Long-distance, Drag-free, Low-thrust, Leo Formation Control for Earth Gravity Monitoring

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. Formation fluctuations are bounded by a 500x50x50 m wide (along-track, cross-track and radial) box. Although at first not seemingly demanding, the formation control induces non-gravitational accelerations, that are obliged to respect tight drag-free requirements, and are constrained by millinewton thrust bounds so as to curtail electric thruster throttability. In addition, formation fluctuations due to tide forces should not be impaired as their measurement is the mission goal. Requirements are formulated as a set of four time and frequency–domain inequalities, which are suitably parameterized by control gains. By exploiting the properties and asymptotic approximations of close-loop Hill’s equation, explicit design inequalities are obtained leading to a first-trial control design. Simulated runs through fine spacecraft and low-Earth-orbit simulation, which is dominated by a highly variable thermosphere drag, show that the first-trial design meets the tight control requirements, and demonstrates mission feasibility.