基于迭代学习的动目标多约束弹道成型制导方法

doi:10.12382/bgxb.2025.0667

摘要/Abstract

摘要：

针对二维场景中空地导弹攻击地面运动目标问题，提出一种考虑落角约束、落速约束及视场角约束的多项式制导律。基于多项式成型理论，将视线角构造成相对距离的多项式函数，利用落角约束等边界条件，得到多项式系数的代数关系式。针对落速约束要求，将未知的多项式系数设计为控制参数，采用迭代学习方法对其进行逐次更新，进而得到标称制导指令。考虑导引头存在的视场角边界限制，基于控制障碍函数方法建立安全集合并构建优化问题，对标称制导指令进行修正以保证视场角始终保持在约束边界内。通过数值仿真验证了所提出的制导律能够在保证命中目标的同时，还能满足落角约束、落速约束及视场角约束。

关键词: 落角约束, 落速约束, 视场角约束, 多项式成型, 控制障碍函数

Abstract:

A polynomial guidance law that takes into account the constraints on impact angle，impact speed and seeker’s field-of-view （FOV） is proposed for the issue of air-to-ground missile attacking the moving ground target in a two-dimensional scenario.Based on polynomial shaping theory，the line-of-sight （LOS） angle between the missile and the target is formulated as a polynomial function of the relative distance.An algebraic relationship for the polynomial coefficients is derived by using the boundary conditions such as the impact angle constraint.To address the impact speed constraint，the unknown polynomial coefficient is designed as a control parameter and is updated using an iterative learning method，thereby generating a nominal guidance command.Considering the limitation imposed by the FOV angle constraint of seeker，a safe set is established using the control barrier function method.An optimization problem is formulated to adjust the nominal guidance command，ensuring that the seeker’s FOV remains within the constrained boundary throughout the engagement.Numerical simulations demonstrate that the proposed guidance law can be used to guide the missile to the target while satisfying the constraints on impact angle，impact speed and seeker’s FOV.

Key words: impact angle constraint, impact speed constraint, field-of-view angle constraint, polynomial shaping, control barrier function

石忠佼, 胡海洋, 何镜, 林时尧. 基于迭代学习的动目标多约束弹道成型制导方法[J]. 兵工学报, 2025, 46(S1): 250667-.

SHI Zhongjiao, HU Haiyang, HE Jing, LIN Shiyao. An Iterative Learning-based Trajectory Shaping Guidance Method for Missile Attacking Moving Target under Multiple Constraints[J]. Acta Armamentarii, 2025, 46(S1): 250667-.

图/表 34

图1 弹目相对运动模型

Fig.1 Relative motion model of missile and target

图2 弹目连续时间运动

Fig.2 Continuous time motion of missile and target

图3 终端时刻相对位置

Fig.3 Relative position of missile and target at terminal moment

图4 落角、落速和视场角约束实现算法

Fig.4 Implementation algorithm of impact angle，impact speed and field-of-view angle constraints

表1 导弹和目标参数

Table 1 Missile and target parameters

参数	数值
导弹初始位置	（-15000m，12000m）
导弹初始速度	500/600m/s
目标初始位置	（0m，0m）
导弹初始前置角	0deg
期望落角	-30/-60/-90deg
期望落速	300/350/400m/s

表2 固定仿真参数

Table 2 Fixed simulation parameters

参数	数值
m/kg	532
S/m²	0.246
r₀/（kg·m^-3）	1.225
y_a/m	10400
k	0.41
${{C}_{D}}_{0}$	0.131
G/（N²m²kg^-2）	6.67e-11
M/kg	5.972e24
R_e/km	6371

