Position/Velocity Consensus in Formation Flying of Multiple Spacecraft*

This paper investigates the position/velocity consensus problem for multiple spacecraft agents subjected to nonlinear gravitational forces, where the interconnection graph among the agents is assumed to contain a spanning tree. We employ the linear position/velocity coupling control for attaining consensus of the spacecraft agents. With a similarity decomposition approach, the closed-loop networked system is decomposed into two subsystems, i.e., the group dynamics and the formation dynamics. First, we derive the boundedness of the formation errors relying on the input-output analysis of the formation dynamics, where a relatively aggressive sufficient condition is presented. Second, we present a sufficient condition to ensure the exponential convergence of the formation errors using the Lyapunov analysis.