Asteroid hovering missions from a fuel-consumption viewpoint

The aim of this Note is to provide a comprehensive study of asteroid hovering from a fuel-consumption viewpoint, under the assumption that the asteroid is modeled as a second-degree and second-order nonspherical gravitational field. Our analysis first relies on an analytical, although approximate, approach to determine the critical hovering orientations and to quantify the fuel-consumption extrema. The linear stability for a given hovering distance is investigated, and a homotopic method is adopted as an effective tool to emphasize the fuel-optimal control problem. In particular, the optimal trajectories toward a stable minimum-fuel hovering point are found by first solving the simpler energy-optimal problem. The initial (unknown) costate vector is calculated with a normalization technique in such a way that the sensitivity of the two-point boundary-value problem (TPBVP) to the initial guess is significantly mitigated.