多障碍场景下基于多策略进化机制的无人机三维路径规划

朱润泽; 赵静; 陆宁云; 马亚杰; 宋来收

doi:10.16383/j.aas.c250319

多障碍场景下基于多策略进化机制的无人机三维路径规划

doi: 10.16383/j.aas.c250319 cstr: 32138.14.j.aas.c250319

1.
南京邮电大学南京 210023
2.
南京航空航天大学南京 210016

基金项目: 航空航天结构力学及控制国家重点实验室开放课题(MCMS-E-0123G04), 直升机动力学全国重点实验室开放课题(2024-ZSJ-LB-02-05), 江苏省研究生科研与实践创新计划项目(KYCX24_1214)资助

详细信息

作者简介:
朱润泽：南京邮电大学硕士研究生. 2023年获得南通大学学士学位. 主要研究方向为机器人路径规划. E-mail: 19850968797@163.com

赵静：南京邮电大学自动化学院副教授. 2014年获得南京航空航天大学博士学位. 主要研究方向为智能无人系统, 旋翼无人机的容错控制. 本文通信作者. E-mail: zhaojing@njupt.edu.cn

陆宁云：南京航空航天大学自动化学院教授. 2004年获得东北大学博士学位. 主要研究方向为故障诊断和寿命预测. E-mail: luningyun@nuaa.edu.cn

马亚杰：南京航空航天大学自动化学院教授. 2015年获得南京航空航天大学博士学位. 主要研究方向为飞行器智能故障诊断与容错控制, 智能体系统任务规划. E-mail: yajiema@nuaa.edu.cn

宋来收：南京航空航天大学自动化学院副研究员. 2014年获得南京航空航天大学博士学位. 主要研究方向为旋翼机动力学及结构设计. E-mail: lss05012@nuaa.edu.cn

计量
- 文章访问数: 13
- HTML全文浏览量: 12
- 被引次数: 0
出版历程
- 收稿日期: 2025-07-13
- 录用日期: 2025-11-26
- 网络出版日期: 2026-01-27

UAV Three-Dimension Path Planning Based on Multi-strategy Evolution Mechanism in Multi-Obstacle Scenarios

1.
Nanjing University of Posts and Telecommunications, Nanjing 210023
2.
Nanjing University of Aeronautics and Astronautics, Nanjing 210016

Funds: Supported by State Key Laboratory of Aerospace Structural Mechanics and Control (MCMS-E-0123G04), National Key Laboratory Foundation of Helicopter Aeromechanics (2024-ZSJ-LB-02-05), and Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX24_1214)

More Information

Author Bio:
Zhu Run-Ze　Master student of Nanjing University of Posts and Telecommunications. He received his bachelor degree from Nantong University in 2023. His main research interest is path planning of robot

Zhao Jing　Associate professor at the College of Automation, Nanjing University of Posts and Telecommunications. She received her Ph.D. degree from Nanjing University of Aeronautics and Astronautics in 2014. Her research interests include intelligent unmanned systems and fault-tolerant control of UAVs. Corresponding author of this paper

Lu Ning-Yun　Professor at the College of Automation, Nanjing University of Aeronautics and Astronautics. She received her Ph.D. degree from Northeastern University in 2004. Her research interests include fault diagnosis and life prediction

Ma Ya-Jie　Professor at the College of Automation, Nanjing University of Aeronautics and Astronautics. He received his Ph.D. degree from Nanjing University of Aeronautics and Astronautics in 2015. His research interests include intelligent fault diagnosis and fault-tolerant control of aircraft, and task planning of multi-agent systems

Song Lai-Shou　Associate researcher at the College of Automation, Nanjing University of Aeronautics and Astronautics. He received his Ph.D. degree from Nanjing University of Aeronautics and Astronautics in 2014. His research interests include rotorcraft dynamics and structural design

