Automated detection of invariant manifold intersections using adaptive grid method

This paper tackles a critical issue for developing an efficient automated global opti-mization tool for spacecraft trajectory optimization in the three body realm. Specifically, we address the issue of seeding a global optimizer with states that lie near advantageous homoclinic and heteroclinic connections. We accomplish this with a new method that pro-grammatically identifies queried regions of subsets of Poincaré surfaces of section. This method uses an adaptively sized grid approach which scales in size to detect the interior of bounded regions. Additionally, this approach overlaps sets which are the result from intersecting two manifolds with Poincaré surfaces of section to identify various regions of interest. A Delaunay triangulation method is used to detect intersection of sets of points and as an output generates regions which are designed to be queried by a global optimizer.