无动力滑翔飞行器集群实时协同航迹规划方法

doi:10.12382/bgxb.2024.0827

摘要/Abstract

摘要：

为了解决无动力滑翔飞行器集群飞行过程中的编队变换、末端时间约束以及末端进入角度约束的在线航迹规划应用问题,提出一种基于主弹-从弹架构的无动力滑翔飞行器集群实时协同航迹规划方法。通过解耦飞行器航迹的纵向和横向剖面,设计基于分段函数的攻角速度曲线方法,以应对无动力滑翔飞行器再入段的非线性约束。提出基于航向角随时间变化的协同控制方法,通过求解协同控制微分方程,得到无动力滑翔飞行器集群在再入段准平衡滑翔状态下满足编队变换,以及末端时间约束和目标区域进入角约束的航迹规划方案。进一步基于协同控制解析方法提出在线调整策略,以应对目标区域的实时变化,并证明该在线调整策略在线应用的可行性。仿真结果表明,该协同航迹规划方法可以在不同的飞行场景下实现在线协同航迹规划,且适用于多种协同控制方案,具有鲁棒性和实用性,能够为无动力滑翔飞行器集群的实际应用提供支持。

关键词: 无动力滑翔飞行器, 编队控制, 协同控制, 航迹规划

Abstract:

The trajectory planning online applications for the formation transformation,impact time and terminal entry angle constraint of unpowered gliding vehicle clusters during the re-entry phase are studied.A real-time coordinated trajectory planning method for unpowered gliding vehicle cluster based on master-slave architecture is proposed.The trajectories of the vehicles are first decoupled into longitudinal and lateral planes,and a segmented function-based angle-of-attack velocity profile method is developed to handle the nonlinear constraints encountered during the re-entry phase.A cooperative control method based on time-varying heading angles is then proposed,which involves solving differential equations to generate a trajectory that satisfies the formation transformation and the impact time and entry angle constraints under quasi-equilibrium glide conditions.An online adjustment strategy is further introduced to accommodate the real-time updates to the target area,and the feasibility of the proposed method for online application is demonstrated.Simulated results indicate that the proposed method can achieve real-time coordinated trajectory planning across various flight scenarios,thus demonstrating its robustness,adaptability to multiple cooperative control schemes,and practical applicability to unpowered gliding vehicle clusters.

Key words: unpowered gliding vehicle, formation control, coordinated trajectory, trajectory planning

中图分类号:

V448.235

王卓峣, 李传军, 马景权, 于加其. 无动力滑翔飞行器集群实时协同航迹规划方法[J]. 兵工学报, 2025, 46(8): 240827-.

WANG Zhuoyao, LI Chuanjun, MA Jingquan, YU Jiaqi. Real-time Coordinated Trajectory Planning Method of Unpowered Gliding Vehicle Clusters[J]. Acta Armamentarii, 2025, 46(8): 240827-.

图/表 31

图1 无动力滑翔集群协同编队目标区域更新及编队变换过程

Fig.1 The process of target area updating and formation transformation of unpowered gliding vehicle cluster

图2 无动力滑翔飞行器航迹纵向横向剖面解耦示意图

Fig.2 Schematic diagram of longitudinal and lateral planes decoupling of unpowered gliding vehicle trajectory

图3 无动力滑翔飞行器再入段航迹规划流程

Fig.3 Planning flowchart for reentry phase of unpowered gliding vehicle

图4 无动力滑翔飞行器再入段初始时刻横向剖面坐标系

Fig.4 Schematic diagram of the lateral plane coordinate system at the initial time

图5 编队协同控制分段方法

Fig.5 Formation cooperative control segmentation method

图6 末端进入角约束任务协同规划分段方法

Fig.6 Collaborative planning segmentation method for terminal entry angle constraint task

图7 目标更新情况下实时协同控制策略

Fig.7 Real-time cooperative control strategy in the case of target update

表1 无动力滑翔集群再入初始条件

Table 1 Reentry initial conditions of unpowered gliding vehicle cluster

飞行器编号及构型	高度/km	经度/(°)	纬度/(°)
0(主弹)	45.0	100.0	20.000
1(从弹)	45.0	99.8	20.015
2(从弹)	45.0	100.2	20.015
3(从弹)	45.0	100.1	20.010
4(从弹)	45.0	99.9	20.010
散开构型	飞行器集群以主弹为中心横向各弹之间依次距离10km
紧凑构型	飞行器集群以主弹为中心横向各弹之间依次距离1km

