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摘要:
Lambert双脉冲交会问题是航天工程中轨道转移和在轨交会等领域的重要问题，而能量最优和燃料最优Lambert交会问题是针对典型应用背景和工程需求衍生的一类Lambert优化问题。针对能量最优与燃料最优Lambert双脉冲交会问题提出一种基于矢量形式的解析计算方法，给出能量最优和燃料最优Lambert交会问题的矢量形式解析解，同时对2种最优交会问题求解的性质与特点进行了分析对比。仿真结果验证了计算的正确性及燃料最优轨道相比能量最优轨道燃料消耗较少的事实。
Abstract:The Lambert two-impulse rendezvous problem is an important problem in orbital-transfer, rendezvous and docking and other fields in space engineering. Fuel-optimal and energy-optimal Lambert rendezvous problems are a kind of Lambert optimization problem that has the typical application background and engineering requirements. In this paper, an analytical calculation method based on vector form is proposed for energy-optimal and fuel-optimal Lambert rendezvous problems, and then the analytic solution in vector form is developed for the energy-optimal and fuel-optimal Lambert rendezvous problems. The nature and characteristics of the two analytic solutions for optimization rendezvous problem are analyzed and contrasted. The simulation results prove the correctness of this method and that fuel consumption of fuel-optimal orbit is less than that of energy-optimal orbit.
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图 3 ΔVtot和ΔVtot2目标函数值随p变化情况(极点附近)
Figure 3. Variation of ΔVtot and ΔVtot2 function with p (near peak point)
表 1 ALSET 1和ARIANE 44L卫星的轨道参数(NORAD两行轨道根数)[12]
Table 1. Orbit parameters of two satellites ALSET 1 and ARIANE 44L (NORAD two-line element sets)[12]
ALSET 1 1 27 559U 02 054A 08 259.526 859 48 -0.000 000 02 00 000-0 84 653-5 0 6 025 2 27 559 097.980 7 137.478 4 0 009 664 216.549 4 143.504 7 14.629 778 973 095 34 ARIANE 44L 1 28 576U 91 075N 08 351.945 684 14 0.000 001 79 00 000-0 64 019-2 0 6 927 2 28 576 006.553 4 128.062 9 6 595 687 237.361 1 042.002 9 02.835 874 63 72 170 
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表 2 起始点和目标点位置
Table 2. Location of starting point and ending point
km 位置 rx ry rz r1 3 160.125 4 -3 850.670 7 -5 011.985 2 r2 -16 875.892 6 14 279.183 4 516.039 2
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表 3 起始点和目标点速度
Table 3. Velocity of starting point and ending point
km/s 速度 vx vy vz v1 -4.458 3.101 2 -5.191 6 v2 -1.276 5 1.799 5 3.043 9
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表 4 ΔV Lambert问题起止点速度增量
Table 4. Velocity increments at starting point and ending point of ΔV Lambert problem
km/s 速度增量 Δwx Δwy Δwz Δw1 -1.361 22 0.147 84 -1.625 77 Δw2 8.786×10-6 8.841×10-6 10.017×10-6
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表 5 ΔV2 Lambert问题起止点速度增量
Table 5. Velocity increments at starting point and ending point of ΔV2 Lambert problem
km/s 速度增量 Δwx Δwy Δwz Δw1 -1.300 08 0.085 91 -1.670 27 Δw2 -0.076 03 0.066 70 0.012 16
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表 6 转移轨道参数
Table 6. Transition orbit parameter
目标函数 p/km 
目标函数值/
(km·s-1)ΔVtot 11 360.100 67 291.462 2.125 56 ΔVtot2 11 285.930 67 071.429 4.497 8
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