New attitude penalty functions for spacecraft optimal control problems
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© 1996 by Hanspeter Schaub. Published by the American Institute of Aeronautics and Astronautics, Inc A universal attitude penalty function g() is presented which renders spacecraft optimal control problem solutions independent of attitude coordinate choices. This function will return the same scalar penalty for a given attitude regardless of the choice of attitude coordinates used to describe this attitude. The only singularities the g() function might encounter are solely due to the choice of attitude coordinates. A second attitude penalty function G() is considered which depends specifically on the modified Rodrigues parameter (MRP) vector 3. The function G() is also globally nonsingular and of simpler form than g(). A theorem is presented which allows MRPs, along with a switching condition to their “image or shadow” trajectory, to be used in optimal control problems.
author list (cited authors)
Schaub, H., Junkins, J. L., & Robinett, R. D.