Robust and Safe N-Spacecraft Swarming in Perturbed Near-Circular Orbits

Abstract

This paper presents a new guidance and control methodology for spacecraft swarms based on relative orbital elements, that generalizes flight-proven techniques used for binary formations to accommodate a large number of spacecraft. The formation design problem is cast in the relative orbital elements to allow derivation of linear constraints that ensure passively bounded relative motion in perturbed near-circular orbits. This approach also enables derivation of analytical constraints that ensure collision avoidance including uncertainty at a computational cost that scales only linearly with the number of spacecraft. Additionally, two swarm formations are identified that ensure a user-specified minimum separation between all spacecraft in either the orbit plane or the plane perpendicular to the flight direction. To counteract the effects of differential drag, nonlinear state space control laws are developed that require actuation in only the (anti-)flight direction. These control laws are employed in a hybrid passive/active control architecture that only actuates the spacecraft when necessary to ensure collision avoidance, allowing periodic passive drifts of up to several days. The proposed formation designs and control architectures are validated in simulations of a reference mission scenario using a high-fidelity numerical orbit propagator.