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Journal of ZheJiang University (Engineering Science)  2024, Vol. 58 Issue (10): 2020-2030    DOI: 10.3785/j.issn.1008-973X.2024.10.005
    
Optimization of 3D multi-UAVs low altitude penetration based on bald eagle search algorithm
Xialu WEN1,2(),He HUANG1,2,*(),Huifeng WANG2,Lan YANG1,Tao GAO3
1. Xi’an Key Laboratory of Intelligent Expressway Information Fusion and Control, Chang’an University, Xi’an 710064, China
2. School of Electronics and Control Engineering, Chang’an University, Xi’an 710064, China
3. School of Data Science and Artificial Intelligence, Chang’an University, Xi’an 710064, China
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Abstract  

In response to the complex three-dimensional space environment and the high computational complexity of low altitude penetration path planning for multi-UAVs, the existing multi-objective bald eagle search algorithm has the shortcomings of easily approaching the center point and low accuracy. A 3D multi-UAVs low altitude penetration method based on the improved multi-objective bald eagle search algorithm (IMBES) was proposed. Models for the 3D environment, threat sources, UAV physical constraints, multi-UAVs cooperative constraints, and path smoothness were constructed to define a multi-objective cost function. A coupling chaotic mapping initialization was designed to enhance the quality of the initial population. An adaptive Gauss walk strategy based on the “scout eagle” was devised to balance development and search capabilities. Fast non-dominated sorting was introduced to further enhance algorithm efficiency. By leveraging the correspondence between the bald eagle position and UAV speed, turning angle, and climbing angle, the IMBES efficiently explored the UAV configuration space to identify the optimal Pareto front. Experimental results showed that the success rate of the IMBES was 70.5%. Compared with existing path planning methods, the proposed method demonstrates strong optimization capabilities and low energy consumption, making it suitable for collaborative low-altitude penetration by multiple UAVs.



Key wordsmulti-UAVs      low altitude penetration      autonomous obstacle avoidance      multi-objective algorithm      bald eagle search algorithm     
Received: 18 October 2023      Published: 27 September 2024
CLC:  TP 393  
Fund:  国家自然科学基金资助项目(52172324,52172379);中央高校基本科研业务费专项资金重点科研平台建设计划水平提升项目(300102324501);西安市智慧高速公路信息融合与控制重点实验室(长安大学)开放基金资助项目(300102323502).
Corresponding Authors: He HUANG     E-mail: 2022132053@chd.edu.cn;huanghe@chd.edu.cn
Cite this article:

Xialu WEN,He HUANG,Huifeng WANG,Lan YANG,Tao GAO. Optimization of 3D multi-UAVs low altitude penetration based on bald eagle search algorithm. Journal of ZheJiang University (Engineering Science), 2024, 58(10): 2020-2030.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.10.005     OR     https://www.zjujournals.com/eng/Y2024/V58/I10/2020


基于秃鹰搜索算法优化的三维多无人机低空突防

三维空间环境复杂,多无人机的低空突防航迹规划计算量大,现有多目标秃鹰搜索算法存在求解易趋于中心点及精度低的缺陷,为此提出基于改进多目标秃鹰搜索算法(IMBES)的三维多无人机低空突防方法. 构建三维环境模型、威胁源模型、无人机物理约束模型、多无人机协同约束模型以及路径平滑度约束模型,确定多目标代价函数. 设计耦合混沌映射初始化,有效提高初始化种群质量;设计基于“侦察鹰”的自适应高斯游走策略,平衡开发与搜索能力;引入快速非支配排序,进一步提高算法效率. 利用秃鹰位置与无人机速度、转弯角度、爬升角度的对应关系,采用IMBES高效搜索无人机构型空间,找到最优的帕累托前沿. 实验结果表明,IMBES的成功率为70.5%. 与现有路径规划方法相比,所提方法的优化能力强、能耗低,适用于多无人机协同低空突防.