摘要

摘要: 针对无人机(UAV)在三维多障碍物场景下路径规划存在的收敛精度低、稳定性不足等问题, 提出一种多策略进化粒子群算法(MSEPSO). 在初始化阶段, 针对粒子群算法(PSO)对粒子初始位置敏感的问题, 采用拉丁超立方采样(LHS)优化粒子初始分布, 提高种群多样性; 在进化阶段, 设计“平衡−记忆−增强”进化框架, 即利用非线性迭代策略来平衡全局开发和局部搜索, 采用个体历史记忆启发机制(PHMM)增强算法的全局开发能力, 并引入进化粒子, 增强种群对于群体极值附近空间的探索能力, 降低算法陷入局部最优的概率. 在CEC2020测试函数集上与山地/城市场景下的对比实验结果表明, MSEPSO展现出了稳定的寻优性能, 可以规划长度更短、平滑度更高的安全路径.
- 无人机 /
- 三维路径规划 /
- 粒子群算法 /
- 多策略进化
Abstract: Aiming at the problems such as low convergence accuracy and insufficient stability in path planning for unmanned aerial vehicles (UAVs) in three-dimensional multi-obstacle scenarios, a multi-strategy evolutionary particle swarm optimization (MSEPSO) algorithm is proposed. In the initialization stage, aiming at the problem that particle swarm optimization is sensitive to the initial position of particles, the initial distribution of particles is optimized through Latin hypercube sampling to improve the population diversity; During the evolutionary stage, a “balance-memory-enhancement” evolutionary framework was designed, which utilized a nonlinear iterative strategy to balance global development and local search. The personal history memory mechanism was adopted to enhance the global exploitation ability of the algorithm. Evolutionary particles were introduced to enhance the exploration ability of the population in the vicinity of the group＇s extreme values, reducing the probability of the algorithm getting stuck in local optima. Experimental results from comparisons on the CEC2020 test function set and in mountain/urban scenarios demonstrate that MSEPSO exhibits stable optimization performance, enabling the planning of safer paths with shorter lengths and higher smoothness.
- uav /
- 3D path planning /
- particle swarm optimization /
- multi-strategy evolution

