Study on Trajectory Optimization of Spray Painting Robot Based on Improved Sparrow Search Algorithm

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

Abstract

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

CLC Number:

TP242.2

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.

Figures/Tables 20

Fig. 1

Table 1

Test functions

	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]

Table 1

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Table 2

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Table 4

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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