An Iterative Learning-based Trajectory Shaping Guidance Method for Missile Attacking Moving Target under Multiple Constraints

doi:10.12382/bgxb.2025.0667

Abstract

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

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-.

Figures/Tables 34

Fig.1 Relative motion model of missile and target

Fig.2 Continuous time motion of missile and target

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

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

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

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

Fig.5 Trajectories at different impact angles for moving target

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

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

Fig.8 Accelerations at different impact angles for moving target

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

Fig.10 Speeds at different impact angles for moving target

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

Fig.12 Trajectories at different impact speeds for moving target

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

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

Fig.15 Accelerations at different impact speeds for moving target

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

Fig.17 Speeds under different impact speed for moving target

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

Fig.19 Trajectories at different impact angles for stationary target

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

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

Fig.22 Accelerations at different impact angle for stationary target

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

Fig.24 Speeds at different impact angle for stationary target

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

Fig.26 Trajectories at different impact speeds for stationary target

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

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

Fig.29 Accelerations at different impact speeds for stationary target

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

Fig.31 Speeds at different impact speeds for stationary target

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

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