New Penalty Functions and Optimal Control Formulation for Spacecraft Attitude Control Problems
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A universal attitude penalty function g() is presented that renders spacecraft optimal control problem solutions independent of attitude coordinate choices. This function returns the same scalar penalty for a given physical 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 σ. The MRPs allow for a nonsingular attitude description through a noncontinuous switch to their associated shadow set. A corresponding switching condition is presented for the MRP costates to allow the nonsingular MRP attitude description to be used in optimal control problems. Computational experiments are used to illustrate and validate the analytical results.
author list (cited authors)
Schaub, H., Junkins, J. L., & Robinett, R. D.