考虑避障和攻击角度约束的平行最优制导

doi:10.7527/S1000-6893.2026.33827

Abstract

Abstract:

For high-value offensive precision-strike missions in complex battlefield environments， a robust parallel optimal guidance method considering obstacle-avoidance， flight-time， and impact-angle constraints is proposed. First， to accurately describe the characteristics of obstacles， a three-dimensional cylinder-hemisphere model is constructed， and the LogSumExp function is employed to obtain a smooth representation of the obstacle avoidance constraint. Furthermore， an optimization problem incorporating trajectory length and smoothness indices is formulated， and a time-parameterized optimal trajectory satisfying the obstacle avoidance constraint and the terminal impact angle constraint is generated based on Bézier curves. On this basis， the optimal trajectory is taken as the reference trajectory， and a robust parallel optimal guidance method with composite learning capability is designed by combining the idea of single-network reinforcement learning； in this method， historical data is used to update the weights of the critic network， thereby improving the optimal control law online， relaxing the persistent excitation condition， and eliminating the dependence on an initial admissible control policy. Through Lyapunov stability theory， the uniform ultimate boundedness of the closed-loop system is analyzed and proved. Simulation results show that the proposed method can obtain a safe， smooth， and feasible trajectory with the desired terminal impact angle in complex obstacle environments， and achieve high-precision tracking of the reference trajectory， thereby verifying its effectiveness in complex constrained scenarios.

Key words: obstacle avoidance constraint, impact angle constraint, Bézier curve, reinforcement learning control, robust parallel optimal control

CLC Number:

V249

Junhui LI, Wei WANG, Baokui GENG, Yuchen WANG, Yi JI, Defu LIN. Parallel optimal guidance for obstacle avoidance and impact angle constraints[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(19): 633827.

Figures/Tables 9

Fig.1

Table 1

Fig.2

Fig.3

Table 2

Trajectory length comparison under different impact angle constraints

$θ f, ϕ f$	航迹长度
$θ f, ϕ f$	本方法	IAC-OA	减少率/%
$- 40 °, 10 °$	11 564.8	13 551.9	14.66
$- 40 °, 40 °$	11 905.6	13 478.7	11.67
$- 60 °, 10 °$	11 597.7	14 631.2	20.73
$- 60 °, - 20 °$	11 525.1	15 110.2	23.73
$- 80 °, 40 °$	11 914.7	15 766.7	24.43
$- 80 °, - 20 °$	11 902.1	15 891.3	25.10

Table 2

Table 3

Trajectory smoothness comparison under different impact angle constraints

$θ f, ϕ f$	航迹平滑性
$θ f, ϕ f$	本方法/10⁷	IAC-OA/10¹⁰
$- 40 °, 10 °$	$2.58$	$1.03$
$- 40 °, 40 °$	$6.32$	$8.13$
$- 60 °, 10 °$	$5.64$	$1.19$
$- 60 °, - 20 °$	$4.59$	$1.47$
$- 80 °, 40 °$	$8.40$	$1.43$
$- 80 °, - 20 °$	$7.98$	$1.58$