HTML全文

图 1 环境建模

Fig. 1 Environment model

下载: 全尺寸图片幻灯片

图 2 基于不同采样策略生成1000个随机数

Fig. 2 Generate 1000 random numbers based on different sampling strategies

下载: 全尺寸图片幻灯片

图 3 参数非线性迭代策略

Fig. 3 Nonlinear iterative strategy of parameters

下载: 全尺寸图片幻灯片

图 4 基于PHMM启发粒子探索

Fig. 4 Particle exploration inspired by PHMM

下载: 全尺寸图片幻灯片

图 5 基于进化粒子逼近最优解

Fig. 5 Approach to optimal solution based on evolutionary particles

下载: 全尺寸图片幻灯片

图 6 基于CEC2020基准函数的适应度值曲线

Fig. 6 Fitness curve based on CEC2020 basical function

下载: 全尺寸图片幻灯片

图 7 不同场景下的路径对比图

Fig. 7 Path comparison in various scenarios

下载: 全尺寸图片幻灯片

图 8 不同场景下的适应度曲线对比图

Fig. 8 Fitness curve comparison in various scenarios

下载: 全尺寸图片幻灯片

表 1 基于10-D CEC2020基准函数的数值实验

Table 1 Numerical experiments based on 10-D CEC2020 benchmark functions

		PSO	LPSO	PSO-SA	ACVPSO	WOA	SHO	HHO	DBO	MSEPSO
F1	B	1.893E+07	1.000E+03	7.981E+06	5.071E+03	9.614E+05	1.105E+06	5.737E+04	4.140E+09	1.001E+02
	W	5.174E+09	4.415E+09	1.142E+10	6.100E+09	1.230E+10	4.426E+09	2.765E+06	3.774E+10	1.274E+04
	M	9.222E+08	3.598E+08	1.914E+09	7.338E+07	6.539E+08	3.973E+08	5.985E+05	1.913E+10	3.744E+03
	V	7.913E+17	4.678E+17	2.644E+18	1.237E+17	1.492E+18	3.631E+17	9.071E+10	3.617E+19	1.101E+07
F2	B	1.300E+03	1.176E+03	1.234E+03	1.236E+03	1.328E+03	1.236E+03	1.274E+03	2.547E+03	1.129E+03
	W	3.009E+03	3.023E+03	3.809E+03	3.296E+03	3.494E+03	2.860E+03	2.729E+03	3.913E+03	2.422E+03
	M	2.325E+03	2.034E+03	2.455E+03	2.190E+03	2.337E+03	2.061E+03	2.010E+03	3.352E+03	1.815E+03
	V	6.864E+04	1.092E+05	2.010E+05	1.225E+05	1.283E+05	5.768E+04	7.708E+04	5.539E+04	1.003E+04
F3	B	7.410E+02	7.100E+02	7.260E+02	7.180E+02	7.290E+02	7.270E+02	7.220E+02	7.880E+02	7.090E+02
	W	8.890E+02	7.870E+02	9.500E+02	8.560E+02	9.090E+02	8.090E+02	8.440E+02	1.340E+03	7.870E+02
	M	7.870E+02	7.390E+02	7.620E+02	7.630E+02	7.910E+02	7.590E+02	7.850E+02	1.010E+03	7.450E+02
	V	1.790E+02	1.810E+02	5.140E+02	5.020E+02	5.780E+02	1.710E+02	4.530E+02	1.260E+04	1.740E+02
F4	B	1.904E+03	1.900E+03	1.902E+03	1.901E+03	1.902E+03	1.904E+03	1.900E+03	3.410E+03	1.900E+03
	W	1.526E+05	3.840E+03	1.098E+05	3.440E+03	8.571E+04	8.797E+04	1.921E+03	3.074E+06	1.905E+03
	M	2.227E+03	1.987E+03	2.545E+03	1.924E+03	3.048E+03	2.713E+03	1.908E+03	2.978E+05	1.902E+03
	V	2.280E+07	4.104E+04	2.202E+07	6.884E+03	3.645E+07	1.817E+07	8.804E+00	7.966E+10	7.103E-01
F5	B	4.636E+03	1.758E+03	4.178E+03	1.812E+03	3.518E+03	3.116E+03	2.690E+03	7.260E+04	1.754E+03
	W	4.258E+06	2.942E+06	4.426E+06	2.588E+06	4.022E+06	6.114E+05	2.762E+05	5.436E+07	1.660E+04
	M	1.524E+05	2.609E+04	3.046E+05	1.652E+04	5.891E+05	1.250E+05	3.694E+04	4.845E+06	2.425E+03
	V	2.207E+11	4.834E+10	6.701E+11	2.670E+10	5.060E+11	1.719E+10	1.624E+09	4.373E+13	3.242E+05
F6	B	1.610E+03	1.601E+03	1.603E+03	1.602E+03	1.603E+03	1.601E+03	1.602E+03	1.900E+03	1.601E+03
	W	2.452E+03	2.615E+03	2.657E+03	2.445E+03	2.365E+03	2.088E+03	2.301E+03	3.288E+03	1.975E+03
	M	1.858E+03	1.834E+03	1.994E+03	1.860E+03	1.892E+03	1.767E+03	1.833E+03	2.562E+03	1.716E+03
	V	1.763E+04	1.833E+04	2.662E+04	2.207E+04	1.953E+04	8.210E+03	1.557E+04	5.267E+04	6.462E+03
F7	B	2.777E+03	2.112E+03	2.334E+03	2.104E+03	2.971E+03	2.202E+03	2.269E+03	7.448E+03	2.103E+03
	W	3.541E+06	3.541E+06	7.669E+06	3.541E+06	1.497E+06	2.011E+05	2.449E+05	2.621E+07	4.111E+03
	M	7.344E+04	2.477E+04	1.569E+05	4.227E+04	3.757E+05	1.053E+04	1.350E+04	2.926E+06	2.610E+03
	V	2.046E+11	7.235E+10	6.043E+11	1.339E+11	1.033E+12	2.370E+08	3.252E+08	6.092E+12	6.713E+04
F8	B	2.254E+03	2.222E+03	2.254E+03	2.229E+03	2.225E+03	2.220E+03	2.221E+03	2.415E+03	2.213E+03
	W	3.796E+03	4.052E+03	5.085E+03	4.065E+03	4.544E+03	3.681E+03	4.016E+03	5.117E+03	3.450E+03
	M	2.375E+03	2.342E+03	2.465E+03	2.341E+03	2.449E+03	2.366E+03	2.336E+03	3.970E+03	2.305E+03
	V	1.076E+04	1.892E+04	7.994E+04	1.807E+04	1.299E+05	1.410E+04	2.766E+04	2.444E+05	4.133E+03
F9	B	2.530E+03	2.500E+03	2.508E+03	2.501E+03	2.501E+03	2.502E+03	2.501E+03	2.790E+03	2.400E+03
	W	2.890E+03	2.931E+03	2.919E+03	3.071E+03	3.038E+03	2.851E+03	2.975E+03	3.254E+03	2.784E+03
	M	2.773E+03	2.730E+03	2.796E+03	2.774E+03	2.787E+03	2.765E+03	2.796E+03	2.969E+03	2.743E+03
	V	2.705E+03	4.136E+03	2.554E+03	5.596E+03	5.747E+03	4.010E+03	7.850E+03	4.251E+03	2.754E+03
F10	B	2.882E+03	2.600E+03	2.657E+03	2.633E+03	2.650E+03	2.654E+03	2.614E+03	3.073E+03	2.600E+03
	W	3.356E+03	3.310E+03	4.056E+03	3.300E+03	3.240E+03	3.179E+03	3.056E+03	6.467E+03	3.024E+03
	M	2.992E+03	2.956E+03	3.027E+03	2.951E+03	2.972E+03	2.937E+03	2.934E+03	4.307E+03	2.930E+03
	V	1.874E+03	2.961E+03	9.400E+03	2.028E+03	3.124E+03	1.649E+03	1.576E+03	2.929E+05	1.178E+03

