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Title: Trajectory Planning For Spacecraft Formations Near Elliptical Orbits
Authors: Zanon, Darren
Keywords: Elliptical Orbits
Issue Date: 19-Aug-2009
Abstract: Hamilton-Jacobi-Bellman (HJB) optimization is used to ?nd optimal solutions to cost functions for spacecraft formation maneuver planning. Such solutions are ?rst explored using splines to approximate functions which are otherwise di?cult to evaluate. This technique is applied to simple problems of formation transits for a four-satellite tetrahedron performing maneuvers similar to those proposed for the Magnetospheric Multiscale (MMS) mission by assuming thrust along two axes. This scenario and mission are further used as a basis for generating a mixed-metric cost function in which the tetrahedron is evaluated for ability to take meaningful scienti?c data. The methods derived for solving this cost function can be utilized for advanced exploration of mission pro?les for MMS-type formations with constraints. These HJB methods are then combined with Linear Programming (LP) methods and extended to apply to problems in which the spacecraft thrust is applied by a set of thrusters on a spacecraft which is rotating, providing a practical method for determining optimal formation maneuvers for realistic multi-spacecraft missions with complex thruster layouts. Several parameterizations are also derived which can describe single-spacecraft relative orbits and multiple-spacecraft formations. In many cases, these parameterizations provide insight into general properties which apply to underlying optimal formation maneuvers. These can be readily adapted by mission designers to enhance mission performance and extend mission life.
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