一种多约束条件下的三脉冲交会优化设计方法

doi:10.12305/j.issn.1001-506X.2022.08.26

Abstract

Abstract:

The optimal three-impulse remote rendezvous between coplanar circles under multi-constraints including rendezvous time constraint and transfer path constraint is studied for the fast approaching and fixed-point observation mission in space. The Hill guidance and particle swarm optimization are combined to solve the optimal solution of transfer path point and transfer time. An equivalent transformation is proposed to transform the original variables to be solved into a new set of variables which are independent of each other. By applying this transformation algorithm, the original constraints are converted into the searching space boundaries which are easy to describe and cope with, such that it is convenient to perform the initialization and conduct the algorithm design. Finally, two simulation experiments of optimal three-impulse rendezvous are given. The results not only verify effectiveness of the proposed algorithm, but also indicate that compared with the conventional penalization method used to deal with constraints, the algorithm adopting the proposed equivalent transformation shows more powerful search ability and stronger stability.

Key words: three-impulse rendezvous, Hill guidance, particle swarm optimization, multi-constraint, equivalent transformation

CLC Number:

V488

Junlong LI, Songzhou LI, Di ZHOU. Optimization method for three-impulse rendezvous under multi-constraints[J]. Systems Engineering and Electronics, 2022, 44(8): 2612-2620.

Figures/Tables 13

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References 32

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轨道参数	目标飞行器	追赶飞行器
半长轴a/km	7 178	7 128
偏心率e	1.900 52e-16	7.547 06e-16
轨道倾角i/(°)	0	0
升交点赤经Ω/(°)	0	0
近心点角距ω/(°)	0	0
真近角f/(°)	0.693 7	0

初始化参数	变换前	变换后
k_max	100	100
w	0.8	0.8
c_p	2	2
c_g	2	2
N	100	100
X_min	[0, 0, 0, －100, －50]^T	[0,0,0,0,0]^T
X_max	[600, 600, 600, －1, 50]^T	[1,1,1,1,1]^T
V_min	－[6, 6, 6, 0.5, 0.5]^T	－[0.01, 0.01, 0.01, 0.01, 0.01]^T
V_max	[6, 6, 6, 0.5, 0.5]^T	[0.01, 0.01, 0.01, 0.01, 0.01]^T

结果参数	变换前	变换后
总冲量最小值/(m/s)	293.08	272.17
总冲量最大值/(m/s)	430.44	329.68
总冲量平均值/(m/s)	352.89	300.02
总冲量标准差/(m/s)	32.44	11.52
终端误差最小值/m	0.01	1.21
终端误差最大值/m	18.11	21.27
终端误差平均值/m	4.30	9.83
终端误差标准差/m	4.45	3.94

结果参数	变换前	变换后
最优解([Δt₀, Δt₁, Δ t₂, x₂, y₂]^T)	[16.18, 296.50, 285.63, －33.36, －35.45]^T	[4.23, 333.55, 259.42, －30.52, －30.95]^T
第一脉冲/(m/s)	[108.60, 17.17]^T	[104.56, 22.59]^T
第二脉冲/(m/s)	[－8.29, 15.70]^T	[1.14, 2.13]^T
第三脉冲/(m/s)	[－73.88, －147.95]^T	[－79.22, －142.13]^T
总冲量/(m/s)	293.08	272.17
终端误差/m	18.11	16.02

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Optimization method for three-impulse rendezvous under multi-constraints

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