Distributed Connectivity Maintenance and Collision Avoidance Control of Spacecraft Formation Flying

This paper studies the distributed control of spacecraft formation flying with collision avoidance and connectivity maintenance. Until now, almost all studies do not consider the impact of the spacecraft's relative position on the communication graph between spacecraft, instead, merely assume that the communication graph satisfies certain connectivity conditions, such as connectivity of an undirected graph, strong connectivity of a directed graph, or joint connectivity of a switching graph. This paper proposes a distributed connectivity maintenance controller to ensure the connectivity of communication graph during spacecraft formation flying. First, a dynamic graph based on the relative distance between the spacecraft is employed to model the real-time communication graph. In addition, two artificial potential functions, respectively, regarded as the repulsive force and the attractive force, are established to preserve the graph connectivity and avoid the collisions at the same time. A distributed connectivity preserving control law is proposed to eliminate the computing burden of a single satellite and enhance the reliability of the spacecraft system. The distributed control algorithm ensures that if the graph is connected at the initial time, then it will connect in the future. The mass uncertainties are also taken into account for implementation in the complex space environment. Numerical simulations of the proposed method are presented to show the effectiveness of the distributed controller during spacecraft formation flying.