下载: 导出CSV

表 2 算法参数

Table 2 Algorithm parameters

算法	参数	取值
PSO	惯性权重	1
	学习因子$ c_1 $和$ c_2 $	1.5, 1.5
	速度范围	[−10, 10]
LPSO	惯性权重范围	[0.3, 1.2]
	学习因子$ c_1 $和$ c_2 $	1.5, 1.5
	速度范围	[−10, 10]
PSO-SA	惯性权重	1
	学习因子$ c_1 $和$ c_2 $	1.5, 1.5
	速度范围	[−10, 10]
ACVDEPSO	惯性权重范围	[0.3, 1.2]
	个体因子范围	[0.1, 1.0]
	群体因子范围	[0.1, 1.0]
	速度范围	[−10, 10]
MSEPSO	惯性权重范围	[0.3, 1.2]
	学习因子$ c_1 $和$ c_2 $	取决于$ w $
	记忆衰减系数$ \mu $	0.5
	速度范围	[−10, 10]

下载: 导出CSV

表 3 适应度函数参数

Table 3 Fitness function parameters

参数	取值
$ \omega_1 $	1
$ \omega_2 $	0.1
$ \omega_3 $	10000
$ \omega_4 $	1000

下载: 导出CSV

表 4 不同场景下的实验数据

Table 4 Experimental data in various scenarios

场景	算法	最优解	最劣解	均值	方差
简单山地	PSO	169.646	179.254	173.620	12.406
	LPSO	168.709	177.567	174.373	14.606
	PSO-SA	168.436	179.876	172.464	12.885
	ACVDEPSO	169.797	176.635	173.958	7.560
	MSEPSO	164.126	166.190	165.019	0.562
复杂山地	PSO	173.037	194.175	178.897	79.749
	LPSO	174.499	185.884	178.400	21.195
	PSO-SA	169.102	187.409	179.600	56.882
	ACVDEPSO	166.905	192.133	178.073	89.173
	MSEPSO	164.785	169.644	166.695	6.522
城市场景1	PSO	185.967	195.121	189.353	12.045
	LPSO	324.035	487.195	420.122	5183.551
	PSO-SA	183.576	190.903	187.306	7.711
	ACVDEPSO	185.522	215.841	194.130	168.304
	MSEPSO	182.906	187.127	184.020	3.124
城市场景2	PSO	165.621	175.897	169.139	17.071
	LPSO	163.833	173.548	167.518	15.471
	PSO-SA	163.906	168.039	165.526	2.675
	ACVDEPSO	165.009	177.137	170.999	30.845
	MSEPSO	161.070	162.970	162.491	0.640

下载: 导出CSV

参考文献(32)