图5 运动目标不同落角约束下的弹道曲线

Fig.5 Trajectories at different impact angles for moving target

图6 运动目标不同落角约束下的相对距离曲线

Fig.6 Relative distance at different impact angles for moving target

图7 运动目标不同落角约束下的弹道倾角曲线

Fig.7 Trajectory inclination angles at different impact angles for moving target

图8 运动目标不同落角约束下的加速度曲线

Fig.8 Accelerations at different impact angles for moving target

图9 运动目标不同落角约束下的前置角曲线

Fig.9 Leading angles at different impact angles for moving target

图10 运动目标不同落角约束下的速度曲线

Fig.10 Speeds at different impact angles for moving target

图11 运动目标不同落角约束下的设计参数曲线

Fig.11 Design parameters at different impact angles for moving target

图12 运动目标不同落速约束下的弹道曲线

Fig.12 Trajectories at different impact speeds for moving target

图13 运动目标不同落速约束下的相对距离曲线

Fig.13 Relative distance at different impact speeds for moving target

图14 运动目标不同落速约束下的弹道倾角曲线

Fig.14 Trajectory inclination angles at different impact speeds for moving target

图15 运动目标不同落速约束下的加速度曲线

Fig.15 Accelerations at different impact speeds for moving target

图16 运动目标不同落速约束下的前置角曲线

Fig.16 Leading angles at different impact speed for moving target

图17 运动目标不同落速约束下的速度曲线

Fig.17 Speeds under different impact speed for moving target

图18 运动目标不同落速约束下的设计参数曲线

Fig.18 Design parameters at different impact speed for moving target

图19 静止目标不同落角约束下的弹道曲线

Fig.19 Trajectories at different impact angles for stationary target

图20 静止目标不同落角约束下的相对距离曲线

Fig.20 Relative distances at different impact angle for stationary target

图21 静止目标不同落角约束下的弹道倾角曲线

Fig.21 Trajectory inclination angles at different impact angles for stationary target

图22 静止目标不同落角约束下的加速度曲线

Fig.22 Accelerations at different impact angle for stationary target

图23 静止目标不同落角约束下的前置角曲线

Fig.23 Leading angles at different impact angle for stationary target

图24 静止目标不同落角约束下的速度曲线

Fig.24 Speeds at different impact angle for stationary target

图25 静止目标不同落角约束下的设计参数曲线

Fig.25 Design parameters at different impact angles for stationary target

图26 静止目标不同落速约束下的弹道曲线

Fig.26 Trajectories at different impact speeds for stationary target

图27 静止目标不同落速约束下的相对距离曲线

Fig.27 Relative distances at different impact speed for stationary target

图28 静止目标不同落速约束下的弹道倾角曲线

Fig.28 Trajectory inclination angles under different impact speed for stationary target

