基于MDEPSO算法的无人机三维航迹规划

doi:10.12382/bgxb.2024.0710

摘要/Abstract

摘要：

针对经典粒子群算法在无人机三维航迹规划过程中全局搜索能力不足、易陷入局部最优等问题,研究提出一种多维增强粒子群优化算法。算法首先通过引入改善因子,在粒子寻优各个阶段实现动态调整惯性权重,提升种群适应性和克服局部最优能力;其次依靠动态约束方程实现学习因子增强,促使粒子间信息共享更为高效,改善算法自学习能力;随后有序融合混沌初始化和精英反向学习进化等策略优势,重新规划粒子群进化流程,增强粒子在迭代过程中的均衡性和多样性,提升算法收敛精度。实验中通过测试函数横向对比和复杂三维任务场景纵向应用,多维增强粒子群优化算法在新的多维目标函数指标中相较于经典粒子群算法无人机航迹规划能力获得了提升,在5种比对算法中表现出较好的有效性和竞争力。

关键词: 无人机, 航迹规划, 粒子群算法, 混沌, 精英反向学习策略

Abstract:

A multi-dimensional enhanced particle swarm optimization algorithm (MDEPSO) is proposed to address the problem of insufficient global search capability and susceptibility to local optima in the 3D trajectory planning process of unmanned aerial vehicles using classical particle swarm optimization algorithms.This algorithm first introduces improvement factors to dynamically adjust inertia weights in various stages of particle optimization,enhancing population adaptability and overcoming local optima; Secondly,relying on dynamic constraint equations to enhance learning factors promotes more efficient information sharing between particles and improves the algorithm’s self-learning ability; Subsequently,the advantages of orderly integration of chaos initialization and elite reverse learning evolution strategies were utilized to re plan the particle swarm evolution process,enhance the balance and diversity of particles in the iterative process,and improve the convergence accuracy of the algorithm.In the experiment,through horizontal comparison of test functions and vertical application in complex 3D task scenarios,the multi-dimensional enhanced particle swarm optimization algorithm showed an improvement in the UAV trajectory planning ability compared to the classical particle swarm algorithm in the new multi-dimensional objective function indicators.It demonstrated good effectiveness and competitiveness among the five comparison algorithms.

Key words: unmanned aerial vehicle, path planning, particle swarm optimization, chaos, elite backward learning strategy

肖鹏, 于海霞, 黄龙, 张司明. 基于MDEPSO算法的无人机三维航迹规划[J]. 兵工学报, 2025, 46(7): 240710-.

XIAO Peng, YU Haixia, HUANG Long, ZHANG Siming. 3D Path Planning of Unmanned Aerial Vehicle Based on MDEPSO Algorithm[J]. Acta Armamentarii, 2025, 46(7): 240710-.

图/表 11

图1 栅格法环境建模示意图

Fig.1 Grid method environment modeling diagram

图2 惯性权重对比曲线

Fig.2 Inertia weight contrast curve

图3 MDEPSO算法流程

Fig.3 MDEPSO algorithm flow

表1 测试函数

Table1 Trial function

表达式	搜索范围	最优解
$F 1 (x) = ∑ i = 1 D x i 2$	[-100,100]	0
$F 2 (x) = ∑ i = 1 D x i + ∏ i = 1 D x i$	[-10,10]	0
$F 3 (x) = ∑ i = 1 D - 1 [100 (x i + 1 - x i 2) 2 + (x i - 1) 2]$	[-30,30]	0
F₄(x)=max_i{ $x i$ ,1≤i≤D}	[-100,100]	0
$F 5 (x) = 14000 ∑ i = 1 D x i 2 - ∏ i = 1 D c o s x i i + 1$	[-600,600]	0
$F 6 (x) = - 20 e x p - 0.2 1 D ∑ i = 1 D x i 2 - e x p 1 D ∑ i = 1 D c o s 2 π x i + 20 + e$	[-32,32]	0
$F 7 (x) = π D {10 s i n (π y 1) + ∑ i = 1 D - 1 (y i - 1) 2 [1 + 10 s i n 2 (π y i + 1)] + (y D - 1) 2} + ∑ i = 1 D U (x i, 10,100,4), y i = 1 + x i + 1 4, U (x i, a, k, m) = k (x i - a) m x i > a 0 - a < x i < a k (- x i - a) m x i < - a$	[-50,50]	0
$F 8 (x) = 0.1 {s i n 2 (3 π x 1) + ∑ i = 1 D - 1 (x i - 1) 2 [1 + s i n 2 (3 π x i + 1)] + (x D - 1) 2 [1 + s i n 2 (2 π x D)]} + ∑ i = 1 D U (x i, 5,100,4)$	[-50,50]	0

