An Energy-optimal Relative-angle-constrained Cooperative Guidance Method Based on Distributed Convex Optimization

Jiang WANG; Ziyang ZHU; Hongyan LI; Peng WANG

doi:10.12382/bgxb.2024.0739

您当前的位置：

首页 >

文章列表页 >

An Energy-optimal Relative-angle-constrained Cooperative Guidance Method Based on Distributed Convex Optimization

更新时间：2025-09-05

- An Energy-optimal Relative-angle-constrained Cooperative Guidance Method Based on Distributed Convex Optimization
- Acta Armamentarii Vol. 46, Issue 6, Pages: 240739(2025)
- 作者机构：
  
  1. 北京理工大学宇航学院, 北京 100081
  2. 北京理工大学中国-阿联酋智能无人系统“一带一路”联合实验室, 北京 100081
- 作者简介：
- 基金信息：
- DOI：10.12382/bgxb.2024.0739
  CLC：
- Received：27 August 2024，
  
  Published Online：28 June 2025，
  
  Published：10 June 2025
- 稿件说明：
移动端阅览
Jiang WANG, Ziyang ZHU, Hongyan LI, et al. An Energy-optimal Relative-angle-constrained Cooperative Guidance Method Based on Distributed Convex Optimization[J]. Acta Armamentarii, 2025, 46(6): 240739.
DOI：

Jiang WANG, Ziyang ZHU, Hongyan LI, et al. An Energy-optimal Relative-angle-constrained Cooperative Guidance Method Based on Distributed Convex Optimization[J]. Acta Armamentarii, 2025, 46(6): 240739. DOI： 10.12382/bgxb.2024.0739.

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。

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.

关键词

Keywords

references

尤浩 , 常新龙 , 赵久奋 , 等 . 带攻击角度约束的三维领弹-从弹时间协同制导律 [J ] . 兵工学报 , 2023 , 44 ( 11 ): 3369 - 3381 . DOI: 10.12382/bgxb.2023.0174 http://doi.org/10.12382/bgxb.2023.0174 针对多导弹在三维空间以期望角度协同攻击机动目标的问题,提出一种三维领弹-从弹时间协同制导律。根据弹目相对运动关系建立领弹-从弹三维非线性协同制导模型,无需小角度假设;在视线法向和侧向上,基于2阶滑模控制理论和设计的有限时间收敛滑模面,分别设计领弹-从弹三维角度控制制导律,在提高系统收敛速度的同时抑制了抖振现象;在从弹视线方向上提出时间协同制导律,创新性地将领弹-从弹协同制导问题转化为2阶多智能体一致性跟踪控制问题,充分利用导弹间的信息交互,在实现从弹和领弹时间协同的同时避免传统的剩余时间估计造成的误差问题;同时对新算法分别进行严格的Lyapunov稳定性证明。仿真结果表明:新的三维领弹-从弹时间协同制导律可以有效控制领弹和从弹在三维空间以期望角度高精度协同攻击机动目标。

YOU H , CHANG X L , ZHAO J F , et al . Three-dimensional leader-follower cooperative guidance law with impact angle constraints [J ] . Acta Armamentarii , 2023 , 44 ( 11 ): 3369 - 3381 . (in Chinese) DOI: 10.12382/bgxb.2023.0174 http://doi.org/10.12382/bgxb.2023.0174 A three-dimensional leader-follower cooperative guidance law is proposed for the salvo attack of multiple missiles against a maneuvering target with the desired angles of impact. A three-dimensional nonlinear guidance model for the multiple missiles is established based on the relative motion relationship of missile and target, in which it is not necessary to assum a small lead angle. The three-dimensional guidance laws of leader and followers in the normal and lateral directions to the LOS are designed, respectively, based on the second-order sliding mode control (SMC) theory and designed finite-time convergence SMC surface, which can improve the system convergence speed while suppressing chattering phenomenon. The proposed guidance law innovatively transforms the time consistency problem of the leader-following missiles into a second-order multiagent consensus tracking in the LOS direction of the followers, which achieves the time consistency of leader and followers and, effectively solves the practical problem of low guidance precision caused by the time-to-go estimation. Moreover, the proposed guidance algorithms are proved by strict Lyapunov stability, respectively. The simulated results show that the proposed three-dimensional leader-follower cooperative guidance law can effectively control the leader and followers to attack a maneuvering target with high precision at the desired angles of attack.

