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 take advantage of the previous gravimetry missions GOCE [1] and GRACE [2], and will consists of a two-satellite long-distance formation like GRACE where each satellite will be controlled to be drag-free like GOCE [3]. As a significant advancement, 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 radiometric measurements [4]. 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 orbit/formation control. Drag-free control uses the ultrafine accelerometers of the GOCE mission. Orbit and formation control use the receivers of a Global Navigation System (GNS) mounted on each satellite and a suitable satellite interlink. Orbit and 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 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 by itself, being an acceleration control, is not capable of achieving orbit and formation stability, although the non-gravitational acceleration residuals must be very small and bounded. The reason is that Hill's perturbation equations (orbit and formation) are not bounded-input-bounded-output (BIBO) stable (longitudinal and radial components), 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 near-periodical free response of the local gravity field, but it must only zero the 'secular' free response components (bias, drift) and stabilize the perturbed dynamics to achieve BIBO stability. Stabilization programs of this sort are implemented by ground stations through impulsive commands and aim to stabilize orbit altitude (as for GOCE [5]) and to achieve and stabilize formations. 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 stepwise command changing 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 con-trol have been integrated in a unique three degrees-of-freedom (DoF) control system, aiming at stabilizing the 'formation triangle' consisting of the satellite CoMs and of the Earth CoM. The three degrees are the formation distance, the formation radius and the non orthogonality (it expresses the difference between the satellite orbit altitudes). Other degrees to be controlled, but not treated here are yaw and roll rates. Control has been designed using the Embedded Model control methodology [6] and is organized in a hierarchical way where drag-free plays the role of wide-band inner loop, and orbit/formation control plays the role of narrow band, under-sampled outer loop. The paper will start with the formation triangle dynamic model, which is credited to be a new set of formation perturbation equations. They will be converted to discrete time to obtain 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 the control performance are provided.