This paper develops the mathematical framework to use higher-order state transition tensor (STT) approximations of nonlinear dynamics to design impulsive spacecraft maneuvers incorporating the effects of state uncertainty. Several semi-analytic formulations are derived strictly as a function of a reference STT expansion, including minimum-energy, minimum-covariance, and maximum-covariance cost functions; mean state constraints; state chance constraints; and control-linear maneuver execution errors. Analytical gradients are derived for most of the formulations, which can be used to speed up optimization procedures developed with these equations. A tractable approximation of the nonlinear covariance propagation equations is also derived to further speed up these calculations. Example applications for each of the formulations are provided for a multi-impulse, highly nonlinear transfer in the Earth–moon system. The proposed methodology can be used to efficiently compute a variety of maneuvers accounting for the effects of spacecraft state uncertainty using a single STT expansion. This can enable more flexible and rapid maneuver planning in reaction to changing mission priorities, navigation errors, and maneuver execution errors.
Nonlinear Formulations for Spacecraft Maneuver Design Under Uncertainty
2025-06-01
Conference paper , Article (Journal)
Electronic Resource
English
Maneuver of distributed spacecraft
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