复杂环境下无人机路径规划及其改进型人工兔优化

doi:10.16182/j.issn1004731x.joss.23-1103

摘要/Abstract

摘要：

针对复杂障碍物环境下无人机安全、高效飞行的路径规划问题，探讨其优化模型的设计与求解算法。模型设计中，以距离、角度、高度及飞行威胁代价为性能指标，以地域、空域障碍物为约束，建立基于权重系数法与柱坐标系的单性能指标路径规划模型；针对人工兔优化算法存在初始种群分布不均匀、勘探能力和开采能力不平衡，以及局部搜索能力不足的问题，利用SPM混沌映射改善初始种群分布；借助精英个体引导策略增强局部搜索能力；利用改进型能量收缩策略平衡全局与局部搜索能力，提出一种计算复杂度由种群规模确定且能求解大规模优化问题的改进型人工兔优化算法。实验表明，已获路径规划模型的路径规划方案能在一定程度上缓解航迹点数的增加对求解性能的影响，同时优化算法处理大规模优化问题及复杂障碍物威胁环境下无人机路径规划问题具有明显优势。

关键词: 无人机路径规划, 人工兔优化, 柱坐标系, 大规模优化, 精英个体引导策略

Abstract:

The work probes into the model design of reliable and effective UAV path planning in complex obstacle environments and its related optimization algorithm. In the model design, a weight coefficient method and cylindrical coordinate system-based single-objective path planning model is developed to solve the UAV's flight path, in which the distance, angle, height and threat cost are taken as performance indices and obstacles in the ground and spatial regions are regarded as constraints. In the algorithm design, the SPM chaotic mapping is used to improve the initial population distribution of the artificial rabbit optimization algorithm in view of the problems of uneven distribution of the initial population, the imbalance between exploration and exploitation capacities and the insufficient local search capacity. The local search ability is enhanced by the elite individual guidance strategy. An improved artificial rabbits optimization algorithm with computational complexity determined by population size is proposed to solve large-scale optimization problems. The comparative experiments have validated that, the path planning model is available and can alleviate the influence of the increasing number of track points to the quality of the path planning scheme, and at the same time the improved algorithm can effectively handle high-dimensional optimization problems and is of potential value for the UAV path planning problem.

Key words: UAV path planning, artificial rabbit optimization, cylindrical coordinate system, large-scale optimization, elite individual guidance strategy

中图分类号:

TP391.9

尹安琳,张著洪 . 复杂环境下无人机路径规划及其改进型人工兔优化[J]. 系统仿真学报, 2025, 37(1): 79-94.

Yin Anlin,Zhang Zhuhong . UAV Path Planning in Complex Environments and Its Improved Artificial Rabbits Optimization Algorithm[J]. Journal of System Simulation, 2025, 37(1): 79-94.

