基于复杂网络的城市低空飞行计划优化调度

doi:10.7527/S1000-6893.2025.31479

Abstract

Abstract:

With the development of the low-altitude economy， Urban Air Mobility （UAM） confronts the challenges in risk management and efficiency due to dense flight operations. This study addresses the pre-flight phase of urban low-altitude Unmanned Aerial Vehicle （UAV） swarms， and introduces a two-stage optimal scheduling approach for flight plans utilizing complex network. Initially， considering the potential third-party risks of UAV flight， the four-dimensional trajectory for individual UAVs is pre-planned within a digital airspace grid environment to generate an initial four-dimensional flight plan for the UAV swarm. Subsequently， to address flight uncertainty， a conflict detection model is proposed to construct a complex network where flight plans are nodes and conflicts are edges. Important flight plans are identified by analyzing topological metrics of the complex network. Finally， an integrated flight plan optimal scheduling model is established， incorporating strategies such as ground holding， speed adjustment， and local re-routing. A two-stage optimization algorithm frame is developed to globally optimize key flight plans and then locally adjust remaining conflicts， and is solved based on the improved Fata morgana algorithm. Experimental results demonstrate that this method can significantly reduce or eliminate flight conflicts considering flight uncertainty， ensuring that delayed flight plans constitute no more than 3% of the total and increasing operational risk by no more than 1%. These findings offer technical support for urban low-altitude flight plan scheduling management， and are instrumental in fostering safe and orderly progression of urban air traffic.

Key words: urban air mobility, flight plan, complex network, flight conflict management, optimal scheduling

CLC Number:

V355

Gang ZHONG, Junming HUA, Sen DU, Yupu LIU, Hao LIU, Honghai ZHANG. Urban low-altitude flight plan optimal scheduling based on complex network[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(11): 531479.

Figures/Tables 28

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Fig.5

Table 2

Parameters of simulation environment

参数	数值	参数	数值
$v w i n d$ /（m·s^-1）	7	$A p$ /m²	1
风向/rad	0.5	$C D, b$	1.3
$S$	0.5	$C D, p$	0.7
$r b u f$ /m	0.3	$α r$	0.8
$r U A V$ /m	0.2	$α L$	0.2
$m$ /kg	1.4

Table 2

Table 3

Parameters of optimization model

决策变量	取值范围	其他参数	取值
$x$	（1，60）	$t c o n f l i c t$ /s	30
$y$	（1，60）	$t d e l a y m a x$ /s	1 800
$z$	（1，4）	$t b a t t e r y$ /s	1 200
$v$ /（m·s^-1）	（5，20）	$α$	0.05
$t A T D$ /s	（1，3 600）	$v m a x$ /（m·s^-1）	20

Table 3

Fig.6

Fig.7

Fig.8

Table 4

Fig.9

Fig.10

Table 5

Parameters of optimization algorithm

算法参数	取值	权重参数	取值
P_arf	0.2	$ω c$	0.8
$N$ _P	50	$ω d$	0.25
N_gen-max	200	$ω r$	0.5
		$ω t$	0.25