图8 无动力滑翔飞行器高度-时间曲线

Fig.8 Height-time curve of unpowered gliding vehicle

图9 无动力滑翔飞行器弹道倾角-时间曲线

Fig.9 Trajectory inclination angle-time curve of unpowered gliding vehicle

图10 无动力滑翔飞行器攻角-时间曲线

Fig.10 The angle of attack-time curve of unpowered gliding vehicle

图11 无动力滑翔飞行器速度-时间曲线

Fig.11 Velocity-time curve of unpowered gliding vehicle

图12 目标区域更新下飞行器集群编队变换实时航迹曲线

Fig.12 Real-time trajectory curve of vehicle cluster formation transformation under the target area update

表2 编队变换协同控制误差

Table 2 Cooperative control error of formation transformation

参数	从弹编号
参数	1	2	3	4
目标区域更新前协同误差/km	-0.579	0.577	0.316	-0.420
目标区域更新后协同误差/km	-0.677	0.722	0.300	-0.499

图13 目标区域更新后各弹航向角-时间曲线

Fig.13 The heading angle-timr curve of each vehicle after the target area is updated

图14 目标区域更新后各弹倾侧角-时间曲线

Fig.14 The inclination angle curve of each vehicle after the target area is updated

图15 目标区域更新下飞行器集群编队变换及末端进入角约束实时航迹曲线

Fig.15 Formation transformation and entry angle constraint rea; -time trajectory curve of vehicle cluster under the target area update

表3 协同控制误差

Table 3 Collaborative control error

参数	从弹编号
参数	1	2	3	4
目标区域更新前协同误差/km	-0.316	0.172	-1.010	1.040
目标区域更新后协同误差/km	0.004	0.256	-0.087	1.578

图16 目标区域更新后各弹航向角-时间曲线

Fig.16 The heading angle-time curve of each vehicle after the target area is updated

图17 目标区域更新后各弹倾侧角-时间曲线

Fig.17 The inclination angle-time curve of each vehicle after the target area is updated

表4 蒙特卡洛协同控制误差初始条件

Table 4 Monte Carlo cooperative control of the error initial conditions

飞行器	高度/km	经度/(°)	纬度/(°)
主弹	45	100.00	20.000
从弹1	45	99.80	20.015
从弹2	45	99.85	20.018
从弹3	45	99.90	20.016
从弹4	45	99.95	20.014

图18 末端相对进入角0°情况下协同误差蒙特卡洛仿真

Fig.18 Monte Carlo simulation of cooperative error in the case of the terminal relative entry angle of 0°

图19 末端相对进入角5°情况下协同误差蒙特卡洛仿真

Fig.19 Monte Carlo simulation of cooperative error in the case of the terminal relative entry angle of 5°

图20 末端相对进入角10°情况下协同误差蒙特卡洛仿真

Fig.20 Monte Carlo simulation of cooperative error in the case of the terminal relative entry angle of 10°

图21 末端相对进入角20°情况下协同误差蒙特卡洛仿真

Fig.21 Monte Carlo simulation of cooperative error in the case of the terminal relative entry angle of 20°

图22 强干扰环境下不同气动偏差对目标区域更新下飞行器集群编队变换及末端进入角约束实时航迹曲线的影响

Fig.22 The influences of different aerodynamic deviations on the formation transformation of vehicle cluster and the real-time track curve of terminal entry angle constraint under target area renewal

表5 目标区域更新后协同控制误差

Table 5 Collaborative control error after the target area is updated km

气动偏差/%	从弹编号
气动偏差/%	1	2	3	4
0	0.004	0.256	-0.087	1.578
5	-0.617	0.643	0.937	-0.585
10	-0.707	0.870	1.185	-0.294
20	-0.027	1.074	1.337	-0.220

图23 多目标区域更新下飞行器集群编队变换及末端进入角约束实时航迹曲线

Fig.23 Vehicle cluster formation transformation and entry angle constraint real-time trajectory curves under the multi-update of target area

