Design and evaluation of navigation and control algorithms for spacecraft formation flying missions

Formation flying offers space-dependent disciplines such as astrophysics, astrodynamics, and geodesy, to name a few, the possibility of creating large spaceborne sensors from an array of small spacecraft flying in formation. This creates exciting scientific and technical opportunities as the formation could be arranged to work as, for example, an interferometer, thus providing a most unlimited angular resolution or a virtual telescope, thus unrestricted focal distances. Since the first mission including formation flying technology (EO-1) was selected by NASA, some of the challenges to realize full Formation Flying (FF) capabilities has been thought to be the definition of suitable algorithms to navigate and control FF missions. The focus of this dissertation is the design and evaluation of algorithms for navigation and control for formation flying missions. Given its importance, extensive research has been already conducted to fulfill the increase of accuracy, autonomy, and other requirements of the Guidance, Navigation, and Control (GNC) systems that derive from novel applications of formation flying missions. To center the scope of present work, we have mainly focused in three of the present challenges: the difficulties of fusing different non-linear observations for relative navigation; the analysis and extension of behavioral algorithms for controlling a formation of spacecraft; and the design and validation of a control law for formation acquisition and formation keeping of a non-natural relative trajectory. These three interconnected topics cover a wide range of research in formation flying and embody the main algorithm components of formation flying algorithms from the observations to the navigation and to the control. The first challenge consisted, thus, in addressing the difficulties encountered by classical filters to estimate a state vector fusing common observations. We proposed several strategies to improve the robustness of these filters under non-linear conditions. Among these strategies, the modification of the residuals computation for the Unscented Kalman Filter (UKF) deserves special mention due to its excellent results and robustness against nonlinearities. A theoretical basis for these results became, thus, necessary regarding the new update equation of the UKF and has been developed subsequently in the frame of this thesis. This work has been published in Perea et al. (2007) and Perea and Elosegui (2008). The collective motion exhibited by some groups of animals has recently attracted the interest of many research groups who try to take advantage of the robustness and efficiency of natural patterns. With this aim, we have investigated the possibility of extending an interaction model that has shown emergent behavior. In particular, the Cucker-Smale (CS) model has been extended for its application on spacecraft formation flying. Numerical simulations of the Darwin mission have proved that this strategy is suitable for loose formation keeping. Of special relevance is the low cost of the controller, specially compared to an alternative strategy, the Zero Relative Radial Acceleration Cones (ZRRAC). The problem of tight formation keeping is addressed previous publications. In these papers, we first study the relative dynamics of a virtual telescope that follows a non-natural relative trajectory driven by the position of an observed body and not by the natural forces in space. This analysis has originated the design of several controls based on different approximations of the relative dynamics. Their performances have been tested and compared through numerical simulations of the PROBA-3 mission using, first, computer based simulations, and then, a realistic platform with GNSS hardware and operational flight software in the loop. The main conclusions show that simple control definitions, as defined by the Linear Quadratic Regulator (LQR) and Linear Quadratic Regulator with the Integral term (LQRI), can fulfill stringent requirements for formation acquisition and tight formation keeping