Box Covering

Author: Tianjiang Shuo Website: https://cislunarspace.cn

Definition

A set covering method implemented in GAIO software. By subdividing the high-dimensional space containing a Poincare map into progressively smaller rectangular boxes, it constructs a discrete approximation of the target invariant set. Only boxes intersecting the target set are retained, forming a discrete approximation of manifold-section intersections. This enables systematic detection of connecting points between manifolds in different CRTBP models while controlling intersection accuracy in configuration space.

Application Value

This concept plays a key role in trajectory transfer design, helping evaluate transfer costs and flight time to provide quantitative basis for mission trade studies. Combined with global search algorithms, multiple solution families and Pareto frontiers can be identified to guide orbital design decisions.

References

  • Dellnitz and Junge, 2002; Zanzottera et al., 2012
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Contributors: ouyangjiahong, Ou Yang Jiahong