Exploring the Design Space of Low-Thrust Transfers with Ballistic Terminal Coast Segments in Cis-Lunar Space

Spacecraft catering to the Lunar Gateway or other “permanent” stations in the lunar vicinity would require frequent travel between periodic orbits around the Earth–Moon L1 and L2 Lagrange points. The transition through the Hill sphere is often characterized by close passages of our nearest neighbor—rendering the optimization problem numerically challenging due to the increased local sensitivities. Depending on the mission requirements and resource constraints, transfer architectures must be studied, and trade-offs between flight time and fuel consumption quantified. While direct low-thrust transfers between the circular restricted three-body problem periodic orbit families have been studied, the asymptotic flow in the neighborhood of the periodic orbits could be leveraged for expansion and densification of the solution space. This paper presents an approach to achieve a dense mapping of manifold-assisted, low-thrust transfers based on initial and terminal coast segments. Continuation schemes are utilized to attain the powered intermediate time-optimal segment through a multi-shooting approach. Interesting insights regarding the linear correlation between ΔV and change in reduced two-body osculating elements associated with the initial-terminal conditions are discussed. These insights could inform the subsequent filtering of the osculating selenocentric periapsis map and provide additional interesting and efficient solutions. The described approach is anticipated to be extremely useful for future crewed and robotic cis-lunar operations.