面向航空器集群的多尺度保护区模型与改进速度障碍法

艾毅; 庾映雪; 钟庆伟; 韩珣; 万琪峰

doi:10.3963/j.jssn.1674-4861.2024.02.005

面向航空器集群的多尺度保护区模型与改进速度障碍法

doi: 10.3963/j.jssn.1674-4861.2024.02.005

艾毅^1,,
庾映雪¹,
钟庆伟¹,
韩珣^{2, 3, ,},
万琪峰¹

1.
中国民用航空飞行学院空中交通管理学院四川德阳 618307
2.
四川警察学院智能警务四川省重点实验室四川泸州 646000
3.
四川警察学院道路交通管理系四川泸州 646000

基金项目:

国家自然科学基金项目 62203451

智能警务四川省重点实验室开放课题 ZNJW2023KFMS001

四川省科技计划项目 2023JDRC0004

详细信息

作者简介:
艾毅(1988-), 博士, 副教授. 研究方向: 交通运输规划与管理. E-mail: aiyi@cafuc.edu.cn

通讯作者:
韩珣(1991-), 博士, 副教授. 研究方向: 交通信息工程及控制、交通安全等. E-mail: hldwxhx@163.com

中图分类号: U8
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出版历程
- 收稿日期: 2023-03-29
- 网络出版日期: 2024-09-14

Multi-scale Protected Zone Models and an Improved Velocity Obstacle Method for Aircraft Swarms

AI Yi^1
,,
YU Yingxue¹,
ZHONG Qingwei¹,
HAN Xun^{2, 3
, ,},
WAN Qifeng¹

1.
College of Air Traffic Management, Civil Aviation Flight University of China, Deyang 618307, Sichuan, China
2.
Intelligent Policing Key Laboratory of Sichuan Province, Sichuan Police College, Luzhou 646000, Sichuan, China
3.
Department of Transportation Management, Sichuan Police College, Luzhou 646000, Sichuan, China

摘要

摘要: 针对高密度空域中所呈现出的航空器集群现象，研究了1种面向航空器集群的多尺度保护区模型与改进速度障碍法。对比传统单一航空器保护区模型及其速度障碍法存在计算复杂、实时性低等问题，研究了面向航空器的动态椭圆保护区模型以及面向航空器集群的融合保护区模型，在更加精确地刻画单一航空器的飞行状态和安全间隔的同时，创新地实现了由单一航空器保护区向航空器集群保护区的几何变换。所提出的航空器集群保护区模型在融合集群安全间隔特征和运动特征的同时显著降低了模型的特征维度。此外，在多尺度保护区模型的基础上提出了改进速度障碍法，并加入了基于航空器集群的速度障碍边界，降低了算法的计算复杂性。研究模型和算法可以将多航空器刻画为航空器集群，基于航空器集群的实时速度和航向调整边界，在大幅降低计算复杂性的基础上，实现了面向航空器集群的冲突探测与解脱航迹输出。通过仿真实验将本文方法与传统方法进行对比，结果表明：本文方法有效优化了航空器集群的冲突判定机制，将算法所需的计算时间缩短了33%，同时使完成冲突解脱的平均调整幅度降低了60.45%，有效提升了集群现象下的航空器冲突探测与解脱效率。
- 空中交通 /
- 航空器集群 /
- 多尺度保护区模型 /
- 改进速度障碍法
Abstract: The thesis explores aircraft swarming in dense airspace. A multi-scale protected zone model, coupled with an improved velocity obstacle method, is proposed to solve this. Traditional approaches often rely on a single-aircraft protected zone model, which utilizes a velocity obstacle method characterized by complex calculations and suboptimal real-time performance. In contrast, a more advanced approach is introduced, featuring a dynamic ellipsoidal protected zone model and a fusion protected zone model specifically designed for aircraft swarms. These models are crafted to accurately depict the aircraft's flight state and safety intervals. Moreover, the work pioneers the geometric transformation from a single-aircraft protected zone to a swarm-based protected zone. The innovative aircraft swarm protected zone model reduces the dimensional complexity while integrating critical features such as swarm safety intervals and motion characteristics. The paper further develops an improved velocity obstacle method that is grounded on the multi-scale protected zone model. This refined method incorporates a velocity obstacle boundary specifically tailored for aircraft swarms, effectively reducing the computational demands of the algorithm. The proposed models and algorithms successfully portray multiple aircraft as swarms. By establishing boundaries for real-time adjustments in speed and direction specifically for aircraft swarms, they significantly reduce computational complexity. This effectively implements conflict detection and resolution trajectories for aircraft swarms. A comparison of the proposed method with conventional approaches shows a significant improvement in the conflict determination mechanism for aircraft clusters, reducing algorithm computation time by 33%. Additionally, the proposed method leads to a decrease in adjustment amplitude by 60.45%, enhancing its overall performance. The method effectively enhances the efficiency of aircraft conflict detection and resolution under swarming phenomena.
- air traffic /
- aircraft swarms /
- multi-scale protected zone models /
- improved velocity obstacle method

