Manifold-Based Space Mission Design with Poincaré Filtering Algorithm

Abstract

This paper presents the application of manifolds for space mission design in the Circular Restricted Three Body Problem, Bi-Circular Restricted Four Body Problem, and Patched-Planar Circular Restricted Three Body Problem. We tackle these three types of missions by defining each mission's manifold-based transfer roadmap/sequence. The transfer to Sun-Earth L4 and L5 planar Lyapunov orbits utilizing the electric-propulsion-system-assisted artificial stable manifolds and the Sun-Earth system's L1 and L2 stable and unstable manifolds are designed utilizing the circular restricted three-body problem. We also design the weak stability boundary transfers to Earth-Moon's L1 and L2 utilizing Earth-Moon's stable manifold and Sun-Earth's L1 and L2 unstable manifolds utilizing the Bi-Circular Restricted Four Body Problem. We present a manifold projection method to quickly assess manifold reachability for multiple-moon tour analysis utilizing the patched-planar circular restricted three-body problem. A new filter is used during the Poincare section analysis to determine optimal sets of stable and unstable manifolds for several types of missions. The multiple-point differential corrector is utilized with optimal manifolds to determine a continuous smooth trajectory for spacecraft with impulsive burn maneuvers.