Abstract : Our thesis work focuses on the problem of station keeping maneuver planning for geostationary satellites equipped with thrusters at low thrust level. We evaluate the opportunity of substituting such a planning to the more traditional one used for geostationary satellites equipped with thrusters at high thrust.
Since the birth of low thrust technology, its use has always met with the spacecraft companies approval. The well-known advantage of low fuel consumption due to the high specific impulse achieved by the high values of specific impulsion makes this technology highly competitive with respect to the high trust level one, especially during transfer and rendez vous phases of space missions.
The trajectory optimization problems which have to be solved during the mission design in order to analyze the feasibility of transfer and rendez vous mission phases have begun to be solved with alternative optimization solutions, since the low thrust propulsion systems have to be activated for longer periods of the transfer time. High thrust trajectory optimization problems, typically formulated as discrete, have been replaced with low thrust trajectory optimization problems formulated as continuous and solved by continuous control techniques.
The goal of this thesis is to understand what is the impact of the low thrust propulsion technology on the station keeping phase feasibility analysis performed during the design of a geostationary mission. In particular we study the impact that the low thrust propulsion systems have on the station keeping maneuver planning and on the realization of the whole station keeping control loop. The goal is to deduce whether the maneuver planning related with this technology is competitive with respect to the more classical one based on high thrust level.
Usually the well known long term strategies for the SK maneuver are deduced from simplified propagation orbit models
(in function of mean orbital elements) mainly because the following three conditions are met: high thrust level propulsions, SK dead band box sizes not very stringent and the possibility to execute low frequency maneuvers.
In the framework of this dissertation, given the low thrust level propulsion and increasingly stringent dead band requirements, we think it is more appropriate to make the hypothesis of a much higher maneuver execution frequency in order to achieve a finer control of the GEO satellite position and to use an orbit propagation model described by the motion equations in terms of osculating elements.
For the maneuver planning we propose a solution based on a direct approach considered as the transcription in terms of parameter optimization problem of the constrained optimal control problem associated to the planning task. Two optimization techniques have been considered: the fixed horizon optimization under constraints and the receding horizon one.
This second is also used with the linearized motion equations appropriately transformed via a Lyapunov variable change on the state space of the osculating equinoctial element deviations. This Lyapunov transformation leads to the definition of a new set of orbital parameters. It makes the planning process more immediately understandable from a control viewpoint and easier to implement from a numerical viewpoint, thanks to the differential flatness and inclusion concepts.
All the low thrust maneuver planning results are obtained in a first time in terms of thrust velocity increments and in a second time directly in terms of thrust, considering typical propulsion system configurations with the goal of determining the more efficient one in nominal conditions and in the condition of failure of one of the thrusters.
The problem of collocation of more geostationary satellites in a same big box has not been explicitly addressed but is implicitly solved once the fine control technique with a relative stringent dead band requirement is proposed for each satellite.