Table 3

Fig.4

Fig.5

Fig.6

References 35

[1]	DONG W， DENG F， WANG C Y， et al. Three-dimensional spatial-temporal cooperative guidance without active speed control［J］. Journal of Guidance， Control， and Dynamics， 2023， 46（10）： 1981-1996.
[2]	ZHAO R， YU X， WANG D C， et al. Two-stage three-dimensional obstacle avoidance and impact angle control guidance law［J］. Aerospace Science and Technology， 2025， 161： 110104.
[3]	董伟，易鑫，张后军，等. 攻击角度和时间精确控制的制导律设计［J］. 航空学报， 2025， 46（4）： 330787.
	DONG W， YI X， ZHANG H J， et al. Design of guidance law with precise impact angle and time control［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（4）： 330787 （in Chinese）.
[4]	PARK J， JEONG E T， JUNG K W， et al. Proportional navigation guidance with virtual targeting for impact angle control［J］. IEEE Transactions on Aerospace and Electronic Systems， 2025， 61（1）： 457-472.
[5]	YOU H， CHANG X L， ZHAO J F， et al. Three-dimensional impact-angle-constrained cooperative guidance strategy against maneuvering target［J］. ISA Transactions， 2023， 138： 262-280.
[6]	张宏岩，王伟，陈仕伟，等. 基于全驱系统方法的制导控制一体化设计［J］. 航空学报， 2024， 45（1）：628891.
	ZHANG H Y， WANG W， CHEN S W， et al. Integrated guidance and control design based on fully actuated system method［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（1）： 628891 （in Chinese）.
[7]	闫循良，王培臣，郭杨. 再入滑翔机动突防轨迹规划与制导方法综述［J］. 航空学报， 2025， 46（17）： 331810.
	YAN X L， WANG P C， GUO Y. Review of trajectory planning and guidance methods for entry glide maneuvering penetration［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（17）： 331810 （in Chinese）.
[8]	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.
[9]	YU Z， QI N， LI Z， et al. Optimization of multi-target continuous dynamic trajectory for unmanned aerial vehicles［J］. Aerospace Science and Technology， 2024， 150： 108958.
[10]	孙清黎，郭健，王永圣. 考虑非圆禁飞区的空天飞行器TAEM段轨迹规划方法［J］. 航空学报， 2026， 47（11）： 332177.
	SUN Q L， GUO J， WANG Y S. TAEM phase trajectory planning of aerospace vehicle with non-circular no-fly zones［J］. Acta Aeronautica et Astronautica Sinica， 2026， 47（11）： 332177 （in Chinese）.
[11]	LI H， LÜ X K， YU J L， et al. Impact time and angle guidance strategy with maximum lateral acceleration constraints： Theory and experiment［J］. Chinese Journal of Aeronautics， 2026， 39（7）： 103775.
[12]	SHI H， CHENG Z Q， KUANG M C， et al. Four-stage guidance law for impact time and angle control based on the bezier curve［J］. IEEE Transactions on Aerospace and Electronic Systems， 2024， 60（4）： 3766-3778.
[13]	CHEN W X， HU Y D， GAO C S， et al. Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer［J］. Defence Technology， 2024， 32： 412-429.
[14]	ZHAO J， SHI Z J， WANG Y C， et al. Quaternion-based adaptive trajectory tracking control of a rotor-missile with unknown parameters identification［J］. Defence Technology， 2024， 31： 375-386.
[15]	CHEN W X， HU Y D， GAO C S， et al. Three-dimensional trajectory tracking guidance against near-space maneuvering targets with multiple constraints under wind field［J］. Control Engineering Practice， 2024， 142： 105745.
[16]	DENG T B， HUANG H， FANG Y W， et al. Reinforcement learning-based missile terminal guidance of maneuvering targets with decoys［J］. Chinese Journal of Aeronautics， 2023， 36（12）： 309-324.
[17]	PENG C， ZHANG H W， HE Y X， et al. State-following-kernel-based online reinforcement learning guidance law against maneuvering target［J］. IEEE Transactions on Aerospace and Electronic Systems， 2022， 58（6）： 5784-5797.
[18]	ANNASWAMY A M， FRADKOV A L. A historical perspective of adaptive control and learning［J］. Annual Reviews in Control， 2021， 52： 18-41.
[19]	LUO R， PENG Z N， HU J P， et al. Adaptive optimal control of affine nonlinear systems via identifier-critic neural network approximation with relaxed PE conditions［J］. Neural Networks， 2023， 167： 588-600.
[20]	李梦花，王鼎，赵明明，等. 不依赖初始容许控制的非对称约束零和博弈智能评判设计［J］. 控制与决策， 2025， 40（4）： 1347-1356.
	LI M H， WANG D， ZHAO M M， et al. Intelligent critic design for asymmetric constrained zero-sum games without relying on initial admissible control［J］. Control and Decision， 2025， 40（4）： 1347-1356 （in Chinese）.
[21]	ZHANG W G， YI W J. Composite adaptive dynamic programming for missile interception systems with multiple constraints and less sensor requirement［J］. ISA Transactions， 2021， 117： 40-53.
[22]	SUN H， YAN S， LIANG Y， et al. Memory-extraction-based DRL cooperative guidance against the maneuvering target protected by interceptors［J］. Aerospace Science and Technology， 2024， 155： 109575.
[23]	ORTEGA R， NIKIFOROV V， GERASIMOV D. On modified parameter estimators for identification and adaptive control. A unified framework and some new schemes［J］. Annual Reviews in Control， 2020， 50： 278-293.
[24]	WANG D， HE H B， LIU D R. Intelligent optimal control with critic learning for a nonlinear overhead crane system［J］. IEEE Transactions on Industrial Informatics， 2018， 14（7）： 2932-2940.
[25]	WEI Q L， LI H Y， WANG F Y. Parallel control for continuous-time linear systems： A case study［J］. IEEE/CAA Journal of Automatica Sinica， 2020， 7（4）： 919-928.
[26]	JIAO S S， WEI Q L， XIAO J. Parallel control with event-based adaptive critic implementation for robust optimal tracking of uncertain nonlinear systems［J］. IEEE Transactions on Automation Science and Engineering， 2025， 22： 5673-5686.
[27]	GREENE M L， DEPTULA P， NIVISON S， et al. Approximate optimal trajectory tracking with sparse bellman error extrapolation［J］. IEEE Transactions on Automatic Control， 2023， 68（6）： 3618-3624.
[28]	CHO N， SHIN H S， KIM Y， et al. Composite model reference adaptive control with parameter convergence under finite excitation［J］. IEEE Transactions on Automatic Control， 2018， 63（3）： 811-818.
[29]	LI H Y， HE S M， WANG J， et al. Near-optimal midcourse guidance for velocity maximization with constrained arrival angle［J］. Journal of Guidance， Control， and Dynamics， 2021， 44（1）： 172-180.
[30]	CHEN S W， WANG W， FAN J F， et al. Robust enhanced model-predictive guidance for impact angle constraints and obstacle avoidance［J］. IEEE Transactions on Aerospace and Electronic Systems， 2025， 61（6）： 19366-19382.
[31]	MOLNAR T G， AMES A D. Composing control barrier functions for complex safety specifications［J］. IEEE Control Systems Letters， 2023， 7： 3615-3620.
[32]	KONG X W， ZHANG C， XIONG F F. Impact speed and angle constrained guidance law for unpowered gliding vehicle［J］. Chinese Journal of Aeronautics， 2025， 38（4）： 103196.
[33]	GRINFELD N， BEN-ASHER J Z. Minimal-jerk missile guidance law［J］. Journal of Guidance， Control， and Dynamics， 2015， 38（8）： 1520-1525.
[34]	LU J W， WEI Q L， WANG F Y. Parallel control for optimal tracking via adaptive dynamic programming［J］. IEEE/CAA Journal of Automatica Sinica， 2020， 7（6）： 1662-1674.
[35]	OUYANG Y C， DONG L， SUN C Y. Critic learning-based control for robotic manipulators with prescribed constraints［J］. IEEE Transactions on Cybernetics， 2022， 52（4）： 2274-2283.