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图 1 航空器集群划分

Figure 1. Aircraft swarm division

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图 2 航空器动态椭圆保护区模型

Figure 2. A dynamic elliptic protection zone model for aircraft

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图 3 面向航空器集群的融合保护区

Figure 3. Fusion protection zone for aircraft swarms

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图 4 二维平面传统速度障碍模型

Figure 4. Model of two-dimensional plane traditional VO

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图 5 沿$ \vec{\boldsymbol{V}}_j$平移后的速度障碍模型

Figure 5. Model of the VO after translation along $ \vec{\boldsymbol{V}}_j$

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图 6 多航空器冲突解脱模型

Figure 6. Model of multi-aircraft conflict relief

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图 7 面向航空器集群的改进速度障碍模型

Figure 7. Model of improved VO for aircraft swarms

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图 8 t₁时刻航空器解脱策略

Figure 8. Aircraft release strategies at t₁

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图 9 面向航空器集群的改进速度障碍法冲突解脱流程

Figure 9. Improved VO method conflict resolution process for aircraft swarms

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图 10 融合保护区模型

Figure 10. Fusion protection zone model

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图 11 传统速度障碍模型仿真

Figure 11. Traditional VO model simulation

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图 12 改进速度障碍模型仿真

Figure 12. Improved VO model simulation

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表 1 3组不同机型航空器位姿信息

Table 1. Position information of three groups of aircraft of different types

实验组	模型	航空器i机型	(x_j，y_j)/km	a_j /km	b_j /km	θ_j /°	$ \left\|\vec{\boldsymbol{V}}_i\right\| /(\mathrm{km} / \mathrm{min})$	航空器j机型	(x_j，y_j)/km	a_j /km	b_j /km	θ_j /°	$ \left\|\vec{\boldsymbol{V}}_i\right\| /(\mathrm{km} / \mathrm{min})$
1	动态	Cessna172	(70，65)	1.51	0.79	50	3.77	DA40	(50，90)	1.81	0.93	5	4.53
1	传统	Cessna172	(70，65)	5.00	5.00	50	3.77	DA40	(50，90)	5.00	5.00	5	4.53
2	动态	B737-800	(265，260)	3.67	3.01	135	9.17	DA40	(250，300)	1.81	0.93	180	4.53
2	传统	B737-800	(265，260)	5.00	5.00	135	9.17	DA40	(250，300)	5.00	5.00	180	4.53
3	动态	A320	(50，50)	3.60	3.00	20	9	B737-800	(70，90)	3.67	3.01	280	9.17
3	传统	A320	(50，50)	5.00	5.00	20	9	B737-800	(70，90)	5.00	5.00	280	9.17

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表 2 传统保护区与动态椭圆保护区模型对比

Table 2. Comparison of traditional and dynamic elliptical protected zone models

实验组	模型	$ \left\|\boldsymbol{V}_i^{\prime}\right\| /(\mathrm{km} / \mathrm{min})$	$ \left\|\boldsymbol{V}_i^{\prime \prime}\right\| /(\mathrm{km} / \mathrm{min})$	θ′_i/°	θ_i^′′ /°	最小解脱速度差/(km/min)	最大解脱速度差/(km/min)	最小解脱航向差/(km/min)	最大解脱航向差/(km/min)
1	动态	3.56	4.17	23.39	63.98	0.21	0.40	26.61	13.98
1	传统	2.82	5.02	14.77	98.95	0.95	1.25	35.23	48.95
2	动态	8.39	13.38	132.01	143.51	0.78	4.21	2.99	8.51
2	传统	7.31	19.83	126.38	148.24	1.86	10.66	8.62	13.24
3	动态	5.58	11.37	8.61	42.52	3.42	2.37	11.39	22.52
3	传统	4.42	13.73	-0.26	52.24	4.58	4.73	20.26	32.24

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表 3 航空器位姿信息

Table 3. Aircraft position information

序号	机型	(x_i，y_i)/km	a_i /km	b_i /km	θ_i /(°)	V_i /(km/min)
1	A320	(30，90)	3.60	3.00	0	9.00
2	A320	(38，90)	3.50	3.00	－5	8.74
3	A320	(30，98)	3.32	3.00	1	8.30
4	Cessna172	(70，80)	1.51	0.79	110	3.77

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表 4 航空器集群位姿信息

Table 4. Aircraft swarm position information

集群信息	参数值
(X_k，Y_k)/km	(32.67，92.67)
a_k/km	9.50
b_k/km	8.89
θ_k/°	[－5，1]
$ \left\|\vec{\boldsymbol{V}}_k^{C L}\right\| /(\mathrm{km} / \mathrm{min})$	[8.3，9]

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表 5 障碍航空器解脱策略

Table 5. Obstacle aircraft relief strategies

集群	T/min	$\left\|\boldsymbol{V}_i^{\prime}\right\| /(\mathrm{km} / \mathrm{min})$	$\left\|\boldsymbol{V}_i^{\prime \prime}\right\| /(\mathrm{km} / \mathrm{min})$	θ′_i/°	θ′′_i/°
集群左下边界	2.75	-	6.63	-5.56	176.49
集群右上边界	2.60	0.95	8.63	8.75	162.23

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