L2-L1 Homotopy

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A homotopy continuation method connecting the energy minimization problem (L2-norm) to the minimum-fuel problem (L1-norm) via convex combination of the two cost functionals. Starting from the smooth energy-optimal solution, it progressively transitions to the bang-bang minimum-fuel solution. Its drawback is that shooting precision degrades significantly at low thrust as the number of control switchings grows rapidly.

Application Value

L2-L1同伦法是地月空间研究的基础概念，为理解更复杂的航天器动力学问题提供了理论支撑 在实际工程应用中，L2-L1同伦法的准确计算和分析对于任务成功至关重要 掌握L2-L1同伦法的概念有助于工程师进行轨道设计和任务规划 L2-L1同伦法为航天器轨道力学研究提供了基本框架，是进一步学习高级概念的基础

References

  • Caillau et al. 2012 - Minimum fuel control of the planar circular restricted three-body problem
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Contributors: ouyangjiahong, Ou Yang Jiahong