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

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (5): 1738-1751.doi: 10.12305/j.issn.1001-506X.2026.05.29

基于VPPSO算法的无人机三维航迹规划

胡杰¹^,²^,*, 褚瑞峰¹, 朱倚娴³, 陈平¹^,², 鲍帆¹^,²

1. 中国电子科技集团公司第二十八研究所，江苏南京 210007
2. 空中交通管理系统全国重点实验室，江苏南京 210007
3. 南通大学机械工程学院，江苏南通 226019

收稿日期:2025-03-27 出版日期:2026-05-27 发布日期:2026-05-27
通讯作者: 胡杰
作者简介:褚瑞峰（1990—），男，工程师，硕士，主要研究方向为无人机航迹规划、飞行计划调配
朱倚娴（1989—），女，讲师，博士，主要研究方向为无人机导航、航迹规划、飞行计划调配
陈　平（1965—），男，研究员，主要研究方向为空中交通管理、无人机飞行管理
鲍　帆（1982—），女，研究员，硕士，主要研究方向为交通运输规划、智慧机场总体设计
基金资助:
国家自然科学基金（52402412）；中国工程院战略研究与咨询项目（2024-DFZD-18）资助课题

Three-dimensional trajectory planning of UAV based on VPPSO algorithm

Jie HU¹^,²^,*, Ruifeng CHU¹, Yixian ZHU³, Ping CHEN¹^,², Fan BAO¹^,²

1. The 28th Research Institute of China Electronics Technology Group Corporation，Nanjing 210007，China
2. State Key Laboratory of Air Traffic Management System，Nanjing 210007，China
3. School of Mechanical Engineering，Nantong University，Nantong 226019，China

Received:2025-03-27 Online:2026-05-27 Published:2026-05-27
Contact: Jie HU

摘要/Abstract

摘要：

针对复杂多威胁环境中的无人机（unmanned aerial vehicle，UAV）航迹规划问题，提出一种基于速度暂停粒子群优化（velocity pausing particle swarm optimization，VPPSO）算法的航迹规划方法。首先，构建一个综合考虑UAV运行最优性与安全性需求的目标函数集合，将UAV航迹规划转化为多目标优化问题。其次，在标准粒子群优化算法中引入速度暂停策略、双种群策略、速度方程改进策略，有效平衡算法的全局探索和局部开发能力。最后，利用标准测试函数对VPPSO算法寻优性能进行验证并将其应用于UAV三维航迹规划中。实验结果表明：VPPSO算法具有较强的全局寻优能力，规划的航迹结果性能在比较算法中最优。

关键词: 无人机, 航迹规划, 速度暂停粒子群算法, 双种群策略

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

中图分类号:

V 249

胡杰, 褚瑞峰, 朱倚娴, 陈平, 鲍帆. 基于VPPSO算法的无人机三维航迹规划[J]. 系统工程与电子技术, 2026, 48(5): 1738-1751.

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.

