Optimization of the control of a satellite formation in a near-geostationary orbit by means of solar sail

Abstract

Space debris, composed of man-made objects orbiting around Earth in an uncontrolled fashion, represents a critical issue for long-term sustainability of outer space activities and for space safety. A reliable and accurate mapping and monitoring of space debris is therefore a critical necessity for modern space industry. For relatively low-altitude orbits, most debris can be accurately tracked by means of ground-based observations. However, for higher-altitude orbits, this debris detection method becomes less precise and smaller debris cannot be tracked anymore. The solution to this problem that will be analyzed in this thesis is the possibility to triangulate the position of the debris with the use of a formation of two or three satellites orbiting near the area of interest. In particular, the possibility of monitoring debris in the geostationary ring will be investigated. Due to the presence of perturbations, the satellites of the formation will deviate from their nominal orbit and by consequence from the optimal debris triangulation conditions. It will therefore be necessary to maneuver them in order to maintain a relative distance and position between spacecraft that results in a accurate and constant tracking of the geostationary debris. These maneuvers require a form of propulsion in order to provide the necessary thrust. Among the various propulsion technologies available for spacecraft control, this thesis will explore the possibility of using solar sailing. Solar sailing is a propulsion method theorized 100 years ago, but only developed in recent years, that uses the pressure exerted by electromagnetic radiation on a large and lightweight surface attached to the satellite in order to generate thrust. In this thesis, the possibility of maneuvering the satellites by means of solar sail propulsion in order to maintain the formation in an optimal position and shape for the triangulation of debris will be analyzed. This concept will be studied by developing a simulation model describing the orbital dynamics of the spacecraft under the influence of the Earth’s gravitational attraction, the thrust generated by the sail and a number of perturbations. The control of the formation will be parametrized and subsequently optimized with a self-adaptive differential evolution algorithm. This optimizer will work towards maintaining each satellite of the formation on an optimal orbit, characterized by a number of orbital requirements such as minimum and maximum inclination and inter-satellite distance. Among the simulations that were performed with different parametrizations of the formation control and with different optimization set-ups, only one complied with all the defined requirements. In fact, it is noticeable that maintaining the inter-satellite distance within the required range for time spans of a year or longer is very challenging and the developed optimization formulation in most cases cannot determine the necessary control law. It can also be noticed that the perturbations that tend to make the formation drift to larger orbital inclinations are more difficult to counteract and that a particular attention needs to be directed to this phenomenon in case long duration simulations are considered. Furthermore, it was found that better results are obtained if the decision variables representing the solar sail attitude are optimized simultaneously for the entire simulation duration rather than separately over limited time periods. However, the results obtained also show that the developed concept tends to control the satellites towards an improvement in the objective function and it is the opinion of the author that a better definition of the control parametrization coupled with a larger computational effort and eventually more suitable optimization algorithms could yield better results and comply with the concept requirements.