Dynamics and Control of Low-Altitude Formations
- Paper number
IAC-06-C1.5.03
- Author
Dr. Giovanni B. Palmerini, University of Rome "La Sapienza", Italy
- Coauthor
Mr. Marco Sabatini, University of Rome "La Sapienza", Italy
- Year
2006
- Abstract
Accurate simulation of the behaviour in time of an orbiting body depends on the realistic modelling of the perturbing effects, strongly varying with the altitude of interest, which modify keplerian motion. Such a basic requirement becomes more strict for formation flying. In fact, precise maintaining of the configuration is usually needed to exploit a formation mission, and some kind of control action is therefore mandatory: in order to compute this action, the knowledge of the dynamics which the formation will be subjected to is required, and the perturbation modelling becomes crucial to obtain suitable solution in terms of propellant consumption and mission lifetime. Different techniques to compute the formation control strategy have been proposed, most of them being based either upon drastically simplified dynamics (linearized Euler Hill equations) or upon non linear dynamics (approaches leading to Lyapunov method). Linearized Keplerian dynamics offers the chance to optimally compute the control action, an asset which however will be granted only under the hypothesis of limited displacement from model reference conditions. Not such an optimality holds for non linear techniques, lacking of validity boundaries but usually requiring a far larger consumption. Recent work suggested that the inclusion, while in a linearized form, of main perturbing effects, could improve the projected performances. Still allowing to make use of linear control theory, the introduction of a more realistic dynamical model pays off when the computed control action is tested by means of a fully perturbed orbital propagator. This paper, focusing on the low altitude orbits, first recalls the models adopted for the most significant effects, i.e. the air drag and the J2 effects, and show how these models could be introduced in a classical Linear Quadratic Regulator approach. Furthermore, a realistic evaluation of the performances should not forget that control strategies will depend on the knowledge of the kinematic state of the spacecraft belonging to the formations. In the frame of the control selection, the determination of the kinematic state adds the deficiencies of the navigation system to the errors generated by the approximation of the dynamics involved. With the aim to simulate a formation behaviour in time as close as possible to the one faced in the real orbital environment, this work includes in the global system chart a navigation section, supposed to be completely on-board in order to cope with the autonomy requirements typical to formation flying. Therefore, uncertainties of a GPS(GNSS) receiver, assumed as the most fitting navigator currently available, are injected into the model in a statistical way, leading to a Linear Quadratic Gaussian approach, in order to better represent the overall system performances. The final aim of the paper is to show how the selection of a proper orbital dynamics model for the control system implementation generates deep differences in the performances expected, eventually instrumental for actual mission design.
- Abstract document
- Manuscript document
IAC-06-C1.5.03.pdf (🔒 authorized access only).
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