Real time control of satellite formation reconfiguration based on Gauss Pseudospectral Method

In this paper, a real-time controller is presented to control the reconfiguration of satellite formation. The control algorithm is based on Gauss Pseudospectral Method (GPM). Different from the way using GPM for trajectory planning, the proposed controller only utilizes the Karush-Kuhn-Tucker (KKT) multipliers generated during GPM. By using costate mapping theory, the initial costate information is obtained, which, together with the Hamilton canonical model, could be conveniently used to compute the optimal control for the formation reconfiguration. To eliminate the errors caused by model linearization and external disturbance, costate information is re-initialized periodically during the control process. The rapid convergence of GPM ensures that the reinitialization will not cause time lag in the real-time control. Also, compared to the conventional formation control methods, the controller does not need a guidance law during the reconfiguration maneuver. The simulations demonstrated the validity of the controller. The reconfiguration of formation can be carried out effectively both in time optimal case and in fuel optimal case.