Clustering Natural Trajectories in the Earth-Moon Circular Restricted Three-Body Problem

Summaries of the diverse array of natural spacecraft motions that exist within cislunar space could support trajectory design and space situational awareness. This paper uses a clustering-based framework to automatically summarize the prominent geometries of a large set of natural, spatial trajectories in the Earth-Moon circular restricted three-body problem. This procedure is demonstrated using trajectories that begin near the Moon, possess a specified duration, and exist across a range of energy levels. These continuous trajectories are discretized using a curvature-based sampling scheme that efficiently captures their global shape. These samples are used to form finite-dimensional feature vectors that summarize the shape and path of each trajectory. Using these definitions, initial conditions are sampled throughout a desired region of the phase space in a geometry-based manner that relies on the concept of curvature as well as localized clustering. The trajectories associated with these initial conditions are then grouped by their geometry in a distributed manner by applying a two-step, density-based clustering process to their feature vectors. The result is a data-driven summary of prominent geometries exhibited across a large set of trajectories sampled from a complex and diverse solution space.