图/表 15

图1

图2

图3

图4

图5

表1

表2

表3

图6

图7

图8

表4

图9

图10

表5

参考文献 30

1	HE Y, HOU T C, WANG M R. A new method for unmanned aerial vehicle path planning in complex environments[J]. Scientific Reports, 2024, 14, 9257. doi: 10.1038/s41598-024-60051-4
2	DEBNATH D, VANEGAS F, SANDINO J, et al. A review of UAV path-planning algorithms and obstacle avoidance methods for remote sensing applications[J]. Remote Sensing, 2024, 16, 4019. doi: 10.3390/rs16214019
3	LI J, XIONG Y H, SHE J H. UAV path planning for target coverage task in dynamic environment[J]. IEEE Internet of Things Journal, 2023, 10 (20): 17734- 17745. doi: 10.1109/JIOT.2023.3277850
4	PUENTE-CASTRO A, RIVERO D, PAZOS A, et al. A review of artificial intelligence applied to path planning in UAV swarms[J]. Neural Computing and Applications, 2022, 34, 153- 170. doi: 10.1007/s00521-021-06569-4
5	DEBNATH D, HAWARY A F, RAMDAN M I, et al. QuickNav: an effective collision avoidance and path-planning algorithm for UAS[J]. Drones, 2023, 7, 678. doi: 10.3390/drones7110678
6	YANG L, TAN L, ZHANG F Q. UAV 3D trajectory planning based on improved A* algorithm and differential evolution[J]. Journal of Network Intelligence, 2023, 8 (4): 1150- 1163.
7	WU T, ZHANG Z, JING F, et al. A dynamic path planning method for UAVs based on improved in-formed-RRT* fused dynamic windows[J]. Drones, 2024, 8, 539. doi: 10.3390/drones8100539
8	唐宇洋, 郑恩辉, 邱潇. 基于优化双向A*与人工势场法的无人机三维航迹规划[J]. 空军工程大学学报, 2024, 25 (5): 69- 75. doi: 10.3969/j.issn.2097-1915.2024.05.009
	TANG Y Y, ZHENG E H, QIU X. 3D UAV trajectory planning based on optimized bidirectional A* and artificial potential field method[J]. Journal of Air Force Engineering University, 2024, 25 (5): 69- 75. doi: 10.3969/j.issn.2097-1915.2024.05.009
9	PEHLIVANOGLU Y V, PEHLIVANOGLU P. An enhanced genetic algorithm for path planning of autonomous UAV in target coverage problems[J]. Applied Soft Computing, 2021, 112, 107796. doi: 10.1016/j.asoc.2021.107796
10	LIN S Q, LI F F, LI X Y, et al. Improved artificial bee colony algorithm based on multi-strategy synthesis for UAV path planning[J]. IEEE Access, 2022, 10, 119269. doi: 10.1109/ACCESS.2022.3218685
11	朱润泽, 赵静, 蒋国平, 等. 基于改进粒子群算法的无人机三维路径规划[J]. 南京邮电大学学报（自然科学版）, 2024, 44 (6): 120- 127.
	ZHU R Z, ZHAO J, JIANG G P, et al. UAV 3D path planning based on improved particle swarm optimization algorithm[J]. Journal of Nanjing University of Posts and Telecommunications （Natural Science Edition）, 2024, 44 (6): 120- 127.
12	QI D, ZHANG Z H, ZHANG Q R. Path planning of multirotor UAV based on the improved ant colony algorithm[J]. Journal of Robotics, 2022, 2022, 2168964.
13	PHUNG M D, QUACH C H, DINH T H, et al. Enhanced discrete particle swarm optimization path planning for UAV vision-based surface inspection[J]. Automation in Construction, 2017, 81, 25- 33. doi: 10.1016/j.autcon.2017.04.013
14	宋志强, 夏庆锋, 陈少博, 等. 基于改进球面向量粒子群优化的UAV航迹规划[J]. 电光与控制, 2023, 30 (4): 56- 60.
	SONG Z Q, XIA Q F, CHEN S B, et al. UAV path planning with improved spherical vector based particle swarm optimization[J]. Electronics Optics & Control, 2023, 30 (4): 56- 60.
15	LIU Y F, ZHANG H, ZHENG H, et al. A spherical vector-based adaptive evolutionary particle swarm optimization for UAV path planning under threat conditions[J]. Scientific Reports, 2025, 15, 2116. doi: 10.1038/s41598-025-85912-4
16	LYU L X, YANG F. MMPA: a modified marine predator algorithm for 3D UAV path planning in complex environments with multiple threats[J]. Expert Systems with Applications, 2024, 257, 124955.
17	隋东, 杨振宇, 丁松滨, 等. 基于EMSDBO算法的无人机三维航迹规划[J]. 系统工程与电子技术, 2024, 46 (5): 1756- 1766.
	SUI D, YANG Z Y, DING S B, et al. Three-dimensional path planning of UAV based on EMSDBO algorithm[J]. Systems Engineering and Electronics, 2024, 46 (5): 1756- 1766.
18	NIU B, WANG Y J, LIU J, et al. Path planning for unmanned aerial vehicles in complex environment based on an improved continuous ant colony optimization[J]. Computers and Electrical Engineering, 2025, 123, 110034. doi: 10.1016/j.compeleceng.2024.110034
19	DUONG T T N, BUI D N, PHUNG M D. Navigation variable-based multi-objective particle swarm optimization for UAV path planning with kinematic constraints[J]. Neural Computing and Applications, 2025, 37, 5683- 5697. doi: 10.1007/s00521-024-10945-1
20	YANG J Q, YAN F, ZHANG J, et al. Hybrid chaos game and grey wolf optimization algorithms for UAV path planning[J]. Applied Mathematical Modelling, 2025, 142, 115979. doi: 10.1016/j.apm.2025.115979
21	王飞, 杨清平. 基于改进粒子群算法的城市物流无人机路径规划[J]. 科学技术与工程, 2023, 23 (30): 13187- 13194. doi: 10.12404/j.issn.1671-1815.2023.23.30.13187
	WANG F, YANG Q P. Route planning of urban logistics unmanned aerial vehicle based on improved particle swarm optimization algorithm[J]. Science Technology and Engineering, 2023, 23 (30): 13187- 13194. doi: 10.12404/j.issn.1671-1815.2023.23.30.13187
22	SHAMI T M, EL-SALEH A A, ALSWAITTI M, et al. Particle swarm optimization: a comprehensive survey[J]. IEEE Access, 2022, 10, 10031- 10061. doi: 10.1109/ACCESS.2022.3142859
23	张姝, 汤淼. 改进PSO算法及在无人机路径规划中的应用[J]. 计算机系统应用, 2023, 32 (3): 330- 337.
	ZHANG S, TANG M. Improved PSO algorithm and its application in route planning of UAV[J]. Computer Systems & Applications, 2023, 32 (3): 330- 337.
24	SHI Y, EBERHART R C. A modified particle swarm optimizer[C]//Proc. of the IEEE International Conference on Evolutionary Computation Proceedings, 1998.
25	SHI Y, EBERHART R C. Empirical study of particle swarm optimization[C]//Proc. of the Congress on Evolutionary Computation, 1999.
26	CLERC M, KENNEDY J. The particle swarm-explosion, stability, and convergence in a multidimensional complex space[J]. IEEE Trans. on Evolutionary Computation, 2002, 6 (1): 58- 73. doi: 10.1109/4235.985692
27	RATNAWEERA A, HALGAMUGE S K, WATSON H C. Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients[J]. IEEE Trans. on Evolutionary Computation, 2004, 8 (3): 240- 255. doi: 10.1109/TEVC.2004.826071
28	远翔宇, 杨风暴, 杨童瑶. 基于自适应蜣螂算法的无人机三维路径规划方法[J]. 无线电工程, 2024, 54 (4): 928- 936. doi: 10.3969/j.issn.1003-3106.2024.04.016
	YUAN X Y, YANG F B, YANG T Y. UAV 3D path planning method based on adaptive dung beetle algorithm[J]. Radio Engineering, 2024, 54 (4): 928- 936. doi: 10.3969/j.issn.1003-3106.2024.04.016
29	WANG X F, ZHAO H, HAN T, et al. A grey wolf optimizer using Gaussian estimation of distribution and its application in the multi-UAV multi-target urban tracking problem[J]. Applied Soft Computing, 2019, 78, 240- 260. doi: 10.1016/j.asoc.2019.02.037
30	蒋翱徽, 刘文红. 基于改进蜣螂优化算法的无人机三维路径规划[J]. 电子测量技术, 2024, 47 (13): 128- 135.
	JIANG A H, LIU W H. Unmanned aerial vehicle three-dimensional path planning based on improved dung beetle optimization algorithm[J]. Electronic Measurement Technology, 2024, 47 (13): 128- 135.