图29 静止目标不同落速约束下的加速度曲线

Fig.29 Accelerations at different impact speeds for stationary target

图30 静止目标不同落速约束下的前置角曲线

Fig.30 Leading angles at different impact speed for stationary target

图31 静止目标不同落速约束下的速度曲线

Fig.31 Speeds at different impact speeds for stationary target

图32 静止目标不同落速约束下的设计参数曲线

Fig.32 Design parameters at different impact speed for stationary target

参考文献 24

[1]	RYOO C K, CHO H, TAHK M J. Optimal guidance laws with terminal impact angle constraint[J]. Journal of Guidance,Control and Dynamics, 2005, 28(4):724-732.
[2]	RYOO C K, CHO H, TAHK M J. Time-to-go weighted optimal guidance with impact angle constraints[J]. IEEE Transactions on Control Systems Technology, 2006, 14(3):483-492.
[3]	王思卓, 范世鹏, 林德福, 等. 考虑目标机动和落角约束的二阶滑模制导律[J]. 兵工学报, 2022, 43(12):3048-3061.
	WANG S Z, FAN S P, LIN D F, et al. Second order sliding mode guidance law considering target maneuver and impact angle constraint[J]. Acta Armamentarii, 2022, 43(12):3048-3061. (in Chinese) doi: 10.12382/bgxb.2021.0641
[4]	KIM T H, LEE C H, TAHK M J. Time-to-go polynomial guidance laws with terminal impact angle/acceleration constraints[J]. IFAC Proceedings Volumes, 2011, 44(1):3915-3919.
[5]	CHENG Z T, WANG B, LIU L, et al. Adaptive polynomial guidance with impact angle constraint under varying velocity[J]. IEEE Access, 2019, 7:104210-104217.
[6]	PADHI R, KOTHARI M. Model predictive static programming:a computationally efficient technique for suboptimal control design[J]. International Journal of Innovative Computing Information and Control, 2009, 5(2):399-411.
[7]	TAHK M J, MOON G H, SHIM S W. Augmented polynomial guidance with terminal speed constraints for unpowered aerial vehicles[J]. International Journal of Aeronautical and Space Sciences, 2019, 20(1):183-194.
[8]	MOON G H, TAHK M J, HAN D H, et al. Generalized polynomial guidance for terminal velocity control of tactical ballistic missiles[J]. International Journal of Aeronautical and Space Sciences, 2021, 22(1):163-175.
[9]	CHEN Y D, LIU J H, SHAN J Y, et al. Impact angle,speed and acceleration control guidance via polynomial trajectory shaping[J]. Journal of the Franklin Institute, 2023, 360(7):4923-4946.
[10]	DONG W, WANG C Y, WANG J N, et al. Unified method for field-of-view-limited homing guidance[J]. Journal of Guidance,Control,and Dynamics, 2022, 45(8):1415-1434.
[11]	SURVE P, MAITY A, KUMAR S R. Polynomial shaping-based field-of-view constrained impact time guidance against non-maneuvering targets[J]. IFAC-PapersOnLine, 2022, 55(22):406-411.
[12]	陈升富, 常思江, 吴放. 带有视场角约束的滑模攻击时间控制制导律[J]. 兵工学报, 2019, 40(4):777-787. doi: 10.3969/j.issn.1000-1093.2019.04.013
	CHEN S F, CHANG S J, WU F. A sliding mode guidance law for impact time control with field of view constraint[J]. Acta Armamentarii, 2019, 40(4):777-787. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.04.013
[13]	KIM H G, KIM H J. Field-of-view constrained guidance law for a maneuvering target with impact angle control[J]. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(6):4974-4983.
[14]	JEON I S, LEE J I, TAHK M J, et al. Impact-time-control guidance law for anti-ship missiles[J]. IEEE Transactions on Control Systems Technology, 2006, 14(2):260-266.
[15]	李文, 尚腾, 姚寅伟, 等. 速度时变情况下多飞行器时间协同制导方法研究[J]. 兵工学报, 2020, 41(6):1096-1110. doi: 10.3969/j.issn.1000-1093.2020.06.006
	LI W, SHANG T, YAO Y W, et al. Research on time-cooperative guidance of multiple flight vehicles with time-varying velocity[J]. Acta Armamentarii, 2020, 41(6):1096-1110. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.06.006
[16]	LI H J, LIU Y H, LI K B, et al. Polynomial guidance for impact-time control against maneuvering targets[J]. Journal of Guidance Control & Dynamics, 2023, 46(12):2388-2398.
[17]	WANG Z Q, HU Q L, HAN T, et al. Two-stage guidance law with constrained impact via circle involute[J]. IEEE Transactions on Aerospace & Electronic Systems, 2021, 57(2):1301-1316.
[18]	SURVE P, MAITY A, KUMAR S R. Polynomial based impact time and impact angle constrained guidance[J]. IFAC-PapersOnline, 2022, 55(1):486-491.
[19]	AARON D A, JESSY W.G, PAULO T. Control barrier function based quadratic programs with application to adaptive cruise control[C]// Proceedings of 53rd IEEE Conference on Decision and Control.Los Angeles,CA, US:IEEE,2014:0191- 2216.
[20]	XIAO W, BELTA C. Control barrier functions for systems with high relative degree[C]// Proceedings of 2019 IEEE 58th Conference on Decision and Control.Nice, France:IEEE,2019:0743-1546.
[21]	KHALIL H K. Nonlinear systems[M]. New Jersey: Prentice-Hall, 2002.
[22]	GLOTFELTER P, CORTES J, EGERSTEDT M. Nonsmooth barrier functions with applications to multi-robot systems[J]. IEEE Control Systems Letters, 2017, 1(2):310-315
[23]	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, 2006.
	QIAN X F, LIN R X, ZHAO Y N. Missile flight mechanics[M]. Beijing: Beijing Institute of Technology Press, 2006. (in Chinese)
[24]	NANAVATI R V, KUMAR S R, MAITY A. Lead-angle-based three-dimensional guidance for angle-constrained interception[J]. Journal of Guidance,Control,and Dynamics, 2021, 44(1):190-199.