individuals that do not meet the constraint conditions,and the fitness function is recalibrated by the dynamic linear calibration method.An adaptive adjustment mechanism for crossover probability and variation probability is set to modify the genetic algorithm. The cooling idea of the simulated annealing algorithm is introduced, which effectively avoids the algorithm falling into locally optimal. The results show that the optimized trajectory of the improved simulated annealing genetic algorithm effectively shortens the movement time of the robotic arm compared with the traditional genetic algorithm, and then improves the working efficiency of the robotic arm.

Key words: robotic arm, five-degree polynomial interpolation, simulated annealing genetic algorithms, trajectory optimization, penalty function method

CLC Number:

TP242

Xu Qiang, Xu Jianlei, Hu Yanhai, Chen Haihui, Zhang Xing, Xing Zhaohui. Trajectory Optimization of Robotic Arm Based on Improved Simulated Annealing Genetic Algorithm[J]. Journal of System Simulation, 2025, 37(2): 404-412.

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References 23

1	李雨濛. 基于动力学的工业机器人时间能量最优轨迹规划研究[D]. 杭州: 浙江理工大学, 2022.
	Li Yumeng. Research on Time-energy Optimal Trajectory Planning for Industrial Robots Based on Dynamics[D]. Hangzhou: Zhejiang Sci-Tech University, 2022.
2	王汝贵, 董奕辰, 陈辉庆. 一种变胞式工业机器人时间最优轨迹规划[J]. 机械工程学报, 2023, 59(5): 100-111.
	Wang Rugui, Dong Yichen, Chen Huiqing. A Time Optimal Trajectory Planning of the Metamorphic Industrial Robot[J]. Journal of Mechanical Engineering, 2023, 59(5): 100-111.
3	Lin C, Chang P, Luh J. Formulation and Optimization of Cubic Polynomial Joint Trajectories for Industrial Robots[J]. IEEE Transactions on Automatic Control, 1983, 28(12): 1066-1074.
4	韦素云, 徐敏. 双臂机器人神经网络解耦与路径规划算法研究[J]. 机械设计与制造, 2017(8): 245-248.
	Wei Suyun, Xu Min. Research of Dual-arm Robot Neural Network Decoupling and Trajectory Planning Algorithm[J]. Machinery Design & Manufacture, 2017(8): 245-248.
5	陶超. 基于高斯伪谱法的高超声速飞行器轨迹优化与跟踪控制[J]. 系统仿真学报, 2017, 29(4): 865-872, 879.
	Tao Chao. Trajectory Optimization and Tracking Controller Based on Gauss Pseudo Spectral Method for Hypersonic Vehicle[J]. Journal of System Simulation, 2017, 29(4): 865-872, 879.
6	曹梦龙, 赵文彬, 陈志强. 融合粒子群算法与改进灰狼算法的机器人路径规划[J]. 系统仿真学报, 2023, 35(8): 1768-1775.
	Cao Menglong, Zhao Wenbin, Chen Zhiqiang. Robot Path Planning by Fusing Particle Swarm Algorithm and Improved Grey Wolf Algorithm[J]. Journal of System Simulation, 2023, 35(8): 1768-1775.
7	刘勇, 王腾, 杜喆. 柔性机械臂振动与能量最小的多目标轨迹优化[J]. 机械设计与制造, 2022(8): 297-300, 304.
	Liu Yong, Wang Teng, Du Zhe. Vibration Suppression and Energy Minimization Trajectory Planning of Flexible Manipulator with Multi-objective Optimization[J]. Machinery Design & Manufacture, 2022(8): 297-300, 304.
8	段现银, 张灿, 朱泽润, 等. 逆解多目标优化的六自由度机械手轨迹规划[J]. 系统仿真学报, 2021, 33(9): 2128-2137.
	Duan Xianyin, Zhang Can, Zhu Zerun, et al. Trajectory Planning of 6-DOF Manipulator Based on Inverse Multi-objective Optimization[J]. Journal of System Simulation, 2021, 33(9): 2128-2137.
9	邓伟, 张其万, 刘平, 等. 基于双种群遗传混沌优化算法的最优时间轨迹规划[J]. 计算机集成制造系统, 2018, 24(1): 101-106.
	Deng Wei, Zhang Qiwan, Liu Ping, et al. Optimal Time Trajectory Planning Based on Dual Population Genetic and Chaotic Optimization Algorithm[J]. Computer Integrated Manufacturing Systems, 2018, 24(1): 101-106.
10	杨化林, 钟岩, 姜沅政, 等. 基于时间与急动度最优的并联式采茶机器人轨迹规划混合策略[J]. 机械工程学报, 2022, 58(9): 62-70.
	Yang Hualin, Zhong Yan, Jiang Yuanzheng, et al. Hybrid Strategy of Parallel Tea Picking Robot Trajectory Planning Based on Optimal Time and Jerk[J]. Journal of Mechanical Engineering, 2022, 58(9): 62-70.