Table 5

Fig.11

Fig.12

Fig.13

Fig.14

Table 6

Fig.15

Table 7

Fig.16

Table 8

Fig.17

Table 9

Fig.18

Table 10

References 33

[1]	中华人民共和国国务院，中央军委. 无人驾驶航空器飞行管理暂行条例［EB/OL］. （2023-06-28）［2024-11-20］. .
	The State Council of the People’s Republic of China， Central Military Commission of the People’s Republic of China. Interim regulation on the administration of the flight of unmanned aircraft‍［EB/OL］. （2023-06-28）［2024-11-20］. （in Chinese）.
[2]	中华人民共和国交通运输部. 民用无人驾驶航空器运行安全管理规则［EB/OL］. （2024-01-03）［2024-11-20］. .
	MOT. The safety management rules for the operation of civil unmanned aircraft［EB/OL］. （2024-01-03）［2024-11-20］. （in Chinese）.
[3]	白春玉，郭亚周，刘小川，等. 民用轻小型无人机碰撞安全特性研究进展［J］. 航空学报， 2022， 43（6）： 526832.
	BAI C Y， GUO Y Z， LIU X C， et al. Research progress of collision safety characteristics of civil light and small UAVs‍［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（6）： 526832 （in Chinese）.
[4]	FAA. UTM concept of operations version 2.0 （UTM ConOps v2.0）‍［EB/OL］. （2022-8-16）［2023-12-10］. .
[5]	WU P C， YANG X X， WEI P， et al. Safety assured online guidance with airborne separation for urban air mobi-lity operations in uncertain environments［J］. IEEE Transactions on Intelligent Transportation Systems， 2022， 23（10）： 19413-19427.
[6]	PANG B Z， LOW K H， LV C. Adaptive conflict resolution for multi-UAV 4D routes optimization using stochastic fractal search algorithm［J］. Transportation Research Part C： Emerging Technologies， 2022， 139： 103666.
[7]	谢华，苏方正，尹嘉男，等. 复杂低空无人机飞行冲突网络建模与精细管理［J］. 航空学报， 2023， 44（18）： 328226.
	XIE H， SU F Z， YIN J N， et al. Network modeling and refined management of UAV flight conflicts in complex low altitude airspace［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（18）： 328226 （in Chinese）.
[8]	DAI W， PANG B Z， LOW K H. Conflict-free four-dimensional path planning for urban air mobility considering airspace occupancy［J］. Aerospace Science and Technology， 2021， 119： 107154.
[9]	TANG Y W， XU Y. Incorporating optimization in strategic conflict resolution for UAS traffic management［J］. IEEE Transactions on Intelligent Transportation Systems， 2023， 24（11）： 12393-12405.
[10]	SANT'ANNA SOUZA W S， CONDÉ ROCHA MURÇA M. Simulation of strategic conflict management performance for advanced air mobility operations［C］‍∥2023 IEEE/AIAA 42nd Digital Avionics Systems Conference （DASC）. Piscataway： IEEE Press， 2023： 1-9.
[11]	YANG J， YIN D， NIU Y F， et al. Cooperative conflict detection and resolution of civil unmanned aerial vehicles in metropolis［J］. Advances in Mechanical Engineering， 2016， 8（6）： 51195.
[12]	JOVER J， BERMÚDEZ A， CASADO R. A tactical conflict resolution proposal for U-space zu airspace vo-lumes［J］. Sensors， 2021， 21（16）： 5649.
[13]	SALLAN J M， LORDAN O. Air transport networks and complex networks［M］‍∥Air route networks through complex networks theory. Amsterdam： Elsevier， 2020： 1-15.
[14]	黄洋，汤俊，老松杨. 基于复杂网络的无人机飞行冲突解脱算法［J］. 航空学报， 2018， 39（12）： 322222.
	HUANG Y， TANG J， LAO S Y. UAV flight conflict resolution algorithm based on complex network［J］. Acta Aeronautica et Astronautica Sinica， 2018， 39（12）： 322222 （in Chinese）.
[15]	DING R， UJANG N， HAMID H B， et al. Application of complex networks theory in urban traffic network researches［J］. Networks and Spatial Economics， 2019， 19（4）： 1281-1317.
[16]	吴明功，王泽坤，甘旭升，等. 基于复杂网络理论的关键飞行冲突点识别［J］. 西北工业大学学报， 2020， 38（2）： 279-287.
	WU M G， WANG Z K， GAN X S， et al. Identification of key flight conflict nodes based on complex network theory［J］. Journal of Northwestern Polytechnical University， 2020， 38（2）： 279-287 （in Chinese）.
[17]	WANG S， ZOU T Y， ZHAO W X， et al. Low-carbon mixed traffic route recommendation for community residents based on multilayer complex traffic network‍［J］. IEEE Transactions on Sustainable Computing， 2024， 9（3）： 299-314.
[18]	史妙恬. 航空运输网络中不确定性因素对航班延误波及的影响研究［D］. 南京：南京航空航天大学， 2017.
	SHI M T. Study on the influence of uncertain factors on flight delay spread in air transport network［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2017 （in Chinese）.
[19]	BAURANOV A， RAKAS J. Designing airspace for urban air mobility： a review of concepts and approaches［J］. Progress in Aerospace Sciences， 2021， 125： 100726.
[20]	中国民用航空局. 国家空域基础分类方法［EB/OL］. （2023-12-21）［2024-11-20］. .
	CAAC. National airspace classification method‍［EB/OL］. （2023-12-21）［2024-11-20］. （in Chinese）.
[21]	朱永文，陈志杰，蒲钒，等. 数字化空域系统发展研究［J］. 中国工程科学， 2021， 23（3）： 135-143.
	ZHU Y W， CHEN Z J， PU F， et al. Development of digital airspace system‍［J］. Strategic Study of CAE， 2021， 23（3）： 135-143 （in Chinese）.
[22]	DU S， ZHONG G， WANG F， et al. Safety risk modelling and assessment of civil unmanned aircraft system operations： a comprehensive review［J］. Drones， 2024， 8（8）： 354.
[23]	全权，李刚，柏艺琴，等. 低空无人机交通管理概览与建议［J］. 航空学报， 2020， 41（1）： 023238.
	QUAN Q， LI G， BAI Y Q， et al. Low altitude UAV traffic management： an introductory overview and proposal‍［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（1）： 023238 （in Chinese）.
[24]	PRIMATESTA S， RIZZO A， LA COUR-HARBO A. Ground risk map for unmanned aircraft in urban environments‍［J］. Journal of Intelligent & Robotic Systems， 2020， 97（3）： 489-509.
[25]	LA COUR-HARBO A. Quantifying risk of ground impact fatalities for small unmanned aircraft［J］. Journal of Intelligent & Robotic Systems， 2019， 93（1）： 367-384.
[26]	钟罡，励瑾，张晓玮，等. 物流无人机对地风险评估方法研究［J］. 交通运输系统工程与信息， 2022， 22（4）： 246-254.
	ZHONG G， LI J， ZHANG X W， et al. A risk assessment method of logistics drones on ground［J］. Journal of Transportation Systems Engineering and Information Technology， 2022， 22（4）： 246-254 （in Chinese）.
[27]	DALAMAGKIDIS K， VALAVANIS K， PIEGL L. Evaluating the risk of unmanned aircraft ground impacts［C］‍∥2008 16th Mediterranean Conference on Control and Automation. Ajaccio： IEEE Press， 2008： 4602249.
[28]	PANG B Z， HU X T， POH Y Y， et al. Population density estimation for dynamic ground risk assessment of drone operations［C］‍∥2023 IEEE/AIAA 42nd Digital Avionics Systems Conference （DASC）. Piscataway： IEEE Press， 2023： 1-6.
[29]	张军峰，葛腾腾，陈强，等. 离场航空器四维航迹预测及不确定性分析［J］. 西南交通大学学报， 2016， 51（4）： 800-806.
	ZHANG J F， GE T T， CHEN Q， et al. 4D trajectory prediction and uncertainty analysis for departure aircraft［J］. Journal of Southwest Jiaotong University， 2016， 51（4）： 800-806 （in Chinese）.
[30]	PANG B Z， LOW K H， DUONG V N. Chance-constrained UAM traffic flow optimization with fast disruption recovery under uncertain waypoint occupancy time［J］. Transportation Research Part C： Emerging Technologies， 2024， 161： 104547.
[31]	PAGE L， BRIN S， WINOGRAD T. The PageRank citation ranking： bringing order to the Web‍［EB/OL］. （1999-06-06）［2024-11-15］. .
[32]	MORONE F， MAKSE H A. Influence maximization in complex networks through optimal percolation［J］. Nature， 2015， 524： 65-68.
[33]	QI A L， ZHAO D， HEIDARI A A， et al. FATA： an efficient optimization method based on geophysics［J］. Neurocomputing， 2024， 607： 128289.

