考虑主动远离禁飞区的飞行器再入轨迹快速规划

doi:10.7527/S1000-6893.2025.32509

Abstract

Abstract:

To address the reentry trajectory planning problem for hypersonic vehicles with spherical No-Fly Zone （NFZ） constraints， this paper proposes a Sequential Convex Programming （SCP） method based on dynamic objective reconstruction and a hybrid step-size control strategy， enabling proactive NFZ separation assurance. First， a potential function is introduced to model the spherical NFZs as soft constraints， transforming the reentry trajectory planning problem into a sequence of convex subproblems with coupled soft and hard constraints. Second， to mitigate numerical overflow issues caused by the potential function and reduce sensitivity to initial guesses， a two-phase “feasibility-optimality” dynamic decoupling framework is developed. The first phase focuses on computing a feasible solution to generate a high-quality initial trajectory for subsequent optimization， while the second phase dynamically reconstructs the optimization objective using the soft-constraint potential function to maximize the standoff distance from NFZs without significantly compromising primary performance objectives. Furthermore， a hybrid step-size control strategy is designed by integrating the trust-region method with the line-search algorithm， effectively exploiting descent information from rejected steps and improving computational efficiency. Numerical simulations demonstrate that the proposed algorithm guarantees a sufficient safety margin from spherical NFZs. Compared with the conventional trust-region convex optimization method， the proposed method improves computational speed by a 95%， and reduces terminal altitude and velocity errors by factors of 19 and 6， respectively. Compared to the Gauss pseudospectral method， the proposed approach achieves a threefold increase in computational speed while maintaining comparable terminal altitude and velocity accuracy， highlighting its promising potential for practical applications.

Key words: reentry trajectory planning, sequential convex programming, spherical no-fly zone, trust region, line search

CLC Number:

Yao ZHAO, Xi ZHANG, Di ZHOU, Yutang LI, Siyuan LI. Rapid reentry trajectory planning for hypersonic vehicles with proactive no-fly zone separation assurance[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(6): 332509.

Figures/Tables 19

Fig.1

Table 1

Model-related and problem-specific parameters

参数	数值
$h f$ /km	25
$θ f$ /（ $°$ ）	12
$ϕ f$ /（ $°$ ）	70
$γ f$	-10
$ψ f$ /（ $°$ ）	90
$σ m a x$ /（ $°$ ）	80
$u m a x$ / $((°) ⋅ s - 1)$	15
$Q ˙ m a x$ /（ $k W ⋅ m - 2$ ）	2 000
$n m a x$	$3 g 0$
$q m a x$ /（ $k N ⋅ m - 2$ ）	20

Table 1

Table 2

Model hyperparameters

参数	数值
$δ 0$	$10 000 R 0, 20 π 180, 20 π 180, 500 R 0 g 0, 20 π 180, 20 π 180, 20 π 180$
$w$	10^-3· $N d$ ^-1
$μ$	10³
$η 1$	0
$η 2$	0.3
$ε$	0.01
$k m a x 1$	20
$υ$	0.9
$k 1$	0.4
$k 2$	2
$k 3$	2
$k 4$	0.25
$ϖ$	2×10^-6
$k m a x 2$	500
$λ$	0.4

Table 2

Table 3

Ellipsoidal no-fly zone parameters

参数	禁飞区1	禁飞区2
球心高度/km	0	0
球心经度/（ $°$ ）	-2.5	7
球心纬度/（ $°$ ）	70	40
径向轴长/km	85	85
经度方向轴长/（ $°$ ）	8	10
纬度方向轴长/（ $°$ ）	30	30
势函数权重 $κ / 10 - 3$	0.5	0.5
势函数衰减系数 $ξ$	75	75

Table 3

Table 4

Simulation results

算法	目标函数	迭代次数	拒绝次数	时间/s	最小安全距离/km	最终速度/（ $m ⋅ s - 1$ ）	高度误差/m	速度误差/（ $m ⋅ s - 1$ ）
可行性引导SCP算法	-0.108 8	37	0	90.06	17.165 4	912.24	8.67	1.124 6
信赖域放缩SCP算法	-0.102 2	57	29	178.18	-0.015 7	871.42	168.58	7.419 0
回溯线搜索SCP算法	0.137 4	500	0	1 569.02	0.002 6	937.99	37.30	2.964 6
高斯伪谱法	-0.109 6	18	0	405.39	15.089 6	915.21	10.36	0.467 8

Table 4

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Table 5

Simulation results for different potential function weights κ

势函数权重 $κ / 10 - 3$	势函数衰减系数 $ξ$	最终速度/（ $m ⋅ s - 1$ ）	最小安全距离/km
0.1	75	921.46	8.16
0.5	75	912.24	17.16
1.5	75	898.72	25.68
2.5	75	887.13	26.19
5.0	75	857.32	28.24

Table 5

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

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Rapid reentry trajectory planning for hypersonic vehicles with proactive no-fly zone separation assurance

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