关键词: 多无人机,  低空突防,  自主避障,  多目标算法,  秃鹰搜索算法 
Fig.1 Diagram of turning and climbing angles
Fig.2 Bifurcation diagram of seed mapping
Fig.3 Bifurcation diagram of coupling chaotic mapping
Fig.4 Cost curve comparison of coupling chaotic mapping strategy and original multi-objective bald eagle search algorithm
Fig.5 Cost curve comparison of adaptive Gauss walk strategy based on “scout eagle” and original multi-objective bald eagle search algorithm
Fig.6 Cost curve comparison of fast non-dominated sorting strategy and original multi-objective bald eagle search algorithm
测试函数NOF特点
ZDT12凸,连续
Kursawe2不连续,多模态
DTLZ23不连续,多模态
DTLZ53凹,多模态
DTLZ63凹,连续
Viennet33连续,多模态
Tab.1 Dimensions and characteristics of multi-objective testing functions
Fig.7 Box diagram of test results for different algorithms
算法nal=12nal=16nal=20
ltftt/sltftt/sltftt/s
MOSSA63.601366.3909.8953.583312.92613.2253.943250.57517.63
MOPOA63.422349.17111.2852.964449.86812.2354.267243.18016.81
MOGWO63.899546.9859.6753.025460.49512.9852.797230.54316.94
NSDBO62.343556.64714.5154.790556.07313.2051.940255.94217.83
NSGA-Ⅱ62.804335.40320.0853.104252.54130.0654.245227.36317.69
本研究59.898339.9988.7352.036234.20113.1150.353224.0517.90
Tab.2 Effect of track points on swarm intelligence optimization algorithms
算法主要参数
MOSSA[22]R2= 0.8, SD=0.1, PD=0.2
MOPOA[23]β=1.5, R=2
MOGWO[24]α=3, β=0.1
NSDBO[25]p1=0.2, p2=0.4, p3=0.63, k=0.1, b=0.3
NSGA-Ⅱ[26]交叉率为0.7, 变异率为0.4, μ=0.02, δ=0.2
Tab.3 Main parameter settings of different algorithms
参数数值参数数值
地形威胁系数$K_{_H}^i$100物理约束权值$ {\mathrm{\sigma }}_{1} $0.2
地形威胁系数$K_H^i{'}$10地形约束权值$ {\mathrm{\sigma }}_{2} $0.1
功率威胁系数KW100高程约束权值$ {\mathrm{\sigma }}_{3} $0.2
拐弯角威胁系数$ {K}_{\alpha } $10威胁源约束权值$ {\mathrm{\sigma }}_{4} $0.2
俯仰角威胁系数$ {K}_{\beta } $10平滑度约束权值$ {\mathrm{\sigma }}_{5} $0.15
续航时间威胁系数$ {K_{{t_{\mathrm{d}}}}} $10协同约束权值$ {\mathrm{\sigma }}_{6} $0.15
平滑度惩罚系数λ1λ20.5航迹点数d16
威胁源修正系数$ K_{_{{\mathrm{thr}}}}^m $1/3$ {{R^m_{\max,n}}} $
Tab.4 Main parameters of dual UAV path planning experiment
Fig.8 Path planning results of different algorithms
算法lm/kmfmls/kmfst/s
MOSSA53.583312.92652.821241.5644.059
MOPOA52.964449.86852.329238.5923.879
MOGWO53.025460.49552.232227.3933.144
NSDBO54.790556.07352.031257.0433.136
NSGA-Ⅱ53.104252.54152.730234.8503.114
本研究52.036234.20151.969225.5403.085
Tab.5 Comparison of quality of each algorithm (model one)
算法lm/kmfmls/kmfst/s
MOSSA503.59319.05487.89237.463.639
MOPOA512.93206.59499.44139.393.586
MOJS489.1292.04486.2580.733.290
NSDBO498.21248.64493.21166.523.281
NSGA-Ⅲ478.8617.28476.6416.833.258
LTG-NSMFO479.0341.21477.5621.443.238
本研究477.1316.56476.4914.743.105
Tab.6 Comparison of quality of each algorithm (model two)
Fig.9 Results of dual UAV collaborative planning
Fig.10 Flight altitude variation of dual UAV
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