表1 测试函数

Table1 Trial function

表达式	搜索范围	最优解
$F 1 (x) = ∑ i = 1 D x i 2$	[-100,100]	0
$F 2 (x) = ∑ i = 1 D x i + ∏ i = 1 D x i$	[-10,10]	0
$F 3 (x) = ∑ i = 1 D - 1 [100 (x i + 1 - x i 2) 2 + (x i - 1) 2]$	[-30,30]	0
F₄(x)=max_i{ $x i$ ,1≤i≤D}	[-100,100]	0
$F 5 (x) = 14000 ∑ i = 1 D x i 2 - ∏ i = 1 D c o s x i i + 1$	[-600,600]	0
$F 6 (x) = - 20 e x p - 0.2 1 D ∑ i = 1 D x i 2 - e x p 1 D ∑ i = 1 D c o s 2 π x i + 20 + e$	[-32,32]	0
$F 7 (x) = π D {10 s i n (π y 1) + ∑ i = 1 D - 1 (y i - 1) 2 [1 + 10 s i n 2 (π y i + 1)] + (y D - 1) 2} + ∑ i = 1 D U (x i, 10,100,4), y i = 1 + x i + 1 4, U (x i, a, k, m) = k (x i - a) m x i > a 0 - a < x i < a k (- x i - a) m x i < - a$	[-50,50]	0
$F 8 (x) = 0.1 {s i n 2 (3 π x 1) + ∑ i = 1 D - 1 (x i - 1) 2 [1 + s i n 2 (3 π x i + 1)] + (x D - 1) 2 [1 + s i n 2 (2 π x D)]} + ∑ i = 1 D U (x i, 5,100,4)$	[-50,50]	0

表2 测试函数实验结果

Table2 Test function experiment results

函数	指标	PSO	CMOPSO	NMPSO	SSA-PSO	T-PSO	MDEPSO
F₁	Mean	1.48×10^-1	1.00×10^-1	5.50×10^-2	5.01×10^-2	5.00×10^-2	5.00×10^-2
F₁	SD	3.02×10^-1	2.69×10^-1	2.24×10^-1	2.24×10^-1	2.24×10^-1	2.24×10^-1
F₂	Mean	3.90×10^-1	2.85×10^-1	3.98×10^-1	1.41×10^-1	8.01×10^-2	5.04×10^-2
F₂	SD	4.25×10^-1	3.65×10^-1	4.17×10^-1	2.97×10^-1	2.44×10^-1	2.22×10^-1
F₃	Mean	2.64×10^-1	1.82×10^-1	1.54×10^-1	1.30×10^-1	7.63×10^-2	5.23×10^-2
F₃	SD	3.55×10^-1	3.29×10^-1	2.82×10^-1	2.98×10^-1	2.30×10^-1	2.08×10^-1
F₄	Mean	2.83×10^-1	1.76×10^-1	2.06×10^-1	1.00×10^-2	5.01×10^-5	5.25×10^-17
F₄	SD	3.86×10^-1	3.63×10^-1	3.50×10^-1	4.47×10^-2	2.24×10^-4	2.24×10^-16
F₅	Mean	7.29×10⁵	1.61×10^-5	6.75×10^-5	1.58×10^-5	1.85×10^-5	1.49×10^-4
F₅	SD	3.92×10^-5	1.12×10^-5	2.31×10^-5	2.48×10^-5	3.03×10^-5	3.58×10^-4
F₆	Mean	1.01×10^-1	8.16×10^-2	1.14×10^-1	5.00×10^-2	5.00×10^-2	5.01×10^-2
F₆	SD	2.51×10^-1	2.39×10^-1	2.83×10^-1	2.24×10^-1	2.24×10^-1	2.24×10^-1
F₇	Mean	2.61×10^-1	1.36×10^-1	2.45×10^-1	2.61×10^-1	1.02×10^-1	5.28×10^-17
F₇	SD	3.55×10^-1	2.83×10^-1	3.70×10^-1	3.67×10^-1	2.46×10^-1	2.24×10^-16
F₈	Mean	2.61×10^-1	1.36×10^-1	2.45×10^-1	2.61×10^-1	5.00×10^-2	5.17×10^-27
F₈	SD	3.55×10^-1	2.83×10^-1	3.70×10^-1	3.67×10^-1	2.24×10^-1	2.24×10^-26

