Differential aerodynamic forces as a means to control satellite formation flight

Abstract

In the case of satellite formations, for which perturbing effects must be routinely compensated, the limitations of dedicated propulsion systems can be overcome by exploiting natural resources. In the best case, it is the major perturbing effect that is benefited from. In the Very-Low Earth Orbit regime, an emerging area associated with far-reaching potential but also enormous challenges, this is the aerodynamic drag acting on a satellite. This dissertation aims to contribute to this promising field by addressing the governing research question "How can optimal simultaneous three-dimensional relative motion control of satellite formations in the Very-Low Earth Orbit regime be realized via differential lift and drag?". The goal is to provide a comprehensive and holistic overall system view of the methodology. Particular emphasis is placed on the further development and characterization of the differential lift methodology, which has received little attention in the literature but is essential for three-dimensional formation flight control. The common thread running through this dissertation is the consideration of orbital decay, which is the major challenge that must be overcome to enable a sustained operation in this regime. Whenever possible, efforts were made to minimize it. This ranges from the development of a planning tool for trajectories which are optimal in a sense that the resulting decay during the maneuver is minimized to the design of optimal satellite geometries for Very-Low Earth Orbit applications. In combination, this provides a holistic view of the problem which is not yet available in the literature and insights that could hardly be obtained by other means. In addition, analytic algorithms have been (further) developed and combined to form a flexible analysis tool which allows computationally efficient preliminary assessments. As the nature of the in- and out-of-plane relative motion fundamentally differs, so does its control. The unstable nature of the in-plane motion can be exploited for efficient maneuvers via passive drifting periods during which no control inputs are required. In contrast, the out-of-plane motion is quasi-stable and its sinusoidal nature necessitates that both satellites actively rotate in an oscillating and opposing manner to steadily produce differential lift in the desired direction. The challenge is thus to combine the different requirements in the best possible way, which represents a task which is predestined to be tackled via optimal control theory. In this work, simultaneous in and out-of-plane control is achieved by applying yaw angle deviations. This is the most suitable approach for the given task, as it enables to exert both control forces simultaneously and in the optimal direction, i.e., differential lift perpendicular to the orbital plane. After demonstrating that the proposed approach can be used to schedule arbitrary three-dimensional formation flight maneuvers with minimal orbital decay, parameter studies targeting to explore the design space of possible maneuver variants have been conducted. The results demonstrate that the resulting maneuver characteristics is primarily determined by (a) the balance between the difficulties of the two control tasks with respect to the available maneuver time, (b) the dynamic pressure and (c) the satellite design. These insights enabled to sub-divide the overall resulting decay into three different types and to develop targeted strategies for their respective reduction. Moreover, it allowed to identify the necessary condition which ensures a most efficient maneuver realization. Accordingly, the control tasks have to be balanced in a way that the decay which is inevitably induced during the out-of-plane control can effectively be exploited for the in-plane control. With respect to a real mission application, however, it must be concluded from the results of the analysis that for state-of-the-art satellites the possibilities for out-of-plane adjustments via differential lift are limited and that its application is associated with severe levels of orbital decay. An essential cause is that the deposition of atomic oxygen, the major atmospheric constituent in this orbital regime, on the traditional satellite surface materials causes diffuse re-emission and ultimately the low lift coefficients experienced in-orbit to date. Consequently, it is anticipated that this methodology will find seldom application in the immediate future. As soon as materials with long-term specular or quasi-specular reflective properties become available, this evaluation will turn out differently as they have a far-reaching potential for the methodology. While improvements in the most critical parameter, the achievable lift-to-drag ratio, could be achieved for diffusely emitting materials through targeted design optimization (around 8 %), the potential for reflective materials exceeds this by orders of magnitude (around 1520 %). The tools and methods developed within this work, however, can not only equally be employed for state-of-the-art and improved satellites designs, but in addition help to identify ideal designs in the first place. Consequently, they represent a lasting contribution to the research field. Furthermore, they serve as a valuable basis for a variety of other promising research tasks, which are briefly outlined at the end of this dissertation.