Spacecraft Formation Control for the Next Generation Gravity Mission

The expression ‘formation flying’ refers to a group of satellites performing their mission objectives in a cooperative and coordinated way, to achieve an increased scientific return, with respect to single-satellite systems. Formation flying concepts have been applied to several classes of space missions, in the last decade. In this thesis, we devoted our attention to the European next-generation space gravimetric missions. After the successful European gravity mission GOCE, which provided a static global map of the Earth’s gravity field, the European Space Agency has proposed several preparatory studies for a Next Generation Gravity Mission (NGGM). It aims to measure the temporal variations of the Earth’s gravity field, over a long time span, with an unprecedented level of accuracy. NGGM will consist of a two-satellite long-distance drag-free formation, flying in a polar orbit at a low-Earth altitude. Satellite-to-satellite distance variations, encoding gravity anomalies, will be measured by laser interferometry. This thesis explores the design, implementation, and simulation of the guidance, navigation, and control system for the science phase of the NGGM mission; with a focus on two baseline formation configurations: (i) in-line, and (ii) pendulum (slightly separated but intersecting orbits). The control unit was designed according to the Embedded Model Control methodology (EMC). EMC encompasses three model classes of the system to be controlled, by means of the uncertainty description, which lead to the definition of the so-called Embedded Model (EM). The EM is the core of the control unit, and its states drive the model-based control law. The NGGM overall control architecture is organized in a hierarchical way, where drag-free control plays the role of a wide-band inner loop, while the orbit/formation and the attitude/pointing are narrow band outer loops. Such hierarchical control pursues a frequency coordination among the several control tasks, to prevent inner/outer loops interference. The drag-free control uses ultra-fine accelerometers to counteract the atmospheric drag, making the satellite orbit ideally determined by the local gravity only. Thus, the EMC dragfree architecture of the GOCE satellite was extended to accomplish the demanding NGGM control performances. Further, the long-term formation stability requires an attitude, and an orbit and formation control counteracting bias and drift of the residual drag-free accelerations. A pointing control was designed to reach the inter-satellite mutual alignment, via specific optical sensors. As shown in this dissertation, since the drag-free control constrains the pointing control, the attitude and the accelerometer measurements must be wisely coordinated. Such hybridization, leading to a proper pointing performance, highlighted some criticality in the preliminary scientific requirements. On the other side, the orbit and formation control was addressed through an innovative control strategy, admitting large fluctuations around the reference values due to the gravity effect (loose control), and with a continuous control action, to respect the drag-free requirements. Further, the orbit and formation dynamics were integrated into a unique model, through the formation triangle concept. A multi-rate and hierarchical control law, designed with care to reduce as much as possible the demanded thrust, completes the formation controller, actuated by millinewton-range electric thrusters. Concerning the pendulum formation configuration, an effort has been spent to demonstrate that it can be affected by some peculiar dynamic effects, coherently with the semi-aperture angle. This analysis led to an on-purpose designed roll compensation control law. Simulated results, from a long-run campaign via a high-fidelity simulator, prove the concept validity and show that the control strategy is capable of keeping the attitude and formation variables stable, through a few millinewton thrust authority. Finally, in this thesis, an optimisation-based worst-case analysis framework was applied to the drag-free formation, finalized at the verification and validation of the control performance. Specifically, this preliminary study tried to evaluate the optimization-based methods and tools for enhancing the performance verification process, in a complex and highly uncertain mission scenario. The first preliminary simulated results indicate that it could be possible to improve the controller performance according to the worst-case expected behaviour, due to possible system uncertainties and environmental condition variations. Future work should address the suggested theoretical developments of the integrated formation model, while the highlighted critical points of the current design should be tackled, also considering the devised strategies and system reassessments. Yet, the current preliminary worst-case analysis should be extended to the entire AOCS.