New Methodology for Precise Satellite Formation-keeping in the Presence of System Uncertainties

Over the past few years satellite formation flying has been extensively investigated as a means to expand the capabilities of existing space missions. To successfully achieve a formation flying mission goal it is essential to accurately control the relative motion of satellites and each satellite’s attitude as desired under a variety of perturbations and system uncertainties. Previous work mainly focuses on linearized approaches and only a few researchers have incorporated attitude dynamics in the formation-keeping problem. Furthermore, in real-world situations, there are always model uncertainties which are unknown, which should be considered when designing the proper controller. In this paper, a simple analytical approach for formation-keeping in the presence of attitude requirements under model uncertainties is presented. First, a nonlinear exact controller is developed in closed form for satellites to keep a specific configuration, assuming that the leader satellite follows an unperturbed circular orbit and the follower satellite points towards the leader satellite at all times. The main controller is designed using a recent finding in analytical dynamics. In the next step, in order to mitigate the effects of system uncertainties this nonlinear controller is augmented by an additional additive controller based on a generalization of the notion of sliding surface control. In the current paper, it is assumed for brevity that the uncertainties mainly originate from inexact modeling of the masses and the moments of inertia of the satellites. As a result, a continuous set of controllers are developed that have no chattering and that can allow the trajectory of the nominal system to be tracked with pre-assigned accuracy.