Controlled and Uncontrolled Motion in the Circular, Restricted Three-body Problem: Dynamically Natural Spacecraft Formations

Spacecraft formation flying involves operating multiple spacecraft in a pre-determined geometrical shape such that the configuration yields both individual and system benefits. One example is an over-flight of the same spatial position by spacecraft in geocentric orbit with the intent to create a complementary data set of remotely sensed observables. Another example is controlling to a high degree of accuracy the distance between spacecraft in heliocentric orbit to create a virtual, large-diameter interferometer telescope. Although Keplerian orbits provide the basic framework for general and precision spacecraft formation flying they also present limitations. Spacecraft are generally constrained to operate only in circular and elliptical orbits, parabolic paths, or hyperbolic trajectories around celestial bodies. Applying continuation methods and bifurcation theory techniques to the circular, restricted three-body problem - where stable and unstable periodic orbits exist around equilibrium points - creates an environment that is more orbit rich. After surmounting a similar challenge with test particles in the circular, restricted three-vortex problem in fluid mechanics as a proof-of-concept, it was shown that spacecraft traveling in uncontrolled motion along separate and distinct planar or three-dimensional periodic orbits could be placed in controlled motion, i.e. a controller is enabled and later disabled at precisely the proper positions, to have them phase-locked on a single periodic orbit. Although it was possible to use this controller in a resonant frequency/orbit approach to establish a formation, it was clearly shown that a separate controller could be used in conjunction with the first to expedite the formation establishment process. Creation of these dynamically natural spacecraft formations or multi-spacecraft platforms will enable the 'loiter, synchronize/coordinate, and observe' approach for future engineering and scientific missions where flexibility is a top-level requirement and key to mission success.