Decomposition and Control of Multiple Spacecraft Formation Flying

We propose a novel control framework for the formation flying of multiple spacecraft. With the passive decomposition, group dynamics of the multiple spacecraft is decomposed into two decoupled dynamics: the shape system representing the internal group formation shape (formation, in short), and the locked system describing the total group maneuver (maneuver, in short). Then, some desired formation and maneuver of the group can be simultaneously achieved by controlling the shape and locked systems individually. Also, due to the decoupling between the shape and locked systems, high precision maneuver and tight formation can be achieved without any dynamic crosstalk between them. By connecting all group agents via bi-directional controls so that slower agents are prevented from being left behind, the proposed scheme enforces a coherence among the agents as one group. Abstracting a group by its locked system whose dynamics is similar to that of a single spacecraft, the proposed control scheme can also impose an hierarchy for a mixed collection of many agents and groups. We also provide a decentralization of the proposed control scheme for applications where only neighboring sensings (or communications) are available. Simulations are performed to illustrate properties of the proposed control schemes.