顺序	节点重要度次序
顺序	度中心性	接近中心性	中介中心性	Page Rank值	集体影响力
1	8	74	74	8	34
2	18	55	55	74	18
3	75	53	34	20	74
4	34	69	8	69	42
5	42	30	10	18	70
6	74	42	18	34	8
7	49	22	51	70	40
8	69	10	53	75	53
9	70	91	62	4	5
10	14	34	91	40	20

算法		剩余冲突数量	延误飞行计划的数量	算法运行时间/s	最终适应度分数	总风险增加比例/%
两阶段优化	最优	0	1.0	97.3	11 542.8	0.28
两阶段优化	平均	0	0.5	97.9	12 322.5	0.31
单阶段优化	最优	0	3.0	148.0	16 904.0	0.84
单阶段优化	平均	4	1.5	127.7	25 583.3	0.76

算法		剩余冲突数量	延误飞行计划的数量	算法运行时间/s	最终适应度分数
PSO	最优	5.0	0	91.1	27 689.9
	平均	6.6	2.2	91.3	34 294.6
	标准差	1.1	1.3	2.2	4 098.0
GA	最优	0	1.0	77.0	13 055.5
	平均	0.3	1.7	80.4	14 716.7
	标准差	0.5	1.3	4.3	1 463.0
FATA	最优	0	1.0	97.3	11 542.8
	平均	0	0.5	99.7	12 322.5
	标准差	0	0.5	5.5	527.7

