基于速度预测的防空导弹中制导末段协同弹道规划方法

doi:10.12305/j.issn.1001-506X.2023.09.31

摘要/Abstract

摘要：

针对防空导弹中制导末段协同探测时间、空间、速度和角度的一致性弹道规划问题, 提出一种基于速度预测的协同弹道规划方法。考虑攻角、弹道、气动间的相互耦合和拦截弹被动减速特性, 借助半解析预测方法精准预报速度变化, 将需用过载转化为升力系数约束, 减少需处理的约束数量; 在此基础上, 通过弹道整形变量将多弹协同规划问题转化为非线性优化问题, 解析生成参考轨迹, 预报需用/可用过载; 综合改进粒子群优化算法, 采用自适应惯性权重和无效粒子再利用策略, 提高粒子利用率的同时提升种群脱离局部最优解的概率, 克服飞行散布和弹道偏差, 快速规划满足终端时、空、角一致性约束的中制导协同弹道。数学仿真验证了中制导末段多约束协同弹道规划算法的有效性。

关键词: 协同探测, 协同弹道规划, 改进粒子群优化

Abstract:

A synergistic guidance method is proposed for interceptor missiles in the later part of midcourse. For cooperative detection, time-to-go, range-to-go, terminal velocity and terminal angle should be controlled independently. The semi-analytic prediction method is used to predict the velocity, needed overload and supplied overload; convert the required overload into the lift coefficient requirements. The cooperative trajectory planning problem is transformed into a nonlinear optimization problem through the selection of trajectory shaping variables, and the reference trajectory is generated online. To improve the particle swarm optimization algorithm, adaptive inertia weight selection and invalid particle substitution strategy were adopted, which can improve the probability of the population and escaping from the local optimal point. Trajectory that meets the terminal constrains can be planning fast on consider of the flight dispersion and trajectory deviation. Finally the effectiveness is verified based on mathematical simulation.

Key words: cooperative detection, cooperative trajectory planning, improved particle swarm optimization

中图分类号:

V448.2

崔正达, 魏明英, 李运迁. 基于速度预测的防空导弹中制导末段协同弹道规划方法[J]. 系统工程与电子技术, 2023, 45(9): 2912-2921.

Zhengda CUI, Mingying WEI, Yunqian LI. Cooperative trajectory planning method in later part of midcourse based on velocity estimation[J]. Systems Engineering and Electronics, 2023, 45(9): 2912-2921.