图4 单模态函数收敛曲线

Fig.4 Convergence curve of single mode function

图5 多模态函数收敛曲线

Fig.5 Convergence curve of multimodal function

表3 任务场景建模参数

Table 3 Task scenario modeling parameters

场景名称	山体中心/km	山体坡度衰减量	山体高度/km	雷达中心/km	最大探测距离/km	有效探测距离/km
场景一	(20,40) (40,10) (40,40)	(5,8) (5,5) (6,6)	4 5 6	(35,9) (25,30) (11,15)	6.6 12 7.5	6 10 7
场景二	(15,35) (25,25) (40,10)	(10,10) (10,10) (5,5)	5 5 5.5	(38,40) (20,40) (11,15)	6.5 6.5 8.8	6 6 8.6
场景三	(13,13) (25,25) (40,40)	(8,8) (8,8) (8,8)	4 5 5	(38,11) (26,38) (9,35)	9 7.5 6.5	8 7 6
场景四	(15,25) (30,25) (40,25)	(10,8) (10,8) (10,8)	5 5 5	(40,30) (9,15) (9,40)	9 7.5 6.5	8 7 6

图6 场景一中各算法航迹规划过程

Fig.6 The trajectory planning process of each algorithm in scenario 1

图7 各场景最优航迹规划对比

Fig.7 Comparison of optimal flight path planning for each scenario

图8 各场景多维目标函数迭代曲线

Fig.8 Multidimensional objective function iteration curve of each scene

参考文献 22

[1]	秦潜聪, 吴冠霖, 高原, 等. 面向战场条件的无人机集群分布式存储方法[J]. 西南交通大学学报, 2024, 59(4):942-958.
	QIN Q C, WU G L, GAO Y, et al. Distributed storage methods for unmanned aerial vehicle cluster in battlefield[J]. Journal of Southwest Jiaotong University, 2024, 59(4):942-958. (in Chinese)
[2]	MOHSAN S A H, KHAN M A, NOOR F, et al. Towards the unmanned aerial vehicles (UAVs):a comprehensive review[J]. Drones, 2022, 6(6):147.
[3]	张海阔, 孟秀云. 基于改进RRT^*算法的无人机在线航迹规划[J]. 系统工程与电子技术, 2024, 46(12):4157-4164. doi: 10.12305/j.issn.1001-506X.2024.12.24
	ZHANG H K, MENG X Y. UAV online path planning of based on improved RRT^* algorithm[J]. Systems Engineering and Electronics, 2024, 46(12):4157-4164. (in Chinese)
[4]	李宗刚, 韩森, 陈引娟, 等. 基于角度搜索和深度Q网络的移动机器人路径规划算法[J]. 兵工学报, 2025, 46(2):240265. doi: 10.12382/bgxb.2024.0265
	LI Z G, HAN S, CHEN Y J, et al. Mobile robots path planning algorithm based on angle search and deep Q-network[J]. Acta Armamentarii, 2025, 46(2):240265. (in Chinese)
[5]	TANG G Q, TANG C, ZHOU H, et al. R-DFS:a coverage path planning approach based on region optimal decomposition[J]. Remote Sensing, 2021, 13(8):1525.
[6]	PETER E H, NILS J N, BERTRAM R. A formal basis for the heuristic determination of minimum cost paths[J]. IEEE Transactions on Systems Science and Cybernetics, 1968, 4(2):100-107.
[7]	YU F J, SHANG H Q, ZHU Q L, et al. An efficient RRT-based motion planning algorithm for autonomous underwater vehicles under cylindrical sampling constraints[J]. Autonomous Robots, 2023, 47(3):281-297.
[8]	CUI J G, WU L, HUANG X D, et al. Multi-strategy adaptable ant colony optimization algorithm and its application in robot path planning[J]. Knowledge-Based Systems, 2024,288:111459.
[9]	MOHD N A W, AMRIL N, ASHRAF K, et al. Improved genetic algorithm for mobile robot path planning in static environments[J]. Expert Systems with Applications, 2024,249:123762.
[10]	XU G, LUO K, JING G X, et al. On convergence analysis of multiobjective particle swarm optimization algorithm[J]. European Journal of Operational Research, 2020, 286(1):32-38.
