针对机动目标的三维领从协同制导律

doi:10.12382/bgxb.2023.0777

摘要/Abstract

摘要：

针对多飞行器协同拦截机动目标的实际需求,提出一种三维领从时空协同制导律。在视线方向上,基于齐次度理论和固定时间稳定理论设计一种领从协同制导律,确保从飞行器与领飞行器的相对距离和相对速度在固定时间内趋于一致,并且给出一致性误差收敛时间的上界,实现多飞行器的同时刻拦截。在视线法向上为实现以特定的碰撞角度拦截目标,设计一种固定时间收敛的非奇异终端滑模制导律,实现攻击角度的固定时间收敛,并避免了制导指令奇异引起的控制饱和问题。考虑到目标的机动对制导系统产生的不利影响,引入固定时间扰动观测器对目标加速度进行前馈补偿。运用李雅普诺夫稳定性理论来证明系统的固定时间稳定特性。通过仿真实验验证所设计制导律可以有效控制多飞行器在领从框架下同时打击机动目标,并以期望的终端角度攻击目标。

关键词: 领从式协同制导, 时间空间角度约束, 固定时间一致性, 状态观测器, 机动目标

Abstract:

In response to the actual need for coordinated interception of multiple flight vehicle targets, this paper presents a three-dimensional spatio-temporal coordinative guidance law. Firstly, a leader-follower cooperative guidance law is developed based on the homogeneity theory and the fixed-time stability theory. This law ensures that the relative distance and relative velocity between the follower and the leader converge to a consistent value within a fixed time, respoectively. Furthermore, an upper bound for the convergence time of consistency error is provided to enable the simultaneous interception of multiple flight vehicles. Secondly, a non-singular terminal sliding mode guidance law with fixed time convergence is proposed to intercept the target with a specific collision angle in the normal direction of the line of sight. This law achieves the fixed time convergence of attack angle and mitigates the control saturation problem caused by the singularity of guidance command. Additionally, a fixed-time disturbance observer is introduced to compensate for the effects of the target's maneuvering on the guidance system. This observer performs feedforward compensation for the target acceleration. Finally, the Lyapunov stability theory is employed to prove the fixed-time stability properties of the system. The simulated results show that the proposed guidance law can be used to effectively control multiple aircrafts to attack the maneuvering targets at the same time under the leader-follower framework, and attack the targets at the desired terminal angle.

Key words: leader-follower cooperative guidance, time-space angle constraint, fixed time consistency, state observer, maneuvering target

中图分类号:

TJ301

王伟, 于之晨, 林时尧, 杨婧, 王宏. 针对机动目标的三维领从协同制导律[J]. 兵工学报, 2024, 45(10): 3538-3554.

WANG Wei, YU Zhichen, LIN Shiyao, YANG Jing, WANG Hong. Three-dimensional Leader-follower Cooperative Guidance Law for Maneuvering Targets[J]. Acta Armamentarii, 2024, 45(10): 3538-3554.

图/表 10

图1 三维多飞行器协同示意图

Fig.1 Schematic diagram of three-dimensional multiple flight vehicles collaboration

图2 三维制导模型

Fig.2 Three-dimensional guidance model

图3 多飞行器通讯拓扑

Fig.3 Multiple flight vehicles communication topology

表1 多飞行器初始条件

Table 1 Initial conditions of multiple flight vehicles

飞行器	相对距离/ km	相对速度/ (m·s^-1)	视线倾角/ (°)	视线偏角/ (°)	期望终端视线倾角/(°)	期望终端视线偏角/(°)
M₀	10.0	-400	-45	30	-35	15
M₁	11.0	-320	-60	10	-30	30
M₂	13.0	-400	-45	30	-20	50
M₃	12.0	-380	-30	40	-60	10
M₄	10.5	-350	-20	60	-50	40

表2 目标初始条件

Table 2 Initial condition of target

x/m	y/m	z/m	速度/(m·s^-1)
0	0	0	100

表3 协同制导律参数

Table 3 Cooperative guidance law parameters

参数	数值	参数	数值	参数	数值
L^r	100	L^θ	100	L^ϕ	150
σ^r	0.1	$κ 1 r$ = $κ 1 λ$	6	δ_θ=δ_ϕ	0.01
T_u	0.1	$κ 2 r$ = $κ 2 λ$	3	q_θ=q_ϕ	1.2
α₁_r	0.7	$κ 3 r$ = $κ 3 λ$	1	η₁_θ=η₁_ϕ	0.01
β₁_r	1.2	σ^θ=σ^ϕ	0.1	η₂_θ=η₂_ϕ	0.01
k₁_r	1	k₁_θ=k₁_ϕ	7	η₃_θ=η₃_ϕ	0.5
k₂_r	1	k₂_θ=k₂_ϕ	7	m₁_θ=m₁_ϕ	1.8
k₃_r	10	p_θ=p_ϕ	0.5	m₂_θ=m₂_ϕ	0.6

表3 协同制导律参数

Table 3 Cooperative guidance law parameters

参数	数值	参数	数值	参数	数值
L^r	100	L^θ	100	L^ϕ	150
σ^r	0.1	$κ 1 r$ = $κ 1 λ$	6	δ_θ=δ_ϕ	0.01
T_u	0.1	$κ 2 r$ = $κ 2 λ$	3	q_θ=q_ϕ	1.2
α₁_r	0.7	$κ 3 r$ = $κ 3 λ$	1	η₁_θ=η₁_ϕ	0.01
β₁_r	1.2	σ^θ=σ^ϕ	0.1	η₂_θ=η₂_ϕ	0.01
k₁_r	1	k₁_θ=k₁_ϕ	7	η₃_θ=η₃_ϕ	0.5
k₂_r	1	k₂_θ=k₂_ϕ	7	m₁_θ=m₁_ϕ	1.8
k₃_r	10	p_θ=p_ϕ	0.5	m₂_θ=m₂_ϕ	0.6

图4 蛇形机动下的仿真结果

Fig.4 Simulated results of snake maneuver

表4 拦截时间及制导误差

Table 4 Interception time and guidance errors

制导律	飞行器	拦截时间/s	脱靶量/m	相对速度误差/(m·s^-1)	视线倾角误差/(°)	视线偏角误差/(°)
	M₀	33.6881	0.0036	0	0.0010	0.0010
	M₁	33.6881	0.0589	0.9397	0.0007	0.0005
本文所设计制导律	M₂	33.6881	0.0344	1.1491	0.0012	0.0008
	M₃	33.6881	0.0922	1.1163	0.0010	0.0009
	M₄	33.6881	0.1131	1.3599	0.0013	0.0007
	M₀	28.6331	0.0049	0	0.0021	0.0021
	M₁	28.6331	1.6427	8.9231	0.0018	0.0019
有限时间协同制导律	M₂	28.6331	1.5375	9.2391	0.0019	0.0021
	M₃	28.6331	1.5188	13.1363	0.0018	0.0016
	M₄	28.6331	1.3368	12.7499	0.0023	0.0025

图5 有限时间协同制导律仿真结果

Fig.5 Simulated results of FTCGL

图6 能量消耗

Fig.6 Energy consumption

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