YOU H , CHANG X L , ZHAO J F , et al . Three-dimensional impact-angle-constrained cooperative guidance law against maneuvering target [J ] . ISA Transactions , 2023 , 138 : 262 - 280 .

FONOD R , SHIMA T . Estimation enhancement by cooperatively imposing relative intercept angles [J ] . Journal of Guidance,Control,and Dynamics , 2017 , 40 ( 7 ): 1711 - 1725 .

SHAFERMAN V , SHIMA T . Cooperative optimal guidance laws for imposing a relative intercept angle [J ] . Journal of Guidance,Control,and Dynamics , 2015 , 38 ( 8 ): 1395 - 1408 .

LI H Y , HE S M , WANG J , et al . Optimal encirclement guidance [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2022 , 58 ( 5 ): 4327 - 4341 .

SHAFERMAN V , SHIMA T . Cooperative differential games guidance laws for imposing a relative intercept angle [J ] . Journal of Guidance,Control,and Dynamics , 2017 , 40 ( 10 ): 2465 - 2480 .

NEDIĆ A , OZDAGLAR A . Distributed subgradient methods for multi-agent optimization [J ] . IEEE Transactions on Automatic Control , 2009 , 54 ( 1 ): 48 - 61 .

NEDIĆ A , OLSHEVSKY A , SHI W . Achieving geometric convergence for distributed optimization over time-varying graphs [J ] . SIAM Journal on Optimization , 2017 , 27 ( 4 ): 2597 - 2633 .

QU G N , LI N . Harnessing smoothness to accelerate distributed optimization [J ] . IEEE Transactions on Control of Network Systems , 2017 , 5 ( 3 ): 1245 - 1260 .

DI LORENZO P , SCUTARI G . Next:in-network nonconvex optimization [J ] . IEEE Transactions on Signal and Information Processing over Networks , 2016 , 2 ( 2 ): 120 - 136 .

PU S , NEDIĆ A . Distributed stochastic gradient tracking methods [J ] . Mathematical Programming , 2021 , 187 ( 1 ): 409 - 457 .

PU S , SHI W , XU J M , et al . Push-pull gradient methods for distributed optimization in networks [J ] . IEEE Transactions on Automatic Control , 2020 , 66 ( 1 ): 1 - 16 .

XIN R , KHAN U A . A linear algorithm for optimization over directed graphs with geometric convergence [J ] . IEEE Control Systems Letters , 2018 , 2 ( 3 ): 315 - 320 .

SOLMAZ S K , JORGE C , SONIA M . Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication [J ] . Automatica , 2015 , 55 : 254 - 264 .

SHI W , LING Q , WU G , et al . Extra:an exact first-order algorithm for decentralized consensus optimization [J ] . SIAM Journal on Optimization , 2015 , 25 ( 2 ): 944 - 966 .

KIA S S , CORTÉS J , MARTÍNEZ S . Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication [J ] . Automatica , 2015 , 55 : 254 - 264 .

SHI W , LING Q , YUAN K , et al . On the linear convergence of the ADMM in decentralized consensus optimization [J ] . IEEE Transactions on Signal Processing , 2014 , 62 ( 7 ): 1750 - 1761 .

ALGHUNAIM S A , SAYED A H . Linear convergence of primal-dual gradient methods and their performance in distributed optimization [J ] . Automatica , 2020 , 117 : 109003 .