[11]	HOUSSEIN E H, GAD A G, HUSSAIN K, et al. Major advances in particle swarm optimization:theory,analysis,and application[J]. Swarm and Evolutionary Computation, 2021,63:100868-100905.
[12]	DE CARVALHO A B, POZO A. Measuring the convergence and diversity of CDAS multi-objective particle swarm optimization algorithms:a study of many-objective problems[J]. Neurocomputing, 2012, 75(1):43-51.
[13]	MOUBAYED NA, PETROVSKI A, MCCALL J. D²MOPSO:MOPSO based on decomposition and dominance with archiving using crowding distance in objective and solution spaces[J]. Evolution Computation, 2014, 22(1):7-47.
[14]	ZHANG X Y, ZHENG X T, CHENG R, et al. A competitive mechanism based multi-objective particle swarm optimizer with fast convergence[J]. Information Sciences, 2018,427:63-76.
[15]	LIN Q Z, LIU S B, ZHU Q L, et al. Particle swarm optimization with a balanceable fitness estimation for many-objective optimization problems[J]. IEEE Transactionsactions on Evolutionary Computation, 2018, 22(1):32-46.
[16]	张志文, 刘伯威, 张继园, 等. 麻雀搜索算法-粒子群算法与快速扩展随机树算法协同优化的智能车辆路径规划[J]. 中国机械工程, 2024, 35(6):993-999,1009.
	ZHANG Z W, LIU B W, ZHANG J Y, et al. Cooperative optimization of intelligent vehicle path planning based on PSO-SSA and RRT[J]. China Mechanical Engineering, 2024, 35(6):993-999,1009. (in Chinese)
[17]	张睿, 李万睿, 肖勇, 等. 基于航迹规划的无人机地形辅助导航[J]. 哈尔滨工程大学学报, 2024, 45(3):459-465.
	ZHANG R, LI W R, XIAO Y, et al. Path planning-based terrain contour matching navigation of unmanned aerial vehicles[J]. Journal of Harbin Engineering University, 2024, 45(3):459-465. (in Chinese)
[18]	陈亚萍, 王楠, 洪华杰, 等. 面向多无人平台区域监视任务的信息素正向激励栅格方法[J]. 兵工学报, 2023, 44(9):2859-2870. doi: 10.12382/bgxb.2022.0537
	CHEN Y P, WANG N, HONG H J, et al. Pheromone positive incentive grid method for multi-unmanned platform regional surveillance task[J]. Acta Armamentarii, 2023, 44(9):2859-2870. (in Chinese) doi: 10.12382/bgxb.2022.0537
[19]	KENNEDY J, EBERHART R. Particle swarm optimization[C]//Proceedings of ICNN’95-International Conference on Neural Networks.Perth,WA, Australia:IEEE, 1995,4:1942-1948.
[20]	黄樊晶, 吴盘龙, 李星秀, 等. 考虑执行能力约束的多机协同目标分配AEPSO算法[J]. 宇航学报, 2024, 45(6):948-957.
	HUANG F J, WU P L, LI X X, et al. Multi-UAV cooperative target allocation AEPSO algorithm considering execution capability constraints[J]. Journal of Astronautics, 2024, 45(6):948-957. (in Chinese)
[21]	LI X, LI K W. Imbalanced data classification based on improved EIWAPSO-AdaBoost-C ensemble algorithm[J]. Applied Intelligence, 2021,52:6477-6502.
[22]	薛阳, 燕宇铖, 贾巍, 等. 基于改进灰狼算法优化长短期记忆网络的光伏功率预测[J]. 太阳能学报, 2023, 44(7):207-213. doi: 10.19912/j.0254-0096.tynxb.2022-0320
	XUE Y, YAN Y C, JIA W, et al. Photovoltaic power prediction model based on IGWO-LSTM[J]. Acta Energiae Solaris Sinica, 2023, 44(7):207-213. (in Chinese) doi: 10.19912/j.0254-0096.tynxb.2022-0320