图/表 15

图1

图2

图3

表1

图4

图5

图6

表2

表3

表4

图7

图8

表5

表6

图9

参考文献 19

1	魏明英, 崔正达, 李运迁. 多弹协同拦截综述及展望[J]. 航空学报, 2020, 41 (S1): 723804.
	WEI M Y , CUI Z D , LI Y Q . Reviev and future development of multi-missile coordinated interception[J]. Acta Aeronautica et Austronautica Sinca, 2020, 41 (S1): 723804.
2	赵建博, 杨树兴. 多导弹协同制导研究综述[J]. 航空学报, 2017, 38 (1): 17- 29.
	ZHAO J B , YANG S X . A review of multi missile cooperative guidance research[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38 (1): 17- 29.
3	李文, 尚腾, 姚寅伟, 等. 速度时变情况下多飞行器时间协同制导方法研究[J]. 兵工学报, 2020, 41 (6): 1096- 1110.
	LI W , SHANG T , YAO Y W , et al. Research on time-cooperative guidance of multiple flight vehicles with time-varying velocity[J]. Acta Armamentaii, 2020, 41 (6): 1096- 1110.
4	乔浩, 李师尧, 李新国. 多高超声速飞行器静态协同再入制导方法[J]. 宇航学报, 2020, 41 (5): 541- 552.
	QIAO H , LI S Y , LI X G . Static cooperative reentry guidance method for multi-hypersonic vehicles[J]. Journal of astronautics, 2020, 41 (5): 541- 552.
5	YU W B , CHEN W C , JIANG Z G , et al. Analytical entry guidance for coordinated flight with multiple no-fly-zone constrains[J]. Aerospace Science and Technology, 2018, 84, 273- 290.
6	YU W B , YAO Y Z , CHEN W C . Analytical cooperative entry guidance for rendezvous and formation flight[J]. Acta Astronautica, 2020, 171, 118- 138. doi: 10.1016/j.actaastro.2020.02.044
7	周宏宇, 王小刚, 单永志, 等. 基于改进粒子群算法的飞行器协同轨迹规划[J]. 自动化学报, 2022, 48 (11): 2670- 2676.
	ZHOU H Y , WANG X G , SHAN Y Z , et al. Synergistic path planning for multiple vehicles based on an improved particle swarm optimization method[J]. Acta Automatic Sinica, 2022, 48 (11): 2670- 2676.
8	郭明坤, 杨峰, 刘凯, 等. 高超声速飞行器协同制导技术研究进展[J]. 空天技术, 2022, 446 (2): 75- 84.
	GUO M K , YANG F , LIU K , et al. Review on cooperative guidance technology for hypersonic flight vehicle[J]. Aerospace Technology, 2022, 446 (2): 75- 84.
9	LI Z H , HE B , WANG M H , et al. Cooperative guidance strategy for multiple hypersonic gliding vehicles system[J]. Aerospace Science and Technology, 2019, 89, 123- 135.
10	王肖, 郭杰, 唐胜景, 等. 基于解析剖面的时间协同再入制导[J]. 航空学报, 2019, 40 (3): 322565.
	WANG X , GUO J , TANG S J , et al. Time-cooperative entry guidance based on analytic profile[J]. Acta Aeronautica et Austronautica Sinca, 2019, 40 (3): 322565.
11	王浩凝, 唐胜景, 郭杰, 等. 带有动态攻角剖面的时间约束再入制导[J]. 空天防御, 2021, 4 (1): 71- 76.
	WANG H N , TANG S J , GUO J , et al. Time-constrained reentry guidance with dynamic angle of attack profile[J]. Air & Space Defense, 2021, 4 (1): 71- 76.
12	崔正达, 魏明英, 李运迁. 考虑阻力系数时变的下压段半解析时间预测方法[J]. 系统工程与电子技术, 2023, 45 (2): 530- 537.
	CUI Z D , WEI M Y , LI Y Q . Semi-analytical encounter time estimation in dive phase with time-varying drag coefficient[J]. Systems Engineering and Electronics, 2023, 45 (2): 530- 537.
13	TIAN D P , ZHAO T X . Particle swarm optimization based on tent map and logistic map[J]. Shaanxi University of Science & Technology, 2010, 28 (2): 17- 23.
14	SHI Y. Particle swarm optimization: developments, applications and resources[C]//Proc. of the IEEE Congress on Evolutionary Computation, 2001: 81-86.
15	王启付, 王战江, 王书亭. 一种动态改变权重的粒子群优化算法[J]. 中国机械工程, 2005, 16 (11): 945- 948.
	WANG Q F , WANG Z J , WANG S T . A modified particle swarm optimizer using dynamic inertia weight[J]. China Mechanical Engineering, 2005, 16 (11): 945- 948.
16	夏辉, 宋勋, 王硕, 等. 集群智能原理、发展和应用[M]. 北京: 电子工业出版社, 2017.
	XIA H , SONG X , WANG S , et al. Swarm intelligence principles, advances, and applications[M]. Beijing: Publishing House of Electronics Industry, 2017.
17	XIE X F, ZHANG W J, YANG Z L. A dissipative particle swarm optimization[C]// Proc. of the Congress on Evolutio-nary Computation, 2002.
18	JEON I S , LEE J I , TAHK M J . Impact-time-control guidance law for anti-ship missiles[J]. IEEE Trans.on Control Systems Technology, 2006, 15 (2): 260- 266.
19	JEON I S , LEE J I , TAHK M J . Impact-time-control guidance with generalized proportional navigation based on nonlinear formulation[J]. Journal of Guidance, Control, and Dynamics, 2016, 39 (8): 1885- 1890.

导弹编号	弹道参数
导弹编号	R_L₀/km	θ₀/(°)	h₀/km	V₀/(m/s)
M₁	200	1	35	2 000
M₂	210	－1	37	1 950
M₃	220	－2	33	2 050

导弹编号	弹道参数
导弹编号	Δθ_f/(°)	V_f/(m/s)	t_f/s	Δr_f/m
M₁	－6.9	1 642.89	107.78	2.8
M₂	－6.4	1 544.28	115.84	1.3
M₃	－4.1	1 532.42	120.18	2.7

导弹编号	弹道参数
导弹编号	Δθ_f/(°)	V_f/(m/s)	t_f/s	Δr_f/m
M₁	－14.7	1 515.3	120.78	1.18
M₂	－9.6	1 487.5	124.14	7.3
M₃	－9.2	1 586.2	122.83	5.7

导弹编号	弹道参数
导弹编号	Δθ_f/(°)	V_f/(m/s)	t_f/s	Δr_f/m
M₁	0.09	1 451.4	119.04	39.6
M₂	0.04°	1 478.6	118.13	32.4
M₃	0.03°	1 548.3	118.77	20.1

统计量	交班条件
统计量	Δθ_f/(°)	Δt_f/s	Δr_f/m
均值	2.4	0.79	32
标准差	3.7	0.90	21
最大值	7.6	3.6	182