New Approach to Formation-Keeping Problem of Multiple Satellites with Attitude Requirements

The control of the relative distance between the satellites in a formation is investigated in this paper. We develop a new analytical approach for formation-keeping of multiple rigid body satellites with attitude constraints, and both orbital and attitude dynamics are simultaneously considered. Each satellite is required to stay in its prescribed, desired reference orbit, and at the same time, to point to a fixed spot in space. For attitude dynamics quaternions are used to realize arbitrary orientations and avoid singularities. Unlike previous research, we directly start from the nonlinear equation of motion and the exact, closed form control force is obtained that captures all the nonlinearities of the nonlinear, non-autonomous system of differential equations. To make the problem more general, the leader satellite is assumed to be in an arbitrary orbit around the oblate Earth, and the follower satellites are not initially on the desired trajectory, thereby taking into account errors that arise during orbit insertion. With the new control scheme it is guaranteed that these initial orbital and attitude errors asymptotically converge to zero so that maintenance of the formation geometry and tracking are successfully performed along with precision attitude control. The problem is solved in the Hill frame, which is more useful than the inertial frame for formation flying because we can directly use the measured data. Both orbital and attitude dynamics are compactly handled in a unified way, and the approach shows the possibility of controlling highly nonlinear systems. A numerical example demonstrates the broad applicability with which the analytical solution proposed in this paper can be implemented for various cases and for even more complex formation-keeping problems.