Application of Hamiltonian structure-preserving control to cluster flight for fractionated spacecraft on an elliptic orbit

This paper deals with the bounded quasi-periodic relative trajectories on an elliptic orbit by the Hamiltonian structure-preserving controller employing only relative positions for feedback without any measurement from relative velocity. The periodic Lawden's equation describing the linearized relative dynamics on an elliptic orbit serves as a nominal reference model for stationkeeping controllers to generate quasi-periodic trajectories near the equilibrium. A Hamiltonian structure-preserving controller is derived to stabilize the three-dimensional time-periodic relative dynamics with the feedback from invariant manifolds. The unstable and stable manifolds are employed to change the hyperbolic equilibrium to elliptic one with the poles assigned on the imaginary axis. The detailed investigations are conducted on the critical controller gain for Floquet stability, and the optimal gains from the views of local and global optimizations for the fuel cost, respectively.