表6 第2次目标区域更新后协同误差

Table 6 Collaborative control error after the second update of target area km

从弹1	从弹2	从弹3	从弹4
-0.124	-0.454	-0.457	1.777

图24 多目标区域更新后各弹航向角-时间曲线

Fig.24 The heading angle curve of each vehicle under the multi-update of target area

图25 多目标区域更新后各弹倾侧角-时间曲线

Fig.25 The inclination angle curve of each vehicle under the multi-update of target area

参考文献 24

[1]	张远, 黄旭, 路坤锋, 等. 高超声速飞行器控制技术研究进展与展望[J]. 宇航学报, 2022, 43(7):866-879.
	ZHANG Y, HUANG X, LU K F, et al. Research progress and prospect of the hypersonic flight vehicle control technology[J]. Journal of Aeronautics, 2022, 43(7):866-879. (in Chinese)
[2]	LIANG Z X, REN Z, LI Q D, et al. Decoupled three-dimensional entry trajectory planning based on maneuver coefficient[J]. Proceedings of the Institution of Mechanical Engineers,Part G:Journal of Aerospace Engineering, 2017, 231(7):1281-1292.
[3]	DING Y B, YUE X K, CHEN G S, et al. Review of control and guidance technology on hypersonic vehicle[J]. Chinese Journal of Aeronautics, 2022, 35(7):1-18
[4]	郭明坤, 杨峰, 刘凯, 等. 无动力滑翔飞行器协同制导技术研究进展[J]. 空天技术, 2022(2):75-84.
	GUO M K, YANG F, LIU K, et al. Research progress on cooperative guidance technology for unpowered vehicles[J]. Aerospace Technology, 2022(2):75-84. (in Chinese)
[5]	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):020256.
	ZHAO J B, YANG S X. Summary of multi-missile collaborative guidance research[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(1):020256. (in Chinese)
[6]	郑卓, 路坤锋, 王昭磊, 等. 飞行器集群协同控制技术分析与展望[J]. 宇航学报, 2023, 44(4):538-545.
	ZHENG Z, LU K F, WANG Z L, et al. Analysis and prospect of collaborative control technology of aircraft cluster[J]. Journal of Astronautics, 2023, 44(4):538-545. (in Chinese)
[7]	张源, 张冉, 李惠峰. 复杂禁飞区无动力滑翔飞行器路径-轨迹双层规划[J]. 宇航学报, 2022, 43(5):615-627.
	ZHANG Y, ZHANG R, LI H F. Dual-level path-trajectory generation with complex no-fly zone constraints for unpowered vehicle[J]. Journal of Astronautics, 2022, 43(5):615-627. (in Chinese)
[8]	朱金冬, 张方齐, 赵彤. 任务规划系统机动模型与航线设计[J]. 航空工程进展, 2022, 13(4):73-82.
	ZHU J D, ZHANG F Q, ZHAO T. Mission planning system maneuver model and route design[J]. Progress in Aeronautical Engineering, 2022, 13(4):73-82. (in Chinese)
[9]	王磊, 徐超, 李淼, 等. 多飞行器协同任务分配的改进粒子群优化算法[J]. 兵工学报, 2023, 44(8):2224-2232. doi: 10.12382/bgxb.2022.0968
	WANG L, XU C, LI M, et al. Improved particle swarm optimization algorithm for multi-aircraft collaborative task assignment[J]. Acta Armamentarii, 2023, 44(8):2224-2232. (in Chinese) doi: 10.12382/bgxb.2022.0968
[10]	WANG J F, JIA G W, LIN J C, et al. Cooperative task allocation for heterogeneous multi-UAV using multi objective optimization algorithm[J]. Journal of Central South University, 2020, 27(2):432-448.
[11]	魏昀鹏, 都延丽, 王文凯, 等. 无动力滑翔飞行器时间协同预测校正鲁棒制导[J]. 宇航学报, 2024, 45(3):421-432.
	WEI Y P, DU Y L, WANG W K, et al. Time-cooperative Predictor corrector Robust Guidance for unpowered vehicles[J]. Journal of Astronautics, 2024, 45(3):421-432. (in Chinese)
[12]	WANG H N, GUO J, WANG X, et al. Time-coordination entry guidance using a range-determined strategy[J]. Aerospace Science and Technology, 2022, 129:107842.
