Swarm-Keeping Strategies for Spacecraft Under J2 and Atmospheric Drag Perturbations

Abstract

This paper presents several new open-loop guidance methods for spacecraft swarms comprised of hundreds to thousands of agents with each spacecraft having modest capabilities. These methods have three main goals: preventing relative drift of the swarm, preventing collisions within the swarm, and minimizing the fuel used throughout the mission. The development of these methods progresses by eliminating drift using the Hill-ClohessyWiltshire equations, removing drift due to nonlinearity, and minimizing the J2 drift. In order to verify these guidance methods, a new dynamic model for the relative motion of spacecraft is developed. These dynamics are exact and include the two main disturbances for spacecraft in Low Earth Orbit (LEO), J2 and atmospheric drag. Using this dynamic model, numerical simulations are provided at each step to show the eectiveness of each method and to see where improvements can be made. The main result is a set of initial conditions for each spacecraft in the swarm which provides hundreds of collision-free orbits in the presence of J2. Finally, a multi-burn strategy is developed in order to provide hundreds of collision free orbits under the inuence of atmospheric drag. This last method works by enforcing the initial conditions multiple times throughout the mission thereby providing collision free motion for the duration of the mission.