基于改进麻雀算法的喷涂机器人轨迹优化研究

doi:10.16182/j.issn1004731x.joss.25-0756

摘要/Abstract

摘要：

为应对复杂作业环境对喷涂机器人轨迹规划提出的挑战，以时间效率与运动平稳性为双重优化目标，提出一种多策略融合改进麻雀搜索算法(multi-strategy integrated sparrow search algorithm， MISSA)。采用3-5-3多项式插值法设计轨迹曲线，以保证角位移、角速度及角加速度全程连续；以轨迹总时长为性能指标，构建带关节约束的多维优化问题；利用融合折射反向学习、正余弦自适应调节及柯西变异的 MISSA 对插值节点时间参数进行寻优，实现时间最小化。仿真结果表明：MISSA 在 12 个典型测试函数上的表现优于ISSA、SSA、PSO 及 GWO 算法，展现出更强的全局搜索能力与更高的收敛精度。轨迹优化实验显示，优化后轨迹时间由12 s缩短至5.515 5 s，效率提升54.04%，且各关节运动曲线平滑，满足工程约束。激光跟踪仪实测验证机器人在1 600 mm/s速度下直线轨迹重复性RP仅为0.177 mm，满足高精度作业需求，验证了算法的工程适用性与鲁棒性。

关键词: 喷涂机器人, 时间最优轨迹, 麻雀搜索算法, 3-5-3多项式插值, 折射反向学习

Abstract:

To address the challenges posed by the complex working environment to the trajectory planning of the spray painting robot, a multi-strategy integrated sparrow search algorithm (MISSA) was proposed with the dual optimization objectives of time efficiency and motion smoothness.The 3-5-3 polynomial interpolation method was adopted to design the trajectory curve, aiming to ensure continuous angular displacement, angular velocity, and angular acceleration throughout the process. A multi-dimensional optimization problem with joint constraints was constructed using the total trajectory duration as the performance index. MISSA, which integrates refraction reverse learning, sine-cosine adaptive adjustment, and Cauchy mutation, was utilized to optimize the time parameters of interpolation nodes to achieve time minimization. The simulation results show that MISSA outperforms the ISSA, SSA, PSO, and GWO algorithms on 12 typical test functions, demonstrating stronger global search ability and higher convergence accuracy. The trajectory optimization experiment shows that the trajectory time is shortened from 12 s to 5.515 5 s after optimization; the efficiency is improved by 54.04%, and the motion curves of all joints are smooth, meeting engineering constraints. Actual measurements by a laser tracker verify that the straight-line trajectory repeatability RP of the robot at a speed of 1 600 mm/s is only 0.177 mm, which meets the requirements for high-precision operations, thus verifying the engineering applicability and robustness of the algorithm.

Key words: spray painting robot, time-optimal trajectory, sparrow search algorithm, 3-5-3 polynomial interpolation, refraction reverse learning

中图分类号:

TP242.2

杨杰,熊珍凯,王龙严 . 基于改进麻雀算法的喷涂机器人轨迹优化研究[J]. 系统仿真学报, 2026, 38(7): 1978-1992.

Yang Jie,Xiong Zhenkai,Wang Longyan . Study on Trajectory Optimization of Spray Painting Robot Based on Improved Sparrow Search Algorithm[J]. Journal of System Simulation, 2026, 38(7): 1978-1992.