[13]	姜鹏, 郭栋, 韩亮, 等. 多飞行器再入段时间协同弹道规划方法[J]. 航空学报, 2020, 41(增刊1):723776.
	JIANG P, GUO D, HAN L, et al. Cooperative ballistic planning method for multi-craft re-entry time[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(S1):723776. (in Chinese) doi: 10.7527/S1000-6893.2019.23776
[14]	乔浩, 毛瑞, 白凤科, 等. 带时间约束的双参数再入轨迹设计方法[J]. 弹箭与制导学报, 2021, 41(3) :57-61. doi: 10.15892/j.cnki.djzdxb.2021.03.013
	QIAO H, MAO R, BAI F K, et al. Two-parameter reentry trajectory design method with time constraints[J]. Journal of Projectiles,Rockets,Missiles and Guidance, 2021, 41(3):57-61. (in Chinese)
[15]	池海红, 周明鑫. 融合强化学习和进化算法的无动力滑翔航迹规划[J]. 控制理论与应用, 2022, 39(5):847-856.
	CHI H H, ZHOU M X. Trajectory planning for unpowered vehicle combined with reinforcement learning and evolutionary algorithms[J]. Control Theory & Applications, 2022, 39(5):847-856. (in Chinese)
[16]	张晚晴, 余文斌, 李静琳, 等. 基于纵程解析解的飞行器智能横程机动再入协同制导[J]. 兵工学报, 2021, 42(7):1400-1411.
	ZHANG W Q, XU W B, LI J L, et al. Cooperative reentry guidance for intelligent lateral maneuver of hypersonic vehicle based on downrange analytical solution[J]. Acta Armamentarii, 2021, 42(7):1400-1411. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.07.007
[17]	LIANG Z X, LONG J T, ZHU S Y, et al. Entry guidance with terminal approach angle constraint[J]. Aerospace Science and Technology, 2020, 102:105876.
[18]	王少平, 董受全, 隋先辉, 等. 助推滑翔无动力滑翔导弹发展趋势及作战使用研究[J]. 战术导弹技术, 2020(1):9-14.
	WANG S P, DONG S Q, SUI X H, et al. Research on development and operational application of boost-glide unpowered missile[J]. Tactical Missile Technology, 2020(1):9-14. (in Chinese)
[19]	LI Z, WANG Y D, ZHENG W. Adaptively tracking hypersonic gliding vehicles[J]. Aerospace Science and Technology, 2024, 147:109035.
[20]	ZHOU H Y, WANG X G, LI X, et al. Synergistic planning for hypersonic vehicles with an analytic hybrid algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 2025, 61(1):223-232.
[21]	张磊, 罗迎, 张群. 雷达组网系统对抗有源干扰方法综述[J]. 信息对抗技术, 2023, 2(6):1-16.
	ZHANG L, LU Y, ZHANG Q. Summary of counteracting active jamming method of radar networking system[J]. Information Countermeasure Technology, 2023, 2(6):1-16. (in Chinese)
[22]	韩晓斐, 何华锋, 何耀民, 等. 主被动异构弹载雷达组网抑制假目标干扰方法[J]. 兵工学报, 2022, 43(12):3142-3150.
	HAN X F, HE H F, HE Y M, et al. A method against false-target jamming based on active/passive isomerism missile-borne radar network[J]. Acta Armamentarii, 2022, 43(12) :3142-3150. (in Chinese) doi: 10.12382/bgxb.2021.0716
[23]	张俊, 胡生亮, 杨庆, 等. 浮空式角反射体RCS统计特征及识别模型研究[J]. 系统工程与电子技术, 2019, 41(4):780-786.
	ZHANG J, HU S L, YANG Q, et al. RCS statistical features and recognition model of air-floating corner reflector[J]. Systems Engineering and Electronics, 2019, 41(4):780-786. (in Chinese)
[24]	宋瑞, 朱勇, 徐广通, 等. 基于序列凸优化的高超声速飞行器协同再入轨迹规划[J]. 战术导弹技术, 2020(6):7-16.
	SONG R, ZHU Y, XU G T, et al. Cooperative reentry trajectory planning of hypersonic vehicle based on sequential convex programming[J]. Tactical Missile Technology, 2020(6):7-16. (in Chinese)