[1]	Liu M J, Zhang H X, Yang J, Zhang T Z, Zhang C H, Bo L. A path planning algorithm for three-dimensional collision avoidance based on potential field and B-spline boundary curve. Aerospace Science and Technology, 2024, 144, DOI: 10.1016/j.ast.2023.108763
[2]	陈锦涛, 李鸿一, 任鸿儒, 鲁仁全. 基于RRT森林算法的高层消防多无人机室内协同路径规划. 自动化学报, 2023, 49(12): 2615−2626 doi: 10.16383/j.aas.c210368 Chen Jin-Tao, Li Hong-Yi, Ren Hong-Ru, Lu Ren-Quan. Cooperative indoor path planning of multi-UAVs for high-rise fire fighting based on RRT-forest algorithm. Acta Automatica Sinica, 2023, 49(12): 2615−2626 doi: 10.16383/j.aas.c210368
[3]	Savkin A V, Huang C, Ni W. Joint Multi-UAV Path Planning and LoS Communication for Mobile-Edge Computing in IoT Networks with RISs. IEEE Internet of Things Journal, 2023, 10(3): 2720−2727 doi: 10.1109/JIOT.2022.3215255
[4]	Rückin J, Magistri F, Stachniss C, Popovic M. An Informative Path Planning Framework for Active Learning in UAV-Based Semantic Mapping. IEEE Transactions on Robotics, 2023, 39(6): 4279−4296 doi: 10.1109/TRO.2023.3313811
[5]	Liu C, Jiang B, Patton R J, Zhang K. Integrated Fault-Tolerant Control for Close Formation Flight. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(2): 839−852 doi: 10.1109/TAES.2019.2920221
[6]	Ma J, Ma X, Zang S. Multi-destination Path Planning Based on Ant Colony Decision and Rolling Control. IEEE Transactions on Aerospace and Electronic Systems, 2024, 60(6): 8667−8681 doi: 10.1109/TAES.2024.3434777
[7]	Chen Y Q, Yu Q Z, Han D, Jiang H. UAV path planning: Integration of grey wolf algorithm and artificial potential field. Concurrency and Computation-practice & Experience, 2024, DOI: 10.1002/cpe.8120
[8]	蒋林, 李峻, 马先重. 一种改进骨架提取的Voronoi路径规划. 机械工程学报, 2020, 56(13): 1388−148 doi: 10.3901/JME.2020.13.138 Jiang Lin, Li Jun, Ma Xian-Chong. Voronoi path planning based on improved skeleton extraction. Journal of Mechanical Engineering, 2020, 56(13): 1388−148 doi: 10.3901/JME.2020.13.138
[9]	Zhang Y, Su Y, Yang J, Ponce J, Kong H. When Dijkstra Meets Vanishing Point: A Stereo Vision Approach for Road Detection. Journal of Mechanical Engineering, 2018, 27(5): 2176−2188 doi: 10.1109/TIP.2018.2792910
[10]	张凯翔, 毛剑琳, 向凤红, 宣志玮. 基于讨价还价博弈机制的B-IHCA多机器人路径规划算法. 自动化学报, 2023, 49(7): 1483−1497 doi: 10.16383/j.aas.c220065 Zhang Kai-Xiang, Mao Jian-Lin, Xiang Feng-Hong, Xuan Zhi-Wei. B-IHCA, a bargaining game based multi-agent path finding algorithm. Acta Automatica Sinica, 2023, 49(7): 1483−1497 doi: 10.16383/j.aas.c220065
[11]	Huang C, Zhou X B, Ran X J, Wang J M, Chen H Y, Deng W. Adaptive cylinder vector particle swarm optimization with differential evolution for UAV path planning. Engineering Applications of Artificial Intelligence, 2023, 121, DOI: 10.1016/j.engappai.2023.105942
[12]	Patle B K, Babu L G, Pandey A. A Review: On Path Planning Strategies for Navigation of Mobile Robot. Defence Technology, 2019, 15(4): 582−606 doi: 10.1016/j.dt.2019.04.011
[13]	朱润泽, 赵静, 蒋国平, 肖敏, 徐丰羽. 基于改进粒子群算法的无人机三维路径规划. 南京邮电大学学报(自然科学版), 2024, 44(6): 120−127 doi: 10.14132/j.cnki.1673-5439.2024.06.012 Zhu Run-Ze, Zhao Jing, Jiang Guo-Ping, Xiao Min, Xu Feng-Yu. UAV 3D path planning based on improved particle swarm optimization algorithm. Journal of Nanjing University of Posts and Telecommunications (Natural Science Edition), 2024, 44(6): 120−127 doi: 10.14132/j.cnki.1673-5439.2024.06.012
[14]	Tang F F, Li K Y, Xu F, Han L, Zhang H, Yang Z X. Optimal ant colony algorithm for UAV airborne LiDAR route planning in densely vegetated areas. Journal of Applied Remote Sensing, 2023, 17(4), DOI: 10.1117/1.JRS.17.046506
[15]	刘景森, 吉宏远, 李煜. 基于改进蝙蝠算法和三次样条插值的机器人路径规划. 自动化学报, 2021, 47(7): 1710−1719 doi: 10.16383/j.aas.c180855 Liu Jin-Seng, Ji Hong-Yuan, Li Yu. Robot path planning based on improved bat algorithm and cubic spline interpolation. Acta Automatica Sinica, 2021, 47(7): 1710−1719 doi: 10.16383/j.aas.c180855
