北京航空航天大学学报 ›› 2018, Vol. 44 ›› Issue (9): 1888-1893.doi: 10.13700/j.bh.1001-5965.2017.0731

• 论文 • 上一篇    下一篇

能量最优与燃料最优Lambert交会问题

徐利民, 张涛, 陶佳伟   

  1. 清华大学 自动化系, 北京 100084
  • 收稿日期:2017-11-22 出版日期:2018-09-20 发布日期:2018-09-21
  • 通讯作者: 张涛.E-mail:taozhang@tsinghua.edu.cn E-mail:taozhang@tsinghua.edu.cn
  • 作者简介:徐利民 男,博士研究生,讲师。主要研究方向:导航、制导与控制;张涛 男,博士,教授。主要研究方向:导航、制导与控制;陶佳伟 男,博士研究生。主要研究方向:导航、制导与控制。
  • 基金资助:
    国家自然科学基金(61673239)

Energy-optimal and fuel-optimal problems for Lambert rendezvous

XU Limin, ZHANG Tao, TAO Jiawei   

  1. Department of Automation, Tsinghua University, Beijing 100084, China
  • Received:2017-11-22 Online:2018-09-20 Published:2018-09-21
  • Supported by:
    National Natural Science Foundation of China (61673239)

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。

关键词: 双脉冲变轨, Lambert交会, 能量最优, 燃料最优, 两点边值问题, 最优规划

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.

Key words: two-impulse orbital-transfer, Lambert rendezvous, energy-optimal, fuel-optimal, two-point boundary value problem, optimal planning

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