Swarm Keeping Strategies for Spacecraft under J_2 and Atmospheric Drag Perturbations

This paper presents several new open-loop guidance methods for spacecraft swarms composed 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 propellant used throughout the mission. The development of these methods progresses by eliminating drift using the Hill-Clohessy-Wiltshire equations, removing drift due to nonlinearity, and minimizing the J_2 drift. In order to verify these guidance methods, a new dynamic model for the relative motion of spacecraft is developed. These dynamics include the two main disturbances for spacecraft in Low Earth Orbit (LEO), J_2 and atmospheric drag. Using this dynamic model, numerical simulations are provided at each step to show the effectiveness 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 the trajectories for hundreds of collision-free orbits in the presence of J_2. Finally, a multi-burn strategy is developed in order to provide hundreds of collision-free orbits under the influence of atmospheric drag. This last method works by enforcing the initial conditions multiple times throughout the mission thereby providing collision-free trajectories for the duration of the mission.