New Solutions to the Exact Formation-keeping Control of Satellites with Attitude Constraints

This paper provides a new, exact controller for formation-keeping in the presence of attitude tracking requirements. Both orbital and attitude dynamics are simultaneously considered and continuous thrust propulsion systems are assumed. A leader satellite is assumed to be in a given Keplerian orbit around a central body and each follower satellite is required to stay in a prescribed, desired orbit with respect to the leader satellite, and at the same time, to exactly point to a specific spot in inertial space that may be fixed or time varying. The satellites are considered as rigid-bodies and for attitude dynamics quaternions are used to realize arbitrary orientations and avoid singularities. Unlike most studies, no linearizations and/or approximations are made in dynamics or the controllers. It is hoped that the novel controller provides a remarkable improvement over the current state-of-the-art in that the control force and torque to satisfy the given orbital and/or attitude constraints are obtained in completely closed form. This new, analytical solution can be easily used for on-orbit, real-time control with low computational burden. Furthermore, it is useful in estimating the magnitude of the required control inputs and results in some interesting consequences, including the separation principle, which describes when the orbital control can be completely decoupled from the attitudinal control required to be applied to the follower satellite. Extensive computational simulations are performed to demonstrate the simplicity of implementation and accuracy of the control method developed herein.