Aircraft swarm improved velocity obstacle methods considering low carbon and deviation

doi:10.16265/j.cnki.issn1003-3033.2026.04.0144

Abstract

Abstract:

In order to address the requirements of low-carbon operation and safety in aircraft conflict resolution, an IVO method based on adaptive elliptical protected zones was proposed, taking into account aircraft carbon emissions and speed adjustment deviations. First, adaptive elliptical protected zones were constructed according to the velocity differences among aircraft. Second, aircraft flying on the same route with similar velocity vectors and close spatial proximity were grouped into clusters, and key characteristics such as cluster centroids, velocity vectors, and safety regions were defined. Then, a cluster control algorithm was applied to reasonably adjust the velocity vectors of aircraft within each cluster, ensuring the maintenance of safe separation during conflict resolution. Subsequently, velocity obstacle cones were established between clusters. By incorporating constraints on the maximum allowable adjustment per unit time and combining planar geometric analysis with a mathematical optimization model, conflict-free velocities and headings with minimal deviation were determined under low-carbon objectives. Finally, dynamic behaviour analysis was conducted through numerical simulations implemented in Python. The results show that, compared with the traditional velocity obstacle method, the proposed approach improves conflict resolution efficiency by 87.5%, reduces the average adjustment magnitude by 86.67%, and achieves fuel savings of up to 37.36%, demonstrating its effectiveness for aircraft conflict resolution and operational optimization in complex air traffic environments.

Key words: low carbon, velocity adjustment deviation, aircraft swarm, improved velocity obstacle(IVO) method, aircraft conflict resolution

CLC Number:

X949

Zhong Qingwei, Yu Yingxue, Liu Su, Wang Rui, Guo Jingwei, Pan Weijun. Aircraft swarm improved velocity obstacle methods considering low carbon and deviation[J]. China Safety Science Journal, 2026, 36(4): 142-151.

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编号	机型	(x_i, y_i)/ km	a_i/ km	b_i/ km	θ_i/ (°)	v_i/ (km/min)	机型	(x_j, y_j)/ km	a_j/ km	b_j/ km	θ_j/ (°)	v_j/ (km/min)
1	A320	(60,60)	1.65	1.47	50	5.5	DA40	(50,90)	1.35	1.03	5	4.5
1	A320	(60,60)	10.00	10.00	50	5.5	DA40	(50,90)	10.00	10.00	5	4.5
2	CY-09	(200,330)	0.65	0.03	120	2.17	C-172	(215,350)	1.14	0.73	200	3.8
2	CY-09	(200,330)	7.00	7.00	120	2.17	C-172	(215,350)	7.00	7.00	200	3.8
3	CY-12	(60,70)	0.80	0.24	20	2.67	HC-540	(80,100)	0.72	0.13	280	2.4
3	CY-12	(60,70)	7.00	7.00	20	2.67	HC-540	(80,100)	7.00	7.00	280	2.4

编号	$\left\|v{\text{'}}_{i}\right\|$/ (km/min)	$\left\|v{″}_{i}\right\|$/ (km/min)	θ'_i/ (°)	θ″_i/ (°)	min$\left\|v{\text{'}}_{i}\right\|$ 调整量	max$\left\|v{″}_{i}\right\|$ 调整量	minθ″_i 调整量	maxθ″_i 调整量
1	4.75	5.58	48.89	63.03	0.08	0.75	1.11	13.03
1	2.75	12.32	21.76	117.92	2.75	6.82	28.24	67.92
2	2.06	2.48	113.47	167.64	0.11	0.31	6.53	47.64
2	—	6.46	—	17.45	—	4.29	—	102.55
3	2.61	3.02	14.70	21.00	0.06	0.35	1.00	5.30
3	2.03	6.56	-13.32	32.05	0.64	3.89	12.05	33.32

编号	(x_i, y_i)/km	a_i/km	b_i/km	θ_i/(°)	v_i/(km/min)
1	(60,73)	1.65	1.47	2	5.4
2	(20,78)	1.65	1.47	0	5.2
3	(80,58)	1.35	1.03	80	4.5
4	(82,55)	1.35	1.03	83	4.4
5	(50,80)	1.14	0.73	5	3.8
6	(45,73)	1.14	0.73	6	3.7
7	(20,70)	0.72	0.13	10	2.4
8	(85,75)	0.72	0.13	10	2.4
9	(40,50)	0.8	0.24	60	2.6
10	(65,73)	1.65	1.47	4	4.9

集群	航空器	角度差/(°)	速度差/(km/min)
m₅	p₁	0.95	0.25
m₅	p₁₀	1.05	0.25
m₆	p₃	1.48	0.05
m₆	p₄	1.52	0.05