Optimal Formation Design for Magnetospheric Multiscale Mission Using Differential Orbital Elements
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The Magnetospheric Multiscale Mission requires a formation of four satellites in a nearly regular tetrahedron throughout a region of interest defined near the 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 region of interest, including the use of differential mean orbital elements as design variables. In this paper, a robust optimization method is presented 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 factors due to these errors. The robust optimization method is applied to these smaller formations and produces results that 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 NASAGeneral Mission Analysis Tool and are shown to be reasonably accurate, except in predicting very long-term behavior. A physical analysis of the geometry of several magnetospheric multiscale formation designs is provided, and eight distinct optimal tetrahedron orientations are identified (two configurations, in which the chief satellite can be placed at any of the four vertices. Copyright 2011 by Christopher W. T. Roscoe, Srinivas R. Vadali, Kyle T. Alfriend, and Uri P. Desai.
