Satellite formation reconfiguration and station-keeping using state-dependent Riccati equation technique

The current paper presents optimal reconfigurations and formation-keeping for formation flying satellites. The state-dependent Riccati equation (SDRE) technique is utilized as a non-linear controller for both the reconfiguration problem and formation-keeping problem. For the SDRE controller, a state-dependent coefficient (SDC) form is formulated to include non-linearities in the relative dynamics and J₂ orbital perturbation. The Taylor series and a transformation matrix are used to establish the SDC form. Optimal reconfiguration trajectories that minimize energy in satellite formation flying are obtained by the SDRE controller and compared with those obtained from a linear quadratic regulator (LQR) and a linear parameter varying (LPV) control method. It is illustrated that the SDRE non-linear controller of the current study obtains relocation accuracy of less than 0.1% of formation base-line length, while the LQR controller and LPV controller yield relatively large relocation errors. The formation-keeping controller developed using the SDRE technique in the current study also provides robustness under severe orbital perturbations.