基于分布式凸优化的能量最优多向协同制导方法

doi:10.12382/bgxb.2024.0739

摘要/Abstract

摘要：

多飞行器角度最优协同制导能够以最低能耗实现对机动目标的多向拦截,是制导领域的重要研究方向。现有最优协同制导方法需利用全局信息生成最优制导指令,故多采用集中式通信拓扑,而集中式通信可靠性较低,不利于实际应用。针对上述问题,基于分布式凸优化理论,提出一种分布式能量最优多向协同制导方法,以解决分布式信息局部性与协同指令全局最优性之间的矛盾。该方法基于广义弹道成型制导律(Generalized Trajectory Shaping Guidance Law,GTSG),通过解析推导飞行器控制能量与期望终端视线角的映射关系,以总控制能量为目标函数,并结合相对视线角约束构建分布式凸优化问题。提出扩展原始对偶算法,实现分布式全局寻优,实时协调飞行器期望视线角,使多飞行器在GTSG作用下以最小能耗协同拦截目标。仿真结果及其分析表明:相比于现有的集中式多向协同制导算法,所提方法无需依赖中心节点,同时兼顾了全局能量最优性。

关键词: 协同制导, 相对视线角约束, 能量最优, 分布式凸优化, 原始对偶算法, 目标机动

Abstract:

The angle-optimal cooperative guidance of multiple aerial vehicles enables multi-directional interception of maneuvering targets with minimal energy consumption,which is an important research direction in the field of guidance.The current optimal cooperative guidance methods depend on global information and centralized communication which has low reliability in practical applications.To address the issue mentioned above,an energy-optimal relative-angle-constrained cooperative guidance method based on distributed convex optimization is proposed to resolve the contradiction between the locality of distributed information and the global optimality of cooperative commands.Based on the generalized trajectory shaping guidance law (GTSG),the mapping relationship between aerial vehicle control energy and desired terminal line-of-sight (LOS) angle is derived.A convex objective function is formulated using total control energy,and the convex constraints are established based on relative LOS angle constraints,thereby constructing a distributed convex optimization problem.The extended primal-dual algorithm (EPDA) is then introduced to achieve distributed global optimization,enabling the real-time coordination of aerial vehicle LOS angles for minimum-energy interception.The simulated results and analysis demonstrate that the proposed method does not rely on a central node while ensuring global energy optimality compared with existing centralized angle-coordinated guidance algorithms.

Key words: cooperative guidance, relative LOS angle constraint, energy-optimal, distributed convex optimization, primal-dual algorithm, maneuvering target

王江, 朱梓杨, 李虹言, 王鹏. 基于分布式凸优化的能量最优多向协同制导方法[J]. 兵工学报, 2025, 46(6): 240739-.

WANG Jiang, ZHU Ziyang, LI Hongyan, WANG Peng. An Energy-optimal Relative-angle-constrained Cooperative Guidance Method Based on Distributed Convex Optimization[J]. Acta Armamentarii, 2025, 46(6): 240739-.

图/表 20

图1 多飞行器与目标平面几何关系

Fig.1 Geometric relationship between multiple aerial vehicles and target

图2 飞行器—目标模型线性化

Fig.2 Aerial vehicle-target model for linearization

图3 工作原理

Fig.3 Block diagram of the working principle of the proposed guidance method

表1 初始仿真条件

Table 1 Initial simulation conditions

飞行器	位置/m	速度/(m·s^-1)	航迹角/deg
M₁	(0,0)	800	0
M₂	(0,0)	800	5
M₃	(0,0)	800	10
M₄	(0,0)	800	15
T	(0,0)	500	180

图4 4个飞行器之间的拓扑结构

Fig.4 Communication topology for 4 aerial vehicles

图5 所提协同制导方法仿真结果

Fig.5 Simulated results of the proposed guidance method

图6 文献[5]协同制导方法仿真结果

Fig.6 Simulated results of the cooperative guidance method in Ref.[5]