图/表 14

图1

图2

表1

各算法获得统计结果比较

测试函数	$Q$	CDO	SOA	GOA	GJO	SSA	WOA	ARO	IARO
$f 1$	$μ$	1.28E-107	7.21E+01	5.00E-02	4.59E-07	3.44E+05	7.76E-82	2.15E-51	6.83E-172
$f 1$	$σ$	1.19E-107	5.12E+00	2.23E-01	3.17E-07	1.28E+04	2.62E-81	4.26E-51	0
$f 2$	$μ$	5.95E-37	5.71E-02	1.36E+281	9.44E-06	2.05E+03	3.53E-52	2.43E-27	1.17E-91
$f 2$	$σ$	2.12E-36	1.88E-02	9.49E+281	3.11E-06	1.98E+01	6.99E-52	5.26E-27	3.56E-91
$f 3$	$μ$	3.50E+07	3.16E+06	1.76E+06	1.25E+06	1.35E+07	4.21E+08	7.57E-33	7.53E-169
$f 3$	$σ$	1.11E+08	1.75E+06	7.15E+05	4.24E+05	5.58E+06	1.05E+08	1.59E-32	0
$f 4$	$μ$	7.66E-39	9.98E+01	3.78E+01	9.33E+01	3.97E+01	7.75E+01	6.93E-19	2.05E-86
$f 4$	$σ$	1.52E-38	7.52E-02	3.49E+01	1.84E+00	2.25E+00	1.92E+01	9.86E-19	8.15E-86
$f 5$	$μ$	1.99E+03	1.05E+05	1.14E+05	2.00E+03	1.34E+08	1.99E+03	3.70E+01	1.55E+01
$f 5$	$σ$	2.17E-01	7.98E+04	3.32E+05	2.36E-01	8.13E+06	1.33E+00	4.02E+01	8.34E+00
$f 6$	$μ$	0	2.73E+01	5.00E-02	5.00E-02	3.61E+05	0	0	0
$f 6$	$σ$	0	1.53E+01	2.24E-01	2.24E-01	1.38E+04	0	0	0
$f 7$	$μ$	7.56E-05	2.86E+00	2.21E+00	2.20E-02	4.01E+03	2.03E-03	9.08E-04	2.47E-04
$f 7$	$σ$	6.60E-05	1.61E+00	9.82E+00	8.91E-03	3.25E+02	3.57E-03	6.80E-04	1.86E-04
$f 8$	$μ$	-2.35E+04	-4.81E+04	-6.27E+04	-7.44E+04	-1.38E+05	-7.15E+05	-1.42E+05	-1.49E+05
$f 8$	$σ$	1.89E+03	7.06E+03	6.13E+03	3.01E+04	7.22E+03	1.15E+05	4.28E+03	4.13E+03
$f 9$	$μ$	1.26E+00	2.61E+01	4.87E-01	1.18E-08	1.61E+04	3.64E-13	0	0
$f 9$	$σ$	1.54E+00	2.67E+01	2.18E+00	1.30E-08	2.14E+02	1.12E-12	0	0
$f 10$	$μ$	4.44E-15	2.00E+01	2.77E-01	1.26E-05	1.32E+01	3.91E-15	8.88E-16	8.88E-16
$f 10$	$σ$	0	5.52E-06	1.24E+00	2.19E-06	1.39E-01	2.38E-15	0	0
$f 11$	$μ$	0	3.42E-01	1.04E-02	2.14E-08	3.09E+03	2.22E-17	0	0
$f 11$	$σ$	0	2.22E-01	4.22E-02	1.74E-08	1.03E+02	4.56E-17	0	0
$f 12$	$μ$	1.19E+00	9.26E+04	1.39E+00	1.31E+00	4.96E+06	4.44E-02	1.03E-02	7.44E-03
$f 12$	$σ$	4.56E-16	1.42E+05	1.65E+00	7.65E-01	1.18E+06	1.89E-02	3.26E-03	2.32E-03
$f 13$	$μ$	1.99E+02	4.72E+04	2.00E+02	2.01E+02	1.23E+08	3.81E+01	9.31E+00	5.64E+00
$f 13$	$σ$	1.69E+00	9.93E+04	2.49E+00	3.15E+00	1.39E+07	1.59E+01	4.87E+00	2.73E+00
w/t/l		10/2/1	13/0/0	13/0/0	13/0/0	13/0/0	11/1/1	9/4/0	/

表1

图3

表2

表3

算法的飞行代价目标值比较

场景	函数指标	CDO	SOA	GOA	GJO	SSA	WOA	ARO	IARO
1	$μ$	774.6	787.0	739.1	735.1	758.8	930.4	710.3	685.9
	$σ$	31.4	55.5	29.0	44.7	74.2	60.6	31.4	20.1
	$A T$	8.2	7.7	16.7	8.1	7.9	7.8	8.0	7.3
2	$μ$	961.4	892.9	839.9	833.1	872.3	1 131.0	819.4	778.2
	$σ$	73.2	92.0	40.7	47.9	101.2	105.4	40.5	36.5
	$A T$	10.9	9.9	20.1	10.6	11.5	10.5	10.7	10.2
3	$μ$	1 041.8	1 001.0	965.6	944.4	944.5	1 232.3	970.3	814.0
	$σ$	31.7	54.6	87.9	92.5	98.3	83.2	51.6	55.6
	$A T$	15.3	13.8	31.1	15.1	14.9	15.5	13.6	13.4

