共面单脉冲拦截多目标问题

doi:10.7527/S1000-6893.2021.25093

电子电气工程与控制

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共面单脉冲拦截多目标问题

夏存言, 张刚, 耿云海

哈尔滨工业大学卫星技术研究所, 哈尔滨 150001

收稿日期:2020-12-11 修回日期:2021-01-28 出版日期:2022-03-15 发布日期:2021-04-21
通讯作者: 张刚 E-mail:zhanggang@hit.edu.cn
基金资助:
国家自然科学基金（11772104）

Coplanar multi-target interception with a single impulse

XIA Cunyan, ZHANG Gang, GENG Yunhai

Research Center of Satellite Technology, Harbin Institute of Technology, Harbin 150001, China

Received:2020-12-11 Revised:2021-01-28 Online:2022-03-15 Published:2021-04-21
Supported by:
National Natural Science Foundation of China (11772104)

摘要/Abstract

摘要： 针对共面轨道的单脉冲拦截多目标问题，提出了一种求解拦截二、三目标的数值方法。对于单脉冲拦截二目标问题，当脉冲时刻或拦截某目标时刻给定时，通过Gibbs三矢量定轨算法，将该问题转化为求解只包含2个自由变量的非线性方程问题，通过Newton-Raphson迭代算法实现求解；进一步，考虑脉冲时刻自由，通过数值优化可得到燃料最优解。对于单脉冲拦截三目标问题，基于Lambert解将其转化为求解只包含2个自由变量的非线性方程问题，并通过数值迭代求解。两个问题求解时的迭代初值均通过Pork-Chop图法搜索得到。数值算例验证了提出方法的正确性及有效性。

关键词: 单脉冲, 多目标拦截, 三矢量定轨, Lambert理论, Pork-Chop图

Abstract: This paper proposes a numerical method to solve the coplanar two/three-target orbit interception problem with a single impulse.For the two-target interception problem, the impulse time or interception time for the one target is considered to be free.By using the Gibbs method for orbit determination from three position vectors, the problem is transformed into solving the nonlinear equations of only two free variables.Newton-Raphson iterations are adopted to solve the nonlinear equations.The optimal fuel solution is obtained for this problem by numerically optimizing the impulse time.By using the Lambert algorithm, the three-target interception problem is also transformed into solving the nonlinear equations of only two free variables.Numerical iteration is adopted to solve the equations.The initial guesses of both two/three-target interception problem are obtained by the Pork-chop plot method.Numerical examples are provided to verify the correctness and effectiveness of the proposed methods.

Key words: single impulse, multi-target interception, orbit determination from three position vectors, Lambert algorithm, Pork-chop plot

中图分类号:

V412.4⁺1

夏存言, 张刚, 耿云海. 共面单脉冲拦截多目标问题[J]. 航空学报, 2022, 43(3): 325093-325093.

XIA Cunyan, ZHANG Gang, GENG Yunhai. Coplanar multi-target interception with a single impulse[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(3): 325093-325093.

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共面单脉冲拦截多目标问题

Coplanar multi-target interception with a single impulse

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