ESA GNC Conference Papers Repository
Long-Distance, Low-Earth-Orbit, Drag-Free Integrated Orbit and Formation Control for the Next Generation Gravity Mission
The Next Generation Gravity Mission (NGGM) under study by the European Space Agency will consists of a two-satellite long-distance formation like GRACE where each satellite will be controlled to be drag-free like GOCE. Satellite-to-satellite distance variations, encoding gravity anomalies, will be measured by laser interferometry with an accuracy improvement of at least three orders of magnitude with respect to GRACE. The formation will fly in a polar orbit at an Earth altitude between 300 and 400 km, which requires drag cancellation (drag-free control) and formation control. Drag-free control uses the ultrafine accelerometers of the GOCE mission. Formation control use the receivers of a Global Navigation System (GNS) mounted on each satellite and a suitable satellite interlink. Formation actuators have been selected among millinewton electric thrusters. Two kinds of formation have been studied: in line formation where the two satellites move on the same polar orbit and pendulum formation where the satellites move on RAAN separated orbits. The paper focuses on the integrated orbit and formation control, whose aim is the orbit and formation long-term stability (> 10 years) though admitting large natural fluctuations around the reference values. Drag-free control, being an acceleration control, is not capable of achieving orbit and formation stability, although nongravitational acceleration residuals will be very small and bounded. The reason is that Hills perturbation equations are not bounded-input-bounded-output (BIBO) stable, and position/velocity feedback becomes mandatory. The design of the control loop presented here appears not conventional for different reasons. Firstly it must not alter the zero-mean free response of the local gravity field, but it must only zero secular response components and it must stabilize the perturbed dynamics to achieve BIBO stability. Secondly we look for a continuous control with the aim of respecting drag-free residuals above 1 mHz, where gravity anomalies should be detected. A smooth command recomputed at each orbit has been proved being capable of stabilizing orbit and formation without degrading drag-free residuals. The relevant perturbed dynamics sampled at the orbit period has been proved to allow controllability of the required variables. Third, orbit and formation control have been integrated in a unique three degrees-of-freedom control system, aiming at stabilizing the formation triangle consisting of satellite and Earth CoMs. Control has been designed using the Embedded Model control methodology and is organized in a hierarchical way where drag-free control plays the role of a wide-band inner loop, and orbit/formation control plays the role of a narrow band under-sampled outer loop. The paper starts with the formation-triangle dynamic model. The relevant state equations are then converted to discrete time thus obtaining the embedded model part of the control unit. State predictor, control law and reference generator are built on and interface to the embedded model. Simulated results proving control performance are provided.