NMPC Orbit and Formation Control for the Next Generation Gravity Mission

Since the beginning of this century, gravimetric missions have started to become one of the most interesting topics in the field of space research. The reason behind the growing attention paid to this type of missions is certainly to be found in its ambitious objective, which is the accurate measurement of the temporal variations of the Earth gravity field. As a matter of fact, the observation and monitoring of these variations could improve the understanding about some geophysical processes involving Earth’s mass change phenomena. The concept of Next Generation Gravity Mission (NGGM) has been proposed by ESA with the aim to raise the bar on the work started by the previous gravimetric missions, like GOCE and GRACE. Indeed, relying on the heritage gained from these two successful missions, NGGM sets its ambitious goal in the measurement of the temporal variations of the Earth’s gravity field, over a long time span, with an unprecedented level of accuracy. This thesis focuses on the formation control design, implementation, and simulation for the Next Generation Gravity Mission. NGGM formation consists of a group of two satellites, where each of them has to be drag-free controlled, in order to be ideally subject only to the gravity. The main aim of formation control is to counteract bias and drift of the residual drag-free accelerations while guaranteeing, at the same time, the long-term stability of the triangular virtual structure composed by the satellites' and Earth's Center of Masses. At this purpose, a Nonlinear Model Predictive Control (NMPC) framework for autonomous orbit and formation control is considered. The advantages of using this technique mainly consist in its ability to find an optimal control law managing at the same time state and input constraints and providing an online adaptation of the control action to possible variations of the process conditions. A key element of NMPC is an internal prediction model, used to find an optimal trajectory over a finite time interval. Here, an integrated formation control (IFC) model, based on a novel set of Hill-type equations, has been used. This model allows the description of both the formation altitude and inter-satellite distance, by defining a specific orbital reference frame called Formation Local Orbital Frame (FLOF). The obtained results, from long-run simulations performed by means of an accurate nonlinear model, prove the validity of this control strategy and show its capability of guaranteeing the long-term stability of formation variables, although the use of a very approximated internal model and low command effort. Further, to make a more realistic simulator, the difficulty that exists in the transmission of data between satellites is taken into account by assuming long sampling times of measurements due to the absence of a radio-frequency inter-satellite link. In this regard, the last part of this thesis is dedicated to the implementation of low-fidelity orbit propagators whose aim consists in computing, on board of each spacecraft, the companion satellite's orbit during the time intervals in which no real-time information is available. To reduce their computational complexity, these propagators approximate the effects of some forces while completely disregarding others. However, despite their simplicity, simulated results show that they well fit the proposed design scenario, without impinging the NMPC capability of guaranteeing formation long-term stability.