表2 飞行器终端视线角

Table 2 Terminal LOS angles of aerial vehicles

采用制导律	终端视线角/deg
本文制导律	[19.45,9.45,-1.45,-11.45]
文献[5]制导律	[12.72,2.72,-7.28,-17.28]

表3 飞行器能量消耗

Table 3 Energy consumption of aerial vehicles

采用制导律	总能量消耗/(m²·s^-3)
本文制导律	6.42×10⁴
文献[5]制导律	1.70×10⁵

表 4 变量范围

Table 4 Intervals of variables

初始仿真条件	正态分布
飞行器速度V_M/(m·s^-1)	N(800,20²)
飞行器初始航迹角γ₀/deg	N(10,5²)
目标速度V_T/(m·s^-1)	N(600,20²)
目标初始航迹角 $γ T 0$ /deg	N(150,10²)
目标初始横坐标 $x T 0$ /m	N(6000,100²)
目标初始纵坐标 $y T 0$ /m	N(0,100²)
目标加速度 $a M i$ /(m·s^-2)	N(-49.1,4.91²)

表 4 变量范围

Table 4 Intervals of variables

初始仿真条件	正态分布
飞行器速度V_M/(m·s^-1)	N(800,20²)
飞行器初始航迹角γ₀/deg	N(10,5²)
目标速度V_T/(m·s^-1)	N(600,20²)
目标初始航迹角 $γ T 0$ /deg	N(150,10²)
目标初始横坐标 $x T 0$ /m	N(6000,100²)
目标初始纵坐标 $y T 0$ /m	N(0,100²)
目标加速度 $a M i$ /(m·s^-2)	N(-49.1,4.91²)

图 7 蒙特卡洛仿真结果

Fig.7 Monte Carlo simulation results

表5 各性能指标均值

Table 5 The mean values of various performance indicators

采用制导律	总能量消耗/ (m²·s^-3)	脱靶量/m	视线角误差/deg
本文制导律	4.33×10⁴	0.5196	0.4396
文献[5]制导律	2.26×10⁵	0.5245

图 8 4个飞行器之间的拓扑结构

Fig.8 Communication topology for 4 aerial vehicles

图9 分布式拓扑动态变化规律

Fig.9 Dynamic variation law of distributed topology

图10 动态变拓扑仿真结果

Fig.10 Simulated results of dynamic topology variation

表6 对比仿真结果

Table 6 Comparison of simulated results

拓扑是否变化	终端视线角/deg	总能量消耗/(m²·s^-3)
是	[19.45,9.45,-1.45,-11.45]	6.42×10⁴
否	[19.45,9.45,-1.45,-11.45]	6.42×10⁴

表7 初始仿真条件

Table 7 The initial simulation conditions

飞行器	位置/m	速度/(m·s^-1)	航迹角/deg
M₁	(0,3000)	800	0
M₂	(0,3000)	800	5
M₃	(0,3000)	800	10
M₄	(0,3000)	800	15
T	(6000,3000)	500	180

表8 空气动力系数及导数

Table 8 Aerodynamic coefficients and derivatives

马赫数	$C l a l$ /(rad^-1)	C_d0	$C d a l 2$ /(rad^-2)
1.5	27.47	0.575	38.48
2.0	23.83	0.443	30.15
2.5	21.28	0.383	26.12
3.0	19.54	0.352	24.07

表8 空气动力系数及导数

Table 8 Aerodynamic coefficients and derivatives

马赫数	$C l a l$ /(rad^-1)	C_d0	$C d a l 2$ /(rad^-2)
1.5	27.47	0.575	38.48
2.0	23.83	0.443	30.15
2.5	21.28	0.383	26.12
3.0	19.54	0.352	24.07

图11 所提协同制导方法仿真结果

Fig.11 Simulated results of the proposed guidance method

图12 所提方法与文献[5]方法速度变化对比

Fig.12 Comparison of speed changes of aerial vehicles guided by the proposed method and the method in Ref.[5]

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