Spacecraft Relative Motion Control Near an Asteroid With Uncertainties: A Lyapunov Redesign Approach

In this paper, a spacecraft formation control framework is presented aimed at guaranteeing a long-term bounded relative motion in the asteroid's uncertain dynamical environment. The mean-orbital-elements-based invariant boundedness conditions via an approximate gravitational field are adopted to develop a nominal steering control strategy, while a control correction resulting from a Lyapunov redesign method is devised to account for uncertainties, i.e., asteroid's gravity uncertainty and solar perturbations. Contrary to traditional formation flying missions where the relative orbit has to keep some prescribed strict geometry, the proposed (loose) formation control law with only bounded requirement allows more degrees of freedom in formation design, substantially reducing the fuel consumption necessary for formation maintenance.