一种机械臂最优时间-冲击轨迹优化算法

陆佳皓; 平雪良

doi:10.13433/j.cnki.1003-8728.20190012

一种机械臂最优时间-冲击轨迹优化算法

doi: 10.13433/j.cnki.1003-8728.20190012

陆佳皓,
平雪良^,

江南大学机械工程学院江苏省食品先进制造装备技术重点实验室, 江苏无锡 214122

基金项目:

国家自然科学基金项目 61305016

详细信息

作者简介:
陆佳皓(1992-), 硕士研究生, 研究方向为机器人智能控制, jiahaolu@outlook.com

通讯作者:
平雪良, 教授, 硕士生导师, ping@jiangnan.edu.cn

中图分类号: TP242
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- 文章访问数: 566
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- 被引次数: 0
出版历程
- 收稿日期: 2018-10-24
- 刊出日期: 2019-10-05

Time-jerk-optimal Trajectory Planning Algorithm for Manipulators

Lu Jiahao,
Ping Xueliang^,

School of Mechanical Engineering, Jiangnan University, Jiangsu Province Key Laboratory of Advanced Food Manufacturing Equipment and Technology, Jiangsu Wuxi 214122, China

摘要

摘要: 针对工业机械臂执行效率以及运动过程中的冲击产生振动、机械磨损的问题，提出了一种机械臂的最优时间-冲击轨迹规划方法，优化机械臂关节运动时间和加加速度（冲击）两个耦合且矛盾的运动性能指标。通过逆运动学可以将机械臂执行的运动轨迹转换为在关节空间中的位置-时间序列，采用5次非均匀B样条函数在关节空间内构造插值曲线，用各阶B样条曲线控制顶点的约束代替机械臂的运动约束，利用NSGA-Ⅱ（Non-dominated sorting genetic algorithm Ⅱ，NSGA-Ⅱ）对目标函数进行优化。仿真结果表明，采用5次非均匀B样条函数插值，对运动时间和冲击进行优化的运动轨迹，提高了机械臂的执行效率，保证了运动过程中产生较小的冲击，使得机械臂的运动控制性能得到了提高。
- 机械臂 /
- 5次B样条曲线 /
- 轨迹规划 /
- NSGA-Ⅱ /
- 仿真实验 /
Abstract: Aiming at the efficiency of industrial manipulator and the vibration and mechanical wear caused by impact during motion, a time-jerk-optimal trajectory planning algorithm was proposed in this paper. Two mutually coupled and contradictory motion performance indicators of time and jerk were optimized. The trajectory of the task space can be transformed into the corresponding joint spatial position sequence by the inverse kinematics. Interpolation trajectory was constructed in the joint space by a five-order B-spline. The motion constraints of the manipulator were transformed into constraints on the control vertexes of five-order B-spline. The improved penalty function processed the constraints and optimized the objective function by NSGA-Ⅱ(Non-dominated Sorting Genetic Algorithm Ⅱ). Simulation results show that the five -order B-spline trajectory whose indicators of time and jerk are optimized improves the efficiency of the manipulator and guarantees the smallest possible impact during the movement. Finally, the motion control performance of the manipulator is improved.
- manipulator /
- five-order B-spline /
- trajectory planning /
- optimization /
- NSGA-Ⅱ /
- simulation

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图 1 NSGA-Ⅱ优化流程图

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图 2 ER3A-C60机械臂

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图 3 机械臂时间冲击规划Pareto最优解分布

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图 4 各关节位置曲线

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图 5 各关节速度曲线

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图 6 各关节加速度曲线

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图 7 各关节冲击曲线

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表 1 工业机械臂D-H参数表

i	a_i-1	α_i-1	d_i	θ_i(变量范围)
1	0	0	0	0(±167°)
2	50	-π/2	0	-π/2(+90°/-130°)
3	270	π	0	0(+105°/-75°)
4	70	-π/2	299	0(±180°)
5	0	π/2	0	π/2(±110°)
6	0	-π/2	0	0(±360°)

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表 2 工业机械臂各关节位置序列

节点	关节位置/(°)
节点	关节1	关节2	关节3	关节4	关节5	关节6
1	15.99	-86.99	-3.07	0	90.07	-15.99
2	16.63	-92.59	5.40	0	87.19	-16.62
3	16.36	-98.03	13.22	0	84.81	-16.36
4	14.99	-103.13	20.32	0	82.81	-14.99
5	12.37	-107.63	26.57	0	81.06	-12.37
6	8.48	-111.13	31.85	0	79.28	-8.48
7	3.58	-113.20	36.03	0	77.17	-3.58
8	-1.80	-113.44	38.99	0	74.45	1.80
9	-6.94	-111.68	40.63	0	71.05	6.94
10	-11.21	-108.09	40.95	0	67.14	11.21
11	-14.26	-103.09	40.00	0	63.07	14.26

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表 3 工业机械臂各关节运动学约束

约束项	关节1	关节2	关节3	关节4	关节5	关节6
v/(°·s^-1)	230	230	250	320	320	420
a/(°·s^-2)	65	5	95	9	105	100
j/(°·s^-3)	75	7	65	8	95	8

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