Long-term formation keeping of satellite constellation using linear-quadratic controller

Relative formation keeping of a satellite constellation in circular orbits is investigated, The in-plane formation keeping based on tangential maneuvers is defined with use of the averaged equations representing secular relative motion in a neighborhood of a circular reference orbit, The state variables are along-track displacements of satellites (without periodic terms) relative to prescribed intersatellite spacings and displacements of satellite orbital periods with respect to the reference orbit period, A set of along-track relative displacements between satellites is represented by a tree digraph, Long-term behavior of a satellite constellation is described by the linear discrete-time equation in terms of (2N - 1) variables, where N is the total number of satellites, A new linear-quadratic controller for satellite constellations is developed, The formation keeping robustness is discussed, An analytic solution of linear-quadratic formation keeping for two satellites is obtained, Simulation results are presented for the low-altitude satellite constellation affected by atmospheric drag.