Modeling and Analysis of Relative Hovering Control for Spacecraft

This paper deals with the spacecraft relative hovering control problem, which is an important problem of space flight dynamics and one of the critical aspects of satellite relative motion control. Initially, the precise analytic models of the relative hovering control for an active spacecraft with respect to a target spacecraft both in circular and/or elliptical reference orbit with the influence of J(2) perturbation are established. According to the models, the maximum- and minimum-force positions for the relative hovering under a given range are determined by the well-known optimization technique of Lagrange multipliers. In view of the long-term onboard operational requirement, the formula for calculating fuel consumption in an orbital period is derived. Most important, the maximum- and minimum-fuel positions for the relative hovering under a given range are found by the same optimization technique as well. A number of useful numerical examples are provided, illustrating the validness of theoretical results. These closed-form solutions of the minimum-force and minimum-fuel positions can facilitate the practical operation of relative hovering, which could make progress in the design of future relative hovering missions.