Polynomial guidance laws for robust fuel optimal station-keeping of geostationary satellites

Satellite station-keeping strategies are essential for ensuring the precision, safety, and sustainability of geostationary Earth orbit operations. Traditional approaches often face challenges in addressing the nonlinearities inherent in orbital dynamics while maintaining computational efficiency. This work introduces a novel approach aimed at maintaining a geostationary satellite within the assigned latitude-longitude slot under the influence of several orbital perturbations. This is made possible by the Python-based open-source library DACEyPy, which opens up access to advanced differential algebraic methodologies to compute arbitrary-order Taylor series expansions of the optimal control laws. The tool developed here supports mission analysis with precomputed adaptive guidance laws that can be used both onboard and on the ground to estimate the impact of disturbances on the station-keeping mass budget. Three control strategies are proposed with varying level of complexity and accuracy including energy and fuel optimal controls. The proposed methods outperform traditional control techniques in precision and computational efficiency, enabling quick and robust onboard control.