基于改进凸优化算法的多机编队突防航迹规划

doi:10.12305/j.issn.1001-506X.2023.09.21

摘要/Abstract

摘要：

为更好地发挥多机编队在低空突防作战中的优势, 对已有的凸优化算法进行改进, 提出一种多机编队低空突防航迹规划方法。首先, 根据低空突防任务特点进行问题建模, 包含多机编队航迹规划模型、障碍物模型以及任务分配评估模型。其次, 提出基于匈牙利算法的集群任务分组概念, 设计更符合战场需求和运动学规律的预规划航迹。之后, 考虑新类型的外部障碍物和不同任务小组间的组间避障, 通过对约束进行合理的近似与凸优化, 实现多机安全飞行。最后, 通过对比仿真, 验证所提改进方法的可行性和有效性。结果表明, 改进后的航迹规划算法能实现对低空突防任务的合理分配, 求解效率和成功率均有所提高, 对新加入的障碍有良好的避障效果。

关键词: 多机编队, 低空突防, 任务分配, 航迹规划, 凸优化, 避障

Abstract:

In order to better leverage the advantages of mult-aircraft formation in low altitude penetration operations, an improved convex optimization algorithm is proposed for low altitude penetration trajectory planning of multi-aircraft formation. Firstly, problem modeling is carried out based on the characteristics of low altitude penetration missions, including mult-aircraft formation trajectory planning models, obstacle models, and task allocation evaluation models. Secondly, the concept of cluster task grouping based on the Hungarian algorithm is proposed to design a pre planned track that is more in line with the needs of the battlefield and the laws of kinematics. Afterwards, considering new types of external obstacles and inter group obstacle avoidance between different task groups, reasonable approximation and convex optimization of constraints are carried out to achieve safe flight of multi-aircraft. Finally, the feasibility and effectiveness of the proposed improvement method were verified through comparative simulation. The results show that the improved trajectory planning algorithm can achieve reasonable allocation of low altitude penetration tasks, improve solving efficiency and success rate, and have a good obstacle avoidance effect on newly added obstacles.

Key words: multi-aircraft formation, low altitude penetration, task allocation, trajectory planning, convex optimization, obstacle avoidance

中图分类号:

V249

刘玉杰, 李樾, 韩维, 崔凯凯. 基于改进凸优化算法的多机编队突防航迹规划[J]. 系统工程与电子技术, 2023, 45(9): 2819-2830.

Yujie LIU, Yue LI, Wei HAN, Kaikai CUI. Trajectory planning for penetration of multi-aircraft for mation based on improved convex optimization algorithm[J]. Systems Engineering and Electronics, 2023, 45(9): 2819-2830.

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物理量	任务小组1	任务小组2	任务小组3
s(t₀)	(22 000, 20 000, 5 000, 600, π/6, 0)	(40 000, 5 000, 6 000, 600, π/2, 0)	(1 000, 1 000, 5 000, 600, π/4, 0)
	(18 000, 20 000, 5 000, 600, π/6, 0)	(38 000, 5 000, 6 000, 600, π/2, 0)	(1 000, 0, 5 000, 600, π/4, 0)
	(20 000, 22 000, 5 000, 600, π/6, 0)	(36 000, 5 000, 6 000, 600, π/2, 0)	(0, 0, 5 000, 600, π/4, 0)
	(20 000, 18 000, 5 000, 600, π/6, 0)	(42 000, 5 000, 6 000, 600, π/2, 0)	(2 000, 0, 5 000, 600, π/4, 0)
初始队形	菱形	横向平行队形	菱形
s_min	(-∞, -∞, 1 000, 200, -∞, -π/9)	(-∞, -∞, 1 000, 200, -∞, -π/9)	(-∞, -∞, 1 000, 200, -∞, -π/9)
s_max	(∞, ∞, 10 000, 1 000, -∞, π/9)	(∞, ∞, 10 000, 1 000, -∞, π/9)	(∞, ∞, 10 000, 1 000, -∞, π/9)
u_min	(-0.4, -4, 0.8)	(-0.6, -8, 0.8)	(-0.2, -2, 0.8)
u_max	(0.4, 4, 1.2)	(0.6, 8, 1.2)	(0.2, 0.2, 1.2)
$\dot{\boldsymbol{u}}_{\min }$	(0, 0, 0)	(0, 0, 0)	(0, 0, 0)
$\dot{\boldsymbol{u}}_{\max }$	(0.1, 1, 0.1)	(0.15, 2, 0.1)	(0.05, 0.5, 0.1)
R_a	3×10⁴	6×10⁴	3×10⁴
R_c	5×10⁴	7×10⁴	6×10⁴

物理量	任务小组1	任务小组2	任务小组3
真实位置	(75 000, 65 000, 0)	(70 000, 62 000, 0)	(40 000, 84 000, 0)
任务执行点	(74 000, 44 000, 1 500, 600, π/2, 0)	(58 000, 58 000, 1 500, 600, 0, 0)	(40 000, 52 000, 2 000, 600, π/2, 0)
s(t_f)	(74 000, 44 000, 1 500, 600, π/2, 0)	(58 000, 58 000, 1 500, 600, 0, 0)	(40 000, 52 000, 2 000, 600, π/2, 0)
	(76 000, 45 000, 1 500, 600, π/2, 0)	(60 000, 62 000, 1 500, 600, 0, 0)	(40 000, 50 000, 2 000, 600, π/2, 0)
	(77 000, 44 000, 1 500, 600, π/2, 0)	(58 000, 58 000, 1 500, 600, 0, 0)	(40 000, 54 000, 2 000, 600, π/2, 0)
	(74 000, 44 000, 1 500, 600, π/2, 0)	(58 000, 64 000, 1 500, 600, 0, 0)	(40 000, 48 000, 2 000, 600, π/2, 0)
任务执行点队形	楔形	楔形	一字纵向队形
R_b	4×10⁴	2×10⁴	5×10⁴
G	40	100	80

物理量	雷达1	雷达2	禁飞区1	禁飞区2
中心坐标	(78 000, 18 000)	(20 000, 10 000)	-	-
R_r+d_s	7 000	3 000	-	-
边界坐标	-	-	(35 000, 20 000)	(30 000, 35 000)
			(35 000, 25 000)	(30 000, 45 000)
			(45 000, 25 000)	(33 000, 45 000)
			(45 000, 20 000)	(33 000, 35 000)

阶段	物理量	数值
预规划阶段	h₀	2 000
	h_max	10 000
	λ₁	0.5
	λ₂	-0.5
航迹规划阶段	K	50
	R_max	500
	flag	10⁴
	μ_in	0.5
	μ_eq	1
	ε¹	(10⁵, 10⁵, 2×10³, 100, π, π/6)

分组	子任务1			子任务2			子任务3
分组	${\bar T}$	${\bar C}$	${\bar G}$	${\bar T}$	${\bar C}$	${\bar G}$	${\bar T}$	${\bar C}$	${\bar G}$
任务小组1	0.056	-0.03	0.4	0.046	-0.03	1	0.297	-0.01	0.8
任务小组2	0.057	-0.04	0.4	0.096	-0.05	1	0.080	-0.03	0.8
任务小组3	0.051	-0.02	0.4	0.051	-0.01	1	0.135	0.02	0.8