图/表 20

图1

表1

测试函数

	函数名称	测试函数	维数	搜索范围
单峰函数	Sphere	$F 1 (x) = ∑ i = 1 n x i 2$	30	[-100,100]
	Schwefel 2.22	$F 2 (x) = ∑ i = 1 n \| x i \| + ∏ i = 1 n \| x i \|$	30	[-10,10]
	Schwefel 1.2	$F 3 (x) = ∑ i = 1 n (∑ j = 1 i x) 2$	30	[-100,100]
	Schwefel 2.21	$F 4 (x) = m a x i \| x i \|, 1 ≤ i ≤ n$	30	[-100,100]
多峰函数	Quartic	$F 5 (x) = ∑ i = 1 n i x i 4 + r a n d [0,1)$	30	[-1.28,1.28]
	Schwefel 2.26	$F 6 (x) = ∑ i = 1 n - x i s i n (\| x i \|)$	30	[-500,500]
	Rastrigin	$F 7 (x) = ∑ i = 1 n \| x i 2 - 10 c o s (2 π x i) + 10$	30	[-5.12,5.12]
	Ackley	$F 8 (x) = - 20 e x p - 0.2 1 n ∑ i = 1 n x i 2 - e x p 1 n ∑ i = 1 n c o s 2 π x i + 20 + e$	30	[-32,32]
	Griewank	$F 9 (x) = 1 4 000 ∑ i = 1 n x i 2 - ∏ i n c o s (x i / i) + 1$	30	[-600,600]
固定低维多峰函数	Shekel 5	$F 10 (x) = - ∑ i = 1 5 [(x - a i) (x - a i) T + c i] - 1$	4	[0,10]
	Shekel 7	$F 11 (x) = - ∑ i = 1 7 [(x - a i) (x - a i) T + c i] - 1$	4	[0,10]
	Shekel 10	$F 12 (x) = - ∑ i = 1 10 [(x - a i) (x - a i) T + c i] - 1$	4	[0,10]

表1

图2

表2

图3

表3

表4

图4

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

表5

表6

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函数	算法	最优值	平均值	标准差
F1	SSA	1.90×10^-316	1.33×10^-62	5.76×10^-62
	PSO	7.06×10^-1	2.35×10^-1	1.32×10^-1
	GWO	1.06×10^-29	1.06×10^-27	1.45×10^-27
	ISSA	0	0	0
	MISSA	0	0	0
F2	SSA	4.26×10^-203	5.19×10^-30	2.82×10^-29
	PSO	5.78×10^-2	1.19×10^-2	1.11×10^-2
	GWO	1.37×10^-17	8.96×10^-17	6.63×10^-17
	ISSA	6.09×10^-281	2.89×10^-266	1.00×10^-266
	MISSA	0	0	0
F3	SSA	0	1.10×10^-21	6.05×10^-21
	PSO	7.41×10¹	2.58×10¹	1.17×10¹
	GWO	1.77×10^-8	4.68×10^-6	1.14×10^-5
	ISSA	0	0	0
	MISSA	0	0	0
F4	SSA	0	4.71×10^-29	2.38×10^-28
	PSO	1.00×10¹	6.98×10⁰	1.15×10⁰
	GWO	7.48×10^-8	7.38×10^-7	7.69×10^-7
	ISSA	0	2.32×10^-218	5.00×10^-219
	MISSA	0	0	0
F5	SSA	1.39×10^-4	1.61×10^-3	1.20×10^-3
	PSO	2.99×10^-1	1.75×10^-1	5.33×10^-2
	GWO	7.49×10^-4	2.38×10^-3	1.33×10^-4
	ISSA	8.37×10^-6	1.02×10^-4	7.62×10^-5
	MISSA	4.23×10^-6	1.74×10^-4	1.50×10^-4
F6	SSA	-9.76×10³	-8.59×10³	5.85×10²
	PSO	-5.00×10²	-3.97×10²	9.84×10¹
	GWO	-7.20×10³	-6.13×10³	7.28×10²
	ISSA	-9.23×10³	-7.90×10³	6.60×10²
	MISSA	-1.25×10⁴	-1.25×10⁴	8.54×10^-1
F7	SSA	0	0	0
	PSO	5.12×10	2.53×10⁰	9.76×10^-1
	GWO	5.68×10^-14	3.67×10⁰	4.99×10⁰
	ISSA	0	0	0
	MISSA	0	0	0
F8	SSA	4.44×10^-16	4.44×10^-16	0
	PSO	1.09×10⁰	3.62×10^-1	3.98×10^-1
	GWO	7.51×10^-14	1.05×10^-13	1.85×10^-14
	ISSA	4.44×10^-16	4.44×10^-16	0
	MISSA	4.44×10^-16	4.44×10^-16	0
F9	SSA	0	0	0
	PSO	1.10×10¹	3.69×10⁰	3.01×10⁰
	GWO	0	3.46×10^-3	7.67×10^-3
	ISSA	0	0	0
	MISSA	0	0	0
F10	SSA	-1.01×10¹	-7.09×10⁰	2.54×10⁰
	PSO	-1.00×10⁰	-5.40×10⁰	-1.69×10⁰
	GWO	-1.01×10¹	-9.48×10⁰	2.10×10⁰
	ISSA	-1.01×10¹	-8.11×10⁰	2.54×10⁰
	MISSA	-1.01×10¹	-8.86×10⁰	3.36×10⁰
F11	SSA	-1.04×10¹	-8.81×10⁰	2.48×10⁰
	PSO	-3.00×10⁰	-4.47×10⁰	-1.38×10⁰
	GWO	-1.04×10¹	-1.04×10¹	8.01×10^-4
	ISSA	-1.04×10¹	-8.46×10⁰	2.60×10⁰
	MISSA	-1.04×10¹	-1.04×10¹	1.48×10^-15
F12	SSA	-1.05×10¹	-8.01×10⁰	2.74×10⁰
	PSO	-1.01×10⁰	-4.08×10⁰	-1.33×10⁰
	GWO	-1.05×10¹	-1.05×10¹	1.33×10^-3
	ISSA	-1.05×10¹	-9.27×10⁰	2.33×10⁰
	MISSA	-1.05×10¹	-1.02×10¹	1.87×10⁰