11	Lu Yusheng, Lin Yiyi. Smooth Motion Control of Rigid Robotic Manipulators with Constraints on High-order Kinematic Variables[J]. Mechatronics, 2018, 49: 11-25.
12	陈高远, 宋云雪. 改进遗传算法在移动机器人路径规划中的应用研究[J]. 计算机应用与软件, 2023, 40(2): 302-307.
	Chen Gaoyuan, Song Yunxue. Application of Improved Genetic Algorithm in Mobile Robot Path Planning[J]. Computer Applications and Software, 2023, 40(2): 302-307.
13	李林升. 基于惩罚函数法的时间最优机械臂轨迹规划[J]. 机械设计与研究, 2019, 35(5): 56-58, 69.
	Li Linsheng. Time Optimal Trajectory Planning of Manipulator Based on the Penalty Function[J]. Machine Design & Research, 2019, 35(5): 56-58, 69.
14	郑堃, 练志伟, 顾新艳, 等. 采用改进两点交叉算子的改进自适应遗传算法求解不相关并行机混合流水车间调度问题[J]. 中国机械工程, 2023, 34(14): 1647-1658, 1671.
	Zheng Kun, Lian Zhiwei, Gu Xinyan, et al. Hybrid Flow Shop Scheduling Problems with Unrelated Parallel Machine Solved by Improved Adaptive Genetic Algorithm (IAGA) with ITPX[J]. China Mechanical Engineering, 2023, 34(14): 1647-1658, 1671.
15	黄飞. 六自由度刚性机械臂轨迹跟踪控制方法研究[D]. 北京: 北京邮电大学, 2020.
	Huang Fei. The Research on Trajectory Tracking Control Technology for the Six-DOF Rigid Robot[D]. Beijing: Beijing University of Posts and Telecommunications, 2020.
16	胡杰. 基于改进遗传算法的工业机器人去毛刺轨迹规划研究[D]. 佛山: 佛山科学技术学院, 2021.
	Hu Jie. Research on Deburring Trajectory Planning of Industrial Robot Based on Improved Genetic Algorithm[D]. Foshan: Foshan University of Science and Technology, 2021.
17	曾关平, 王直杰. 基于改进遗传算法的机械臂时间最优轨迹规划[J]. 科技创新与应用, 2020(22): 6-9.
	Zeng Guanping, Wang Zhijie. Time-optimal Trajectory Planning of Manipulator Based on Improved Genetic Algorithm[J]. Technology Innovation and Application, 2020(22): 6-9.
18	李国洪, 王远亮. 基于B样条和改进遗传算法的机器人时间最优轨迹规划[J]. 计算机应用与软件, 2020, 37(11): 215-223, 279.
	Li Guohong, Wang Yuanliang. Time-optimal Trajectory Planning of Robots Based on B-spline and Improved Genetic Algorithm[J]. Computer Applications and Software, 2020, 37(11): 215-223, 279.
19	赵睿琦. 基于改进多目标遗传算法的变截面涡旋盘优化设计[J]. 机电信息, 2023(6): 31-35, 39.
20	孟庆宽, 张漫, 仇瑞承, 等. 基于改进遗传算法的农机具视觉导航线检测[J]. 农业机械学报, 2014, 45(10): 39-46.
	Meng Qingkuan, Zhang Man, Qiu Ruicheng, et al. Navigation Line Detection for Farm Machinery Based on Improved Genetic Algorithm[J]. Transactions of the Chinese Society for Agricultural Machinery, 2014, 45(10): 39-46.
21	李朝迁, 裴建朝. 新型模拟退火遗传算法在路径优化的应用[J]. 组合机床与自动化加工技术, 2022(3): 52-55.
	Li Chaoqian, Pei Jianchao. Application of New Simulated Annealing Genetic Algorithm in Path Optimization[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2022(3): 52-55.
22	刘栋财, 董广宇, 杜玉红, 等. 基于网格搜索算法的6-RUS并联机器人时间最优轨迹规划[J]. 中国机械工程, 2023, 34(13): 1589-1598.
	Liu Dongcai, Dong Guangyu, Du Yuhong, et al. Time-optimal Trajectory Planning of 6-RUS Parallel Robots Based on Grid Search Algorithm[J]. China Mechanical Engineering, 2023, 34(13): 1589-1598.
23	王超, 宋公飞, 徐宝珍. 基于IAGA的工业机器人时间最优轨迹规划[J]. 计算机仿真, 2021, 38(8): 368-371.
	Wang Chao, Song Gongfei, Xu Baozhen. Time Optimal Trajectory Planning for Industrial Robots Based on IAGA[J]. Computer Simulation, 2021, 38(8): 368-371.

特性参数	尺寸/mm
机器人高度	1 328
机器人重量	1 582
重复定位精度	0.07
重复循环精度	0.20

关节i	α/(°)	a/mm	d/mm	θ/(°)
1	-90	150	445	θ₁
2	0	-700	0	θ₂
3	90	-115	0	θ₃
4	-90	0	795	θ₄
5	90	0	0	θ₅
6	0	0	85	θ₆

位置	关节1	关节2	关节3
起始点	0	0	0
固定点1	0.17	0.07	0.17
固定点2	0.35	0.10	0.44
固定点3	1.05	0.14	0.70
终止点	1.22	0.17	1.05

关节	角度/(°)	角速度/((°)/s)	角加速度/((°)/s²)
1	-180~180	75	130
2	-95~155	65	135
3	-180~95	80	155
4	-175~175	70	110
5	-120~120	55	105
6	-360~360	30	100

算法	关键点1	关键点2	关键点3	终止点	总计
初始值	2.5	2.5	2.5	2.5	10.0
传统遗传算法	2.30	1.73	1.97	2.36	8.36
改进自适应遗传算法	1.81	1.66	1.79	1.80	7.06
改进模拟退火遗传算法	1.62	1.54	1.63	1.74	6.53