Formation control for the next generation Earth-gravimetry missions

The formation control of a long-distance, drag-free, low-thrust, low-Earth orbit satellite is outlined, in view of future Earth-gravity monitoring missions employing long baseline interferometry (> 10 km) and lasting at least six years. To this purpose, a formation consisting of two drag-free satellites, orbiting at a fixed distance in a sun-synchronous orbit, has been proposed as a baseline. Formation fluctuations are bounded by a box 500x50x50 m. Although at first sight not demanding, the formation control induces non-gravitational accelerations, that are obliged to respect tight drag-free requirements, and are constrained by millinewton thrust bounds. In addition formation fluctuations due to tide forces should not be impaired as their measurement is the mission goal. Requirements are formulated as four time and frequency–domain inequalities, to be suitably parameterized by control gains. Exploiting closeloop Hill’s equation properties and asymptotic approximations, explicit design inequalities are obtained leading to a first-trial control design. Simulated runs through a fine spacecraft and low-Earth-orbit simulation dominated by the highly variable thermosphere drag show the first-trial design meets the tight control requirements, and demonstrates mission feasibility.