Optimal formation reconfiguration of satellites under attitude constraints using only thrusters

An optimal formation reconfiguration method under the constraints of a satellite attitude with respect to an inertial frame is addressed. Both the satellite position and attitude are controlled by only two body-fixed thrusters for an in-plane maneuver. To tackle the underactuated control problem, an attitude controller for tracking reference accelerations is firstly derived on the basis of Lyapunov approach. This controller allows us to consider the attitude constraints as input directional constraints because the satellite attitude is controlled so that the thrust direction is coincide with the force direction required for the orbit transfer. Secondly, a formation reconfiguration method based on the Fourier series is used as the reference inputs, and boundary conditions that make the resulting input trajectory an ellipse are shown. Such elliptic input trajectory changes the input direction monotonically, which enables bounding it around an desired direction. The proposed underactuated-controller achieves a reconfiguration maneuver while keeping the satellite attitude within a range from a specified direction, and thus is useful when several thrusters of a satellite fail due to malfunctions. Finally, numerical simulation results validate the effectiveness of the proposed relocation method by comparing energy consumptions and bounded satellite attitude angles.