函数	SSA	PSO	GWO	ISSA	MISSA
F1	6.68×10^-6	3.10×10^-6	6.64×10^-6	1.03×10^-5	1.85×10^-5
F2	6.70×10^-6	3.18×10^-6	6.60×10^-6	9.95×10^-6	1.73×10^-5
F3	1.91×10^-5	1.00×10^-5	1.34×10^-5	2.98×10^-5	2.74×10^-5
F4	6.40×10^-6	3.04×10^-6	6.60×10^-6	1.02×10^-5	1.74×10^-5
F5	1.29×10^-5	6.52×10^-6	9.77×10^-6	2.04×10^-5	2.16×10^-5
F6	9.08×10^-6	4.07×10^-6	8.45×10^-6	1.43×10^-5	2.05×10^-5
F7	7.62×10^-6	3.54×10^-6	7.43×10^-6	1.14×10^-5	1.84×10^-5
F8	7.64×10^-6	3.89×10^-6	7.49×10^-6	1.22×10^-5	1.89×10^-5
F9	9.16×10^-6	4.10×10^-6	7.56×10^-6	1.33×10^-5	1.87×10^-5
F10	7.45×10^-6	1.85×10^-6	2.43×10^-6	1.02×10^-5	1.72×10^-5
F11	8.67×10^-6	2.33×10^-6	3.04×10^-6	1.02×10^-5	1.88×10^-5
F12	1.01×10^-5	2.97×10^-6	3.61×10^-6	1.36×10^-5	2.03×10^-5

路径点	关节1	关节2	关节3	关节4	关节5	关节6
A	71.42	40.62	60.40	43.57	-48.43	-133.84
B	75.05	28.50	63.36	54.47	-51.41	-131.18
C	-63.30	30.34	74.86	-79.53	-91.99	70.29
D	-46.80	42.21	55.01	-70.86	-77.08	77.54

速度等级/%	实际速度/(mm/s)	AP/mm	RP/mm
10	160	1.604	0.090
50	800	2.716	0.129
100	1 600	6.455	0.177

速度等级/%	实际速度/(mm/s)	AP/mm	RP/mm
10	160	13.330	3.627
50	800	16.552	4.794
100	1 600	25.591	7.710