基于VPPSO算法的无人机三维航迹规划

doi:10.12305/j.issn.1001-506X.2026.05.29

Abstract

Abstract:

A trajectory planning method based on velocity pausing particle swarm optimization （VPPSO） algorithm is proposed for unmanned aerial vehicle （UAV） trajectory planning in complex multi-threat environments. Firstly, an objective function set is formulated that comprehensively considers the optimality and safety requirements of UAV operation, transforming UAV trajectory planning into a multi-objective optimization problem. Secondly, the introduction of velocity pausing strategy, double group strategy, and velocity equation improvement strategy in the standard particle swarm optimization algorithm effectively balances the global exploration and local development capabilities of the algorithm. Finally, the optimization performance of the VPPSO algorithm is validated using standard test functions and applied to the three-dimensional trajectory planning of UAV. The experimental results show that the VPPSO algorithm has strong global optimization ability, and the planned trajectory results have the best performance in the comparison algorithms.

Key words: unmanned aerial vehicle （UAV）, trajectory planning, velocity pausing particle swarm optimization （VPPSO） algorithm, double group strategy

CLC Number:

V 249

Jie HU, Ruifeng CHU, Yixian ZHU, Ping CHEN, Fan BAO. Three-dimensional trajectory planning of UAV based on VPPSO algorithm[J]. Systems Engineering and Electronics, 2026, 48(5): 1738-1751.

Figures/Tables 15

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References 30

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函数类别	函数表达式	维度	搜索范围	理论最优值
单峰函数	$ {f_1}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {x_i^2} $	30	[−100, 100]	0
	$ {f_2}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {\left\| {{x_i}} \right\|} + \displaystyle\prod\limits_{i = 1}^n {\left\| {{x_i}} \right\|} $	30	[−10, 10]	0
	$ {f_3}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {{{\left( {\displaystyle\sum\limits_{j = 1}^i {{x_j}} } \right)}^2}} $	30	[−100, 100]	0
	$ {f_4}\left( x \right) = \displaystyle\sum\limits_{i = 1}^{n - 1} {\left[ {100{{\left( {{x_{i + 1}} - x_i^2} \right)}^2} + {{\left( {{x_i} - 1} \right)}^2}} \right]} $	30	[−30, 30]	0
	$ {f_5}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {{{\left( {\left\| {{x_i} + 0.5} \right\|} \right)}^2}} $	30	[−100, 100]	0
	$ {f_6}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {ix_i^4} +{\mathrm{ random}}\left[ {0,\;1} \right) $	30	[−1.28, 1.28]	0
多峰函数	$ {f_7}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n { - {x_i}\sin {\sqrt {\left\| {{x_i}} \right\|} } } $	30	[−500, 500]	−418.9892n
	$ {f_8}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {\left[ {x_i^2 - 10\cos {2\text{π} {x_i}} + 10} \right]} $	30	[−5.12, 5.12]	0
	$ {f_9}\left( x \right) = - 20\exp \left( { - 0.2\sqrt {\dfrac{1}{n}\displaystyle\sum\limits_{i = 1}^n {x_i^2} } } \right) - \exp \left( {\dfrac{1}{n}\displaystyle\sum\limits_{i = 1}^n {\cos {2\text{π} {x_i}} } } \right) + 20 + e $	30	[−32, 32]	0
	$ {f_{10}}\left( x \right) = \dfrac{1}{{4\;000}}\displaystyle\sum\limits_{i = 1}^n {x_i^2} - \prod\limits_{i = 1}^n {\cos {\frac{{{x_i}}}{{\sqrt i }}} } + 1 $	30	[−600, 600]	0

算法	参数	参数值
VPPSO	N₁，N₂，c₁，c₂，α，β	15、15、2、2、0.3、2.5
标准PSO	c₁，c₂	2、2
时变IPSO	w_max，w_min，c₁，c₂	0.9、0.4、2、2
CFPSO	c₁，c₂	2.05、2.05
AsyLnCPSO	c₁，c₂	[2.5, 0.5]、[0.5, 2.5]

测试函数	统计值	VPPSO	标准PSO	时变IPSO	CFPSO	AsyLnCPSO
f₁	平均值	0.00	43.8627	49.4588	528.9242	28.5399
f₁	标准差	0.00	14.1308	16.6357	214.0489	9.8416
f₂	平均值	0.00	4.5927	5.1817	13.8755	4.8547
f₂	标准差	0.00	1.3588	1.6768	3.2660	1.8522
f₃	平均值	0.00	1.2765 e+03	1.1495 e+03	3.3574 e+03	1.0783 e+03
f₃	标准差	0.00	441.1578	494.0901	1.2658 e+03	376.9577
f₄	平均值	0.0023	1.2696 e+03	1.5123 e+03	4.3892 e+03	1.0122 e+03
f₄	标准差	0.0040	503.6359	1.0087 e+03	2.7626 e+03	583.2012
f₅	平均值	1.1187 e-07	46.7935	41.4933	557.6807	28.6876
f₅	标准差	2.4544 e-08	12.1358	17.4715	243.6593	15.2706
f₆	平均值	8.2585 e-04	0.0457	0.0568	0.1648	0.0670
f₆	标准差	0.0011	0.0145	0.0304	0.0848	0.0323
f₇	平均值	−1.2089 e+04	−5.9224 e+03	−5.9910 e+03	−5.7263 e+03	−6.6040 e+03
f₇	标准差	597.3521	994.2260	887.5876	987.9906	818.3769
f₈	平均值	0.00	58.3834	56.7559	96.4358	51.5046
f₈	标准差	0.00	11.9984	14.4350	18.0777	13.8994
f₉	平均值	7.3127 e-15	3.7175	4.7749	8.0541	4.9158
f₉	标准差	1.2973 e-15	0.3740	0.9284	1.1524	1.2425
f₁₀	平均值	0.00	1.3871	1.4266	6.8483	1.2918
f₁₀	标准差	0.00	0.1019	0.1994	1.8549	0.1125

场景	标准PSO			时变IPSO			VPPSO
场景	平均值	标准差	时效性	平均值	标准差	时效性	平均值	标准差	时效性
1	4787	52	19.45	4778	45	20.12	4758	24	18.11
2	4982	62	20.19	4835	49	21.22	4757	31	19.67
3	5024	72	23.56	4887	59	24.17	4827	40	22.35
4	5413	90	26.18	5025	71	27.30	4935	58	24.50

场景	标准PSO			时变IPSO			VPPSO
场景	平均值	标准差	时效性	平均值	标准差	时效性	平均值	标准差	时效性
1	5389	56	27.11	4943	43	27.86	4853	35	26.25
2	5671	59	27.83	4911	61	28.57	4792	52	27.03
3	5725	68	30.24	5024	72	31.06	4956	59	29.81
4	5563	99	32.37	5224	80	33.11	5157	71	31.96

Three-dimensional trajectory planning of UAV based on VPPSO algorithm

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