Optimal Formation Design for the Magnetospheric Multiscale Mission Using Differential Orbital Elements
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abstract
The Magnetospheric Multiscale (MMS) mission requires a formation of four satellites in a nearly regular tetrahedron throughout a Region of Interest (RoI), defined near apogee of a highly eccentric reference orbit. Previous papers have addressed the design of formations in orbits of high eccentricity to maximize a Quality Factor in a RoI, including the use of differential mean orbital elements as design variables. In this paper, a robust optimization method is presented - based on maximizing the expectation value of the formation lifetime - to improve formation performance in the presence of formation initialization errors. Several design methods are analyzed by applying differential semimajor axis errors, which have a strong effect on the long-term stability of spacecraft formations. It is shown that large formations can satisfy mission requirements for a longer time than smaller formations, when the same magnitude of errors are considered, and generally exhibit less variation in quality factor due to these errors. The robust optimization method is applied to these smaller formations and produces results which are much more stable when semimajor axis errors are included, at a cost of some performance in the nominal, error-free case. The results are verified using the NASA General Mission Analysis Tool and are shown to be reasonably accurate, except in predicting very long-term behaviour. A physical analysis of the geometry of several MMS formation designs is provided, and 8 distinct optimal tetrahedron orientations are identified (2 configurations, in which the chief satellite can be placed at any of the 4 vertices). 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