XU J M , TIAN Y , SUN Y , et al . Distributed algorithms for composite optimization:Unified framework and convergence analysis [J ] . IEEE Transactions on Signal Processing , 2021 , 69 : 3555 - 3570 .

LI Z , SHI W , YAN M . A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates [J ] . IEEE Transactions on Signal Processing , 2019 , 67 ( 17 ): 4494 - 4506

LEI J L , CHEN H F , FANG H T . Primal-dual algorithm for distributed constrained optimization [J ] . Systems & Control Letters , 2016 , 96 : 110 - 117 .

钱杏芳 , 林瑞雄 , 赵亚男 . 导弹飞行力学 [M ] . 北京 : 北京理工大学出版社 , 2008 : 170 .

QIAN X F , LING R X , ZHAO Y N . Missile flight mechanics [M ] . Beijing : Beijing Institute of Technology Press , 2008 : 170 . (in Chinese)

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 .

何智川 , 王江 , 范世鹏 , 等 . 事件触发机制下具有视场约束的三维协同制导 [J ] . 航空学报 , 2024 , 45 ( 3 ): 223 - 237 .

HE Z C , WANG J , FAN S P , et al . Three-dimensional cooperative guidance with field-of-view constraints under event-triggered mechanism [J ] . Acta Aeronautica et Astronautica Sinica , 2024 , 45 ( 3 ): 223 - 237 . (in Chinese)

杨登峰 , 闫晓东 . 多防御弹主动防御系统协同一致拦截 [J ] . 战术导弹技术 , 2023 ( 5 ): 73 - 82 .

YANG D F , YAN X D . Simultaneous and cooperative interception with multiple defense missiles for active defense system [J ] . Tactical Missile Technology , 2023 ( 5 ): 73 - 82 . (in Chinese)

林德福 , 王辉 , 王江 , 等 . 战术导弹自动驾驶仪设计与制导律分析 [M ] . 北京 : 北京理工大学出版社 , 2012 : 159 .

LING D F , WANG H , WANG J , et al . Autopilot design and guidance law analysis for tactical missiles [M ] . Beijing : Beijing Institute of Technology Press , 2012 : 159 . (in Chinese)

LI H Y , WANG J , HE S M , et al . Nonlinear Optimal 3-D impact-angle-control guidance against maneuvering targets [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2022 , 58 ( 3 ): 2467 - 2481 .

HE S M , LEE C H . Gravity-turn-assisted optimal guidance law [J ] . Journal of Guidance,Control,and Dynamics , 2018 , 41 ( 1 ): 171 - 183 .

CHEN Z , SHIMA T . Nonlinear optimal guidance for intercepting a stationary target [J ] . Journal of Guidance,Control,and Dynamics , 2019 , 42 ( 11 ): 2418 - 2431 .

LI H Y , WANG J , TAO H , et al . Near-optimal impact-vector-control guidance [J ] . Journal of Guidance,Control,and Dynamics , 2024 , 47 ( 9 ): 1965 - 1972 .

JUNG C G , LEE C H . Optimal impact angle control guidance law considering aerodynamic drag [J ] . Journal of Guidance,Control,and Dynamics , 2024 , 47 ( 11 ): 2435 - 2443 .

JEON I S , KARPENKO M , LEE J I . Connections between proportional navigation and terminal velocity maximization guidance [J ] . Journal of Guidance,Control,and Dynamics , 2020 , 43 ( 2 ): 383 - 388 .

LU P . What is guidance [J ] . Journal of Guidance,Control,and Dynamics , 2021 , 44 ( 7 ): 1237 - 1238 .

LEE C H , SEO M G . New insights into guidance laws with terminal angle constraints [J ] . Journal of Guidance,Control,and Dynamics , 2018 , 41 ( 8 ): 1832 - 1837 .

LEWIS F L , ZHANG H W , HENGSTER M , et al . Cooperative Control of Multi-Agent Systems [M ] . London,UK : Springer Nature , 2014 : 25 - 27 .