条件	障碍物1	障碍物2	障碍物3
中心坐标/m	（500，300）	（1 000，650）	（1 500，850）
半径/m	50	50	100
高度/m	60	200	200

Parallel optimal guidance for obstacle avoidance and impact angle constraints

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 9

References 35

Related Articles 10

Recommended Articles

Metrics

Comments

[1]	Wencong WANG, Tingting DU, Qingzhong JIA, Hongji YANG, Yichen WANG. Sliding mode guidance law for variable-speed missiles based on predictive estimation and time-space constraints [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(14): 332519-332519.
[2]	Qinglei HU, Shuxin ZHANG, Tuo HAN, Qingyun WANG. Terminal guidance law under multiple constraints of high-order reshaping of relative range profile [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(6): 531405-531405.
[3]	Wei DONG, Xin YI, Houjun ZHANG, Chunyan WANG, Fang DENG. Design of guidance law with precise impact angle and time control [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(4): 330787-330787.
[4]	Haowen LUO, Shaoming HE, Tianyu JIN, Zichao LIU. Impact-angle-constrained with time-minimum guidance algorithm based on transfer learning [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 328400-328400.
[5]	LIU Zichao, WANG Jiang, HE Shaoming, LI Yufei. A computational guidance algorithm for impact angle control based on predictor-corrector concept [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 325433-325433.
[6]	LI Kebo, LIAO Xuanping, LIANG Yan'gang, LI Chaoyong, CHEN Lei. Guidance strategy with impact angle constraints based on pure proportional navigation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(S2): 724277-724277.
[7]	ZHANG Kuanqiao, YANG Suochang, LI Baochen, LIU Chang. Fixed-time convergent guidance law considering autopilot dynamics [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(11): 323227-323227.
[8]	ZHAO Qilun, CHEN Jian, LI Qingdong, REN Zhang, LI Liang. Feasible region of hypersonic and ballistic missiles' cooperative attack strategy [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(7): 2291-2300.
[9]	ZHANG Youan, HUANG Jie, SUN Yangping. Generalized Weighted Optimal Guidance Laws with Impact Angle Constraints [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(3): 848-856.
[10]	HU Xijing, HUANG Xuemei. Three-dimensional Circular Guidance Law with Impact Angle Constraints [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2012, (3): 508-519.