表3

图4

图5

图6

表4

图7

图8

表5

图9

参考文献 27

1	Hu Gang, Zhong Jingyu, Wei Guo. SaCHBA_PDN: Modified Honey Badger Algorithm with Multi-strategy for UAV Path Planning[J]. Expert Systems with Applications, 2023, 223: 119941.
2	Zhang Chaoqun, Zhou Wenjuan, Qin Weidong, et al. A Novel UAV Path Planning Approach: Heuristic Crossing Search and Rescue Optimization Algorithm[J]. Expert Systems with Applications, 2023, 215: 119243.
3	李安醍, 武丁杰, 李诚龙. 低空无人机自主避障算法综述[J]. 电光与控制, 2021, 28(8): 59-64.
	Li Anti, Wu Dingjie, Li Chenglong. A Survey on Autonomous Collision Avoidance Algorithms for UAVs at Low Altitude[J]. Electronics Optics & Control, 2021, 28(8): 59-64.
4	Wang Xing, Pan J S, Yang Qingyong, et al. Modified Mayfly Algorithm for UAV Path Planning[J]. Drones, 2022, 6(5): 134.
5	Arturo De Marinis, Iavernaro Felice, Mazzia Francesca. A Minimum-time Obstacle-avoidance Path Planning Algorithm for Unmanned Aerial Vehicles[J]. Numerical Algorithms, 2022, 89(4): 1639-1661.
6	柯永斌, 谢田, 姜程文, 等. 基于改进袋獾优化算法的无人机路径规划[J]. 电子器件, 2023, 46(2): 397-403.
	Ke Yongbin, Xie Tian, Jiang Chengwen, et al. Path Planning of UAV Based on Improved Tasmanian Devil Optimization Algorithm[J]. Chinese Journal of Electron Devices, 2023, 46(2): 397-403.
7	陈明强, 李奇峰, 冯树娟, 等. 基于改进粒子群算法的无人机三维航迹规划[J]. 无线电工程, 2023, 53(2): 394-400.
	Chen Mingqiang, Li Qifeng, Feng Shujuan, et al. Three-dimensional Trajectory Planning of UAV Based on Improved Particle Swarm Optimization Algorithm[J]. Radio Engineering, 2023, 53(2): 394-400.
8	Amylia Ait Saadi, Soukane Assia, Meraihi Yassine, et al. UAV Path Planning Using Optimization Approaches: A Survey[J]. Archives of Computational Methods in Engineering, 2022, 29(6): 4233-4284.
9	Srinivasan T, Bhandari S. Path-planning Around Obstacles for a Quadrotor UAV Using the RRT Algorithm for Indoor Environments[C]//AIAA Infotech @ Aerospace. Reston: AIAA, 2016: AIAA 2016-2196.
10	Scherer S, Singh S, Chamberlain L, et al. Flying Fast and Low Among Obstacles: Methodology and Experiments[J]. The International Journal of Robotics Research, 2008, 27(5): 549-574.
11	Schøler Flemming, Anders la Cour-Harbo, Bisgaard Morten. Generating Approximative Minimum Length Paths in 3D for UAVs[C]//2012 IEEE Intelligent Vehicles Symposium. Piscataway: IEEE, 2012: 229-233.
12	Chai Xuzhao, Zheng Zhishuai, Xiao Junming, et al. Multi-strategy Fusion Differential Evolution Algorithm for UAV Path Planning in Complex Environment[J]. Aerospace Science and Technology, 2022, 121: 107287.
13	Hu Gang, Du Bo, Wang Xiaofeng, et al. An Enhanced Black Widow Optimization Algorithm for Feature Selection[J]. Knowledge-Based Systems, 2022, 235: 107638.
14	Manh Duong Phung, Quang Phuc Ha. Safety-enhanced UAV Path Planning with Spherical Vector-based Particle Swarm Optimization[J]. Applied Soft Computing, 2021, 107: 107376.
15	舒纬伟, 敬忠良, 董鹏. 基于乌贼算法的无人机航迹规划[J]. 科学技术与工程, 2017, 17(2): 120-125.
	Shu Weiwei, Jing Zhongliang, Dong Peng. UAV Trajectory Planning Based on Cuttlefish Algorithm[J]. Science Technology and Engineering, 2017, 17(2): 120-125.
16	Zhang Daifeng, Duan Haibin. Social-class Pigeon-inspired Optimization and Time Stamp Segmentation for Multi-UAV Cooperative Path Planning[J]. Neurocomputing, 2018, 313: 229-246.
17	Huang Chen, Zhou Xiangbing, Ran Xiaojuan, et al. Adaptive Cylinder Vector Particle Swarm Optimization with Differential Evolution for UAV Path Planning[J]. Engineering Applications of Artificial Intelligence, 2023, 121: 105942.
18	Wang Liying, Cao Qingjiao, Zhang Zhenxing, et al. Artificial Rabbits Optimization: A New Bio-inspired Meta-heuristic Algorithm for Solving Engineering Optimization Problems[J]. Engineering Applications of Artificial Intelligence, 2022, 114: 105082.
19	班多晗, 吕鑫, 王鑫元. 基于一维混沌映射的高效图像加密算法[J]. 计算机科学, 2020, 47(4): 278-284.
	Ban Duohan, Xin Lü, Wang Xinyuan. Efficient Image Encryption Algorithm Based on 1D Chaotic Map[J]. Computer Science, 2020, 47(4): 278-284.
20	Haklı Hüseyin, Uğuz Harun. A Novel Particle Swarm Optimization Algorithm with Levy Flight[J]. Applied Soft Computing, 2014, 23: 333-345.
21	Shehadeh Hisham A. Chernobyl Disaster Optimizer (CDO): A Novel Meta-heuristic Method for Global Optimization[J]. Neural Computing and Applications, 2023, 35(15): 10733-10749.
22	Dhiman Gaurav, Kumar Vijay. Seagull Optimization Algorithm: Theory and Its Applications for Large-scale Industrial Engineering Problems[J]. Knowledge-Based Systems, 2019, 165: 169-196.
23	Agushaka Jeffrey O, Absalom E Ezugwu, Abualigah Laith. Gazelle Optimization Algorithm: A Novel Nature-inspired Metaheuristic Optimizer[J]. Neural Computing and Applications, 2023, 35(5): 4099-4131.
24	Chopra Nitish, Muhammad Mohsin Ansari. Golden Jackal Optimization: A Novel Nature-inspired Optimizer for Engineering Applications[J]. Expert Systems with Applications, 2022, 198: 116924.
25	Mirjalili Seyedali, Gandomi A H, Seyedeh Zahra Mirjalili, et al. Salp Swarm Algorithm: A Bio-inspired Optimizer for Engineering Design Problems[J]. Advances in Engineering Software, 2017, 114: 163-191.
26	Mirjalili Seyedali, Lewis Andrew. The Whale Optimization Algorithm[J]. Advances in Engineering Software, 2016, 95: 51-67.
27	Mirjalili Seyedali, Seyed Mohammad Mirjalili, Hatamlou Abdolreza. Multi-verse Optimizer: A Nature-inspired Algorithm for Global Optimization[J]. Neural Computing and Applications, 2016, 27(2): 495-513.