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 http://doi.org/10.12382/bgxb.2022.1086 面向三维场景下的多导弹协同攻击机动目标问题,基于固定时间稳定理论和自适应滑模控制理论,设计考虑时间及空间约束的分布式协同制导律。在弹目视线方向上,基于固定时间一致性理论提出一种改进型自适应鲁棒协同制导律,驱动弹群以期望的攻击时刻协同拦截机动目标,并避免滑模固有的抖振问题;考虑视线法向的空间约束,基于固定时间非奇异终端滑模控制理论设计一种鲁棒自适应滑模制导律,在实现终端碰撞角约束的同时避免弹群间碰撞。通过Lyapunov稳定性理论证明闭环系统的固定时间稳定性。仿真结果表明:所设计三维协同制导律可以有效控制多发导弹在期望攻击时刻同时打击机动目标,并以期望的终端角度攻击目标。

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 http://doi.org/10.12382/bgxb.2022.1086 Aiming at the problem of three-dimensional multiple missiles intercepting a maneuvering target simultaneously, a three-dimensional distributed cooperative guidance law considering time and space constraints. The proposed guidance law is based on fixed-time stable theory and adaptive sliding mode theory. Along the light-of-sight (LOS) direction, an improved robust adaptive cooperative guidance law is presented based on fixed-time consensus, which can drive a group of missiles to attack maneuvering target at a desired impact time without inherent chattering of sliding mode control. Along the direction vertical to the line-of-sight, a robust adaptive guidance law is proposed based on nonsingular fixed-time terminal sliding mode technique, which can drive missiles attack target with desired impact angle and avoid collision between missiles. Through the Lyapunov stability theory, the fixed-time stability of closed-loop system is demonstrated. The simulation results show that the proposed approach can be implemented to intercept maneuvering targets with desired impact time and impact angle.

GODSIL C , ROYLE GF . Algebraic graph theory [M ] . Berlin,Germany : Springer Science & Business Media , 2001 : 173 - 174 .

BERTSEKAS D . Convex optimization theory [M ] . Nashua, NH,US : Athena Scientific , 2009 : 71

NESTEROV Y . Introductory lectures on convex programming volume I:basic course [J ] . Lecture Notes , 1998 , 3 ( 4 ): 5 .

HONG M Y , WANG Y , RAZAVIYAYN M , et al . Iteration complexity analysis of block coordinate descent methods [J ] . Mathematical Programming , 2017 , 163 : 110 - 114 .

Views

下载量

CNKI被引量

Alert me when the article has been cited

提交

Tools

Publicity Resources

A Cooperative Guidance Law Based on Meta-learning and Reinforcement Learning for Multiple Aerial Vehicles

Target Acquisition Probability of an Airborne Strapdown Missile at Hand-over Point

Multi-platform Networked Guidance Handover Technology

Cooperative Guidance Method of Leader and Seeker-less Follower Flight Vehicles

Unmanned Aerial Vehicle Cluster Cooperative Guidance Technology Based on Conflict Trigger Mechanism

Related Author

Hai LIN

Xiaofang WANG

Cuncan WANG

Shifeng ZHANG

Xibin BAI

Huabo YANG

Jiayang WU

Binlin YUAN

Related Institution

School of Aerospace Engineering, Beijing Institute of Technology

College of Aerospace Science and Engineering, National University of Defense Technology

Hunan Provincial Key Laboratory of Aerospace Cross-Domain Flight Vehicle Systems and Control Technology

School of Electronics and Information, Northwestern Polytechnical University

Shenyang Aircraft Design and Research Institute

Postal code：100089
Tel：010-68963060/68962718 Fax：010-68963025 Email：bgxb@cos.org.cn
Technical support is provided by Beijing Founder electronics co., LTD 京ICP备05059581号-4 京公网安备11010802024360号
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.
Total Visits：44524 Visits Today：504

⁰