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

基于VPPSO算法的无人机三维航迹规划

Three-dimensional trajectory planning of UAV based on VPPSO algorithm

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 15

参考文献 30

相关文章 15

编辑推荐

Metrics

本文评价

[1]	刘瑞航, 刘海颖, 刘宇辰, 陈晨, 李铁香. 基于多特征正交约束的无人机跨视角地理定位方法[J]. 系统工程与电子技术, 2026, 48(6): 2072-2080.
[2]	张国庆, 姚桂鹏, 李纪强. 无人机/船协同降落的鲁棒自适应模糊控制[J]. 系统工程与电子技术, 2026, 48(6): 2081-2088.
[3]	林文斌, 时晨光, 严牧, 汪飞, 周建江. 面向欺骗干扰组网雷达的无人机集群稳健航迹规划算法[J]. 系统工程与电子技术, 2026, 48(5): 1551-1563.
[4]	杨秀霞, 姚文强, 张毅, 于浩. 通信约束下多无人机协同搜索航迹优化[J]. 系统工程与电子技术, 2026, 48(5): 1715-1727.
[5]	武愈涵, 吴晓莉, 张欣悦, 晏彪, 王名珺. 面向认知增强的MUM-T态势图视觉调控方法[J]. 系统工程与电子技术, 2026, 48(4): 1292-1302.
[6]	杨志, 郁丰, 林思颖, 周紫君. 基于视觉协同的蜂群自主导航技术[J]. 系统工程与电子技术, 2026, 48(4): 1396-1403.
[7]	谷旭平, 史贤俊. 基于结构分析与树种优化算法的无人机可重构性分析与设计[J]. 系统工程与电子技术, 2026, 48(3): 932-945.
[8]	杨跃能, 孔希, 张士峰, 邓少永. 低空小型旋翼无人机近距拦截捕获方法[J]. 系统工程与电子技术, 2026, 48(3): 1010-1017.
[9]	魏建林, 林彦超, 唐慧龙, 张旺, 王伟. 基于改进MCTS的多无人机多任务联合决策[J]. 系统工程与电子技术, 2026, 48(2): 556-568.
[10]	晏彪, 吴晓莉, 张蓝, 刘潇, 方泽茜, 韩炜毅, 李琦桉. 有人/无人机协同指挥员的事件相关电位特征[J]. 系统工程与电子技术, 2026, 48(2): 578-587.
[11]	张森, 庞岩, 周福亮. 基于改进Informed-RRT^*算法的无人机三维路径规划[J]. 系统工程与电子技术, 2026, 48(2): 660-668.
[12]	乔毅涛, 李爽. 空地异构无人系统固定时间事件触发编队包含控制[J]. 系统工程与电子技术, 2026, 48(2): 669-683.
[13]	李淑凤, 韩璐羽. 面向飞机表面巡检的多无人机覆盖路径规划[J]. 系统工程与电子技术, 2026, 48(2): 684-693.
[14]	杨许鑫, 季薇. 无人机辅助的安全MEC系统中的能耗优化策略[J]. 系统工程与电子技术, 2026, 48(2): 719-726.
[15]	林志康, 刘甲磊, 马佳智, 施龙飞, 徐进宝. 利用分布式辐射源闪烁诱偏的抗反辐射方法[J]. 系统工程与电子技术, 2026, 48(1): 1-11.