场景	起点坐标	终点坐标	圆柱型威胁个数	球型威胁个数	航迹点数
1	(150,150,100)	(900,900,100)	4	2	8
2	(150,150,100)	(900,900,100)	6	3	10
3	(900,900,100)	(150,150,100)	8	4	12
4	(150,150,100)	(900,820,100)	11	5
5	(180,190,100)	(1800,1810,100)	24	5

场景	航迹点数代价函数	20	40	60	80	110	140	170	200
4	距离	1 428.9	1 258.1	1 293.6	1 198.4	1 225.2	1 253.7	1 230.8	1 215.3
	转向角	0	46.8	155.4	558.6	1 546.3	1 460.9	1 561.4	1 039.5
	爬升角	69.7	163.8	551.5	511.0	1 390.7	1 242.9	1 263.2	1 009.4
	高度	80.9	497.0	864.2	1 262.8	2 667.1	3 994.7	4 875.2	7 603.8
	威胁	39.3	103.2	115.5	160.7	277.5	412.1	452.8	478.7
	目标值	482.0	648.5	938.7	1 165.7	2 107.3	2 880.0	3 393.5	4 926.5
5	距离	2 627.5	2 833.5	2 661.0	2 684.3	2 518.1	2 580.5	2 614.6	2 575.3
	转向角	12.3	13.4	54.8	123.6	419.3	699.9	2 118.3	909.6
	爬升角	42.3	48.6	212.5	522.4	323.7	1 049.8	1 629.5	1 146.2
	高度	108.7	366.1	528.9	777.1	965.7	2 758.3	2 939.4	3 990.0
	威胁	8.3	12.3	18.6	26.7	175.9	155.5	244.9	329.0
	目标值	855.1	1 066.9	1 122.2	1 296.4	1 370.6	2 488.3	2 728.8	3 229.8

代价函数	无人机直径
代价函数	0.5	1.0	1.5
距离	2 770.8	2 376.8	2 759.8
转向角	936.6	59.8	513.7
爬升角	679.0	793.4	761.2
高度	1 389.9	704.3	1 375.2
威胁	163.7	161.9	174.2
目标值	1 829.3	1 182.5	1 803.1

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