Real-time Coordinated Trajectory Planning Method of Unpowered Gliding Vehicle Clusters

doi:10.12382/bgxb.2024.0827

Abstract

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

CLC Number:

V448.235

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-.

Figures/Tables 31

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

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

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

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

Fig.5 Formation cooperative control segmentation method

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

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

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

Fig.8 Height-time curve of unpowered gliding vehicle

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

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

Fig.11 Velocity-time curve of unpowered gliding vehicle

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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