[16]	Mirjalili S, Lewis A. The whale optimization algorithm. Advances in Engineering Software, 2016, 95: 51−67 doi: 10.1016/j.advengsoft.2016.01.008
[17]	Heidari A A, Mirjalili S, Faris H. Harris hawks optimization: Algorithm and applications. Future generation computer systems, 2019, 97: 849−872 doi: 10.1016/j.future.2019.02.028
[18]	Xue J K, Shen B. Dung beetle optimizer: a new meta-heuristic algorithm for global optimization. The Journal of Supercomputing, 2023, 79(7): 7305−7336 doi: 10.1007/s11227-022-04959-6
[19]	Zhao S, Zhang T, Ma S. Sea-horse optimizer: a novel nature-inspired meta-heuristic for global optimization problems. Applied Intelligence, 2023, 53(10): 11833−11860 doi: 10.1007/s10489-022-03994-3
[20]	Tian S, Li Y, Kang Y, Xia J. Multi-robot path planning in wireless sensor networks based on jump mechanism PSO and safety gap obstacle avoidance. Future Generation Computer Systems, 2021, 118: 37−47 doi: 10.1016/j.future.2020.12.012
[21]	Das P K, Behera H S, Das S, Tripathy H K, B.K. Panigrahi, S.K. Pradhan. A hybrid improved PSO-DV algorithm for multi-robot path planning in a clutter environment. Neurocomputing, 2016, 207: 735−753 doi: 10.1016/j.neucom.2016.05.057
[22]	Lin A P, Liu D, Li Z Q, Hasanien H M, Shi Y T. Heterogeneous differential evolution particle swarm optimization with local search. Complex and Intelligent Systems, 2023, 9(6): 6905−6925 doi: 10.1007/s40747-023-01082-8
[23]	Luo J, Liang Q, Li H. UAV penetration mission path planning based on improved holonic particle swarm optimization. Journal of Systems Engineering and Electronics, 2023, 34(1): 197−213 doi: 10.23919/JSEE.2022.000132
[24]	Huang C, Ma X, Zhou H, Deng W. Cooperative Path Planning of Multiple Unmanned Aerial Vehicles Using Cylinder Vector Particle Swarm Optimization With Gene Targeting. IEEE Sensors Journal, 2025, 25(5): 8470−8480 doi: 10.1109/JSEN.2024.3516124
[25]	Zhang C, Li Y, Zhou L. Optimal Path and Timetable Planning Method for Multi-Robot Optimal Trajectory. IEEE Robotics and Automation Letters, 2022, 7(3): 8130−8137 doi: 10.1109/LRA.2022.3187529
[26]	Haris M, Nam H. Path Planning Optimization of Smart Vehicle With Fast Converging Distance-Dependent PSO Algorithm. IEEE Open Journal of Intelligent Transportation Systems, 2024, 5: 726−739 doi: 10.1109/OJITS.2024.3486155
[27]	Gang L, Xinyuan G, Dong H, Kezhong C, Wu L. Multi-Platform Collaborative MRC-PSO Algorithm for Anti-Ship Missile Path Planning. Journal of Systems Engineering and Electronics, 2025, 36(2): 494−509 doi: 10.23919/JSEE.2025.000026
[28]	Wang Y, Hu F, Xu H, Zeng J. A Multigroups Cooperative Particle Swarm Algorithm for Optimization of Multivehicle Path Planning in Internet of Vehicles. IEEE Internet of Things Journal, 2024, 11(22): 35839−35851 doi: 10.1109/JIOT.2024.3367328
[29]	Yu Z H, Si Z J, Li X B, Wang D, Song H B. A Novel Hybrid Particle Swarm Optimization Algorithm for Path Planning of UAVs. IEEE Internet of Things Journal, 2022, 9(2): 22547−22558 doi: 10.1109/JIOT.2022.3182798
[30]	Lin S H, Liu A, Wang J G, Kong X Y. An intelligence-based hybrid PSO-SA for mobile robot path planning in warehouse. Journal of Computational Science, 2023, 67, DOI: 10.1016/j.jocs.2022.101938
[31]	Eberhart R, Kennedy J. A new optimizer using particle swarm theory. MHS'95 Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 1995: 39-43, DOI: 10.1109/MHS.1995.494215
[32]	Shi Y, EBERHART R. A modified particle swarm optimizer. IEEE.1998 Proceedings of the IEEE International Conference on Evolutionary Computation(CEC), 1998: 69-73, DOI: 10.1109/ICEC.1998.699146