算法		延误飞行计划数量	最终适应度分数	总风险增加比例/%
改进FATA	最优	1.0	11 542.8	0.28
	平均	0.5	12 322.5	0.31
	标准差	0.5	527.7	0.10
原FATA	最优	1.0	11 484.8	0.59
	平均	0.5	12 389.3	0.30
	标准差	0.5	638.0	0.11

选取比例	剩余冲突数量均值	延误飞行计划数量均值	算法运行时间均值/s	最终适应度分数均值	总风险增加比例均值/%
0.03	1.2	1.2	114.7	17 925.4	0.60
0.04	1.0	2	113.5	17 999.7	0.62
0.05	1.2	1.6	119.1	17 887.2	0.58
0.06	0.6	1.6	101.9	15 615.6	0.48
0.07	0.2	1.4	103.1	14 697.2	0.51
0.08	0	0.2	106.9	13 302.0	0.44
0.09	0	0.4	95.2	13 077.1	0.39
0.10	0	0.5	97.9	12 322.5	0.31
0.11	0	0.4	96.0	12 418.7	0.32
0.12	0	0.4	96.4	12 353.1	0.32

Urban low-altitude flight plan optimal scheduling based on complex network

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 28

References 33

Related Articles 14

Recommended Articles

Metrics

Comments

飞行计划数量	原有冲突数量	剩余冲突数量	延误飞行计划数量	算法运行时间/s	最终适应度分数
50	23	0	0	37.5	5 658.5
100	97	0	1	97.3	11 542.8
150	149	2	2	158.6	28 164.3
200	299	17	3	265.8	152 226.9
250	403	23	2	495.7	181 243.3
300	637	34	2	590.8	299 354.4

[1]	Jin YANG, Xu HANG, Yanjun WANG. Safety risk assessment of UAVs operations in airport controlled airspace [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(11): 531276-531276.
[2]	Yuhan LI, Shuguang ZHANG, Yibing WU. Handling qualities assessing of SVO-based eVTOL aircraft through EMG and eye data [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(11): 531315-531315.
[3]	Xinglong WANG, Youjie WANG. Safety interval evaluation for multi-aircraft eVTOL in urban low altitude [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(1): 330604-330604.
[4]	Hua XIE, Site HAN, Jianan YIN, Xiaohui JI, Yichen YANG. Cooperative deduction and optimal allocation method for urban low-altitude UAV flight plan [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(19): 330018-330018.
[5]	Xiaohan LIAO, Wenqiu QU, Chenchen XU, Hongbo HE, Junwei WANG, Weibo SHI. A review of urban air mobility and its new infrastructure low⁃altitude public routes [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(24): 28521-028521-.
[6]	ZHANG Honghai, ZOU Yiyuan, ZHANG Qiqian, LIU Hao. Future urban air mobility management: Review [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(7): 24638-024638.
[7]	SUI Dong, XING Yaping, TU Shichen. Repair optimization strategy for air route networks under severe weather conditions [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(2): 324300-324300.
[8]	LI Anti, LI Chenglong, WU Dingjie, WEI Peng. Collision avoidance decision method for UAVs in random search combined with jump point guidance [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(8): 323726-323726.
[9]	QUAN Quan, LI Gang, BAI Yiqin, FU Rao, LI Mengxin, KE Chenxu, CAI Kaiyuan. Low altitude UAV traffic management:An introductory overview and proposal [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(1): 23238-023238.
[10]	QI Yannan, GAO Jingdong. Cascading failure invulnerability and optimization strategy of airspace sector network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(12): 322579-322579.
[11]	HUANG Yang, TANG Jun, LAO Songyang. UAV flight conflict resolution algorithm based on complex network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(12): 322222-322222.
[12]	WU Xiping, YANG Hongyu, HAN Songchen. Analysis of properties and delay propagation of air traffic based on complex network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(S1): 721473-721473.
[13]	XU Xiaohao, LI Shanmei. Identification and prediction of air traffic congestion [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(8): 2753-2763.
[14]	CAI Lin, ZHANG Ling, YANG Shanshui, WANG Li. Reliability Assessment and Analysis of Large Aircraft Power Distribution Systems [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(8): 1488-1496.