Three-dimensional Leader-follower Cooperative Guidance Law for Maneuvering Targets

doi:10.12382/bgxb.2023.0777

Abstract

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

CLC Number:

TJ301

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.

Figures/Tables 10

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

Fig.2 Three-dimensional guidance model

Fig.3 Multiple flight vehicles communication topology

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

Table 2 Initial condition of target

x/m	y/m	z/m	速度/(m·s^-1)
0	0	0	100

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

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

Fig.4 Simulated results of snake maneuver

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

Fig.5 Simulated results of FTCGL

Fig.6 Energy consumption

References 25

[1]	魏明英, 崔正达, 李运迁. 多弹协同拦截综述与展望[J]. 航空学报, 2020, 41(增刊1): 29-36.
	WEI M Y, CUI Z D, LI Y Q. Review and future development of multi-missile coordinated interception[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(S1): 29-36. (in Chinese)
[2]	姚禹正, 余文斌, 杨立军, 等. 多导弹协同制导技术综述[J]. 飞航导弹, 2021(6): 112-121.
	YAO Y Z, YU W B, YANG L J, et al. Overview of multi-missile cooperative guidance technology[J]. Aerodynamic Missile Journal, 2021(6): 112-121. (in Chinese)
[3]	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. Review of multi-missle cooperative guidance[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(1): 17-29. (in Chinese)
[4]	JEON I S, LEE J I, TAHK M J. Impact-time-control guidance law for anti-ship missiles[J]. IEEE Transactions on control systems technology, 2006, 14(2): 260-266.
[5]	CHEN Y D, SHAN J Y, LIU J H, et al. Impact time and angle constrained guidance via range-based line-of-sight shaping[J]. International Journal of Robust and Nonlinear Control, 2022, 32(6): 3606-3624.
[6]	KUMAR S R, MUKHERJEE D. True-proportional-navigation inspired finite-time homing guidance for time constrained interception[J]. Aerospace Science and Technology, 2022, 123: 107499.
[7]	MITCHELL H B. Data fusion: concepts and ideas[M]. Berlin, Heidelberg, Germany: Springer, 2012.
[8]	YU H, DAI K R, LI H J, et al. Distributed cooperative guidance law for multiple missiles with input delay and topology switching[J]. Journal of the Franklin Institute, 2021, 358(17): 9061-9085.
[9]	WANG Z K, FU W X, FANG Y W, et al. Prescribed-time cooperative guidance law against maneuvering target based on leader-following strategy[J]. ISA Transactions, 2022, 129: 257-270.
[10]	YANG X Y, SONG S M. Three-dimensional consensus algorithm for nonsingular distributed cooperative guidance strategy[J]. Aerospace Science and Technology, 2021, 118: 106958.
[11]	LIU S X, YAN B B, ZHANG T, et al. Three-dimensional cooperative guidance law for intercepting hypersonic targets[J]. Aerospace Science and Technology, 2022, 129: 107815.
[12]	SONG J H, SONG S M, XU S L. Three-dimensional cooperative guidance law for multiple missiles with finite-time convergence[J]. Aerospace Science and Technology, 2017, 67: 193-205.
[13]	YU H, DAI K R, LI H J, et al. Three-dimensional adaptive fixed-time cooperative guidance law with impact time and angle constraints[J]. Aerospace Science and Technology, 2022, 123: 107450.
[14]	WANG X X, LU H Q, HUANG X L, et al. Three-dimensional terminal angle constraint finite-time dual-layer guidance law with autopilot dynamics[J]. Aerospace Science and Technology, 2021, 116: 106818.
[15]	王雨辰, 王伟, 林时尧, 等. 考虑攻击时间及空间角度约束的三维自适应滑模协同制导律设计[J]. 兵工学报, 2023, 44(9): 2778-2790. doi: 10.12382/bgxb.2022.1086
	WANG Y C, WANG W, LIN S Y, et al. Three-dimensional adaptive sliding mode cooperative guidance law with impact time and angle constraints[J]. Acta Armamentarii, 2023, 44(9): 2778-2790. (in Chinese) doi: 10.12382/bgxb.2022.1086
[16]	CHEN Z Y, CHEN W C, LIU X M, et al. Three-dimensional fixed-time robust cooperative guidance law for simultaneous attack with impact angle constraint[J]. Aerospace Science and Technology, 2021, 110: 106523.
[17]	ZHANG S, GUO Y, LIU Z G, et al. Finite-time cooperative guidance strategy for impact angle and time control[J]. IEEE Transactions on Aerospace and Electronic Systems, 2020, 57(2): 806-819.
[18]	LI G F, LÜ J H, ZHU G L, et al. Distributed observer-based cooperative guidance with appointed impact time and collision avoidance[J]. Journal of the Franklin Institute, 2021, 358(14): 6976-6993.
[19]	张明洋, 晁涛, 杨明. 带有攻击角约束的机动目标协同拦截制导律[J]. 战术导弹技术, 2022(4): 78-89.
	ZHANG M Y, CHAO T, YANG M. Cooperative intercep-tion guidance law for maneuvering target with im-pact angle constraint[J]. Tactical Missile Technology, 2022(4): 78-89. (in Chinese)
[20]	HE S M, LIN D F. Three-dimensional optimal impact time guidance for antiship missiles[J]. Journal of Guidance, Control, and Dynamics, 2019, 42(4): 941-948.
[21]	DONG W, WANG C Y, WANG J N, et al. Fixed-time terminal angle-constrained cooperative guidance law against maneuvering target[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 58(2): 1352-1366.
[22]	TIAN B L, LU H C, ZUO Z Y, et al. Fixed-time leader-follower output feedback consensus for second-order multiagent systems[J]. IEEE Transactions on Cybernetics, 2018, 49(4): 1545-1550.
[23]	HUANG Y, JIA Y M. Fixed-time consensus tracking control of second-order multi-agent systems with inherent nonlinear dynamics via output feedback[J]. Nonlinear Dynamics, 2018, 91: 1289-1306.
[24]	WANG W, WANG Y C, CHEN S W, et al. Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles[J]. Defence Technology, 2023, 34: 282-294.
[25]	HUANG S H, XIONG L Y, WANG J, et al. Fixed-time fractional-order sliding mode controller for multimachine power systems[J]. IEEE Transactions on Power Systems, 2020, 36(4): 2866-2876.