Suboptimal Formation Reconfiguration of Satellites Under Input Directional Constraints

Proximity operations of satellites such as formation flying and on-orbit servicing offer more advanced missions than missions achieved by a single satellite. In a practical situation of formation flying, thrust directions for keeping and controlling a relative orbit is limited, e.g., for astronomical observation and plume impingement avoidance. The aim of this paper is to provide an energy efficient control method for a formation reconfiguration under input directional constraints with respect to both an inertial and a leader-fixed frames. The proposed controller is designed consisting of two parts: 1) guaranteeing a formation reconfiguration to a desirable formation on the basis of an energy optimal controller and 2) satisfying the input directional constraints by superimposing additional inputs. The analytical form of the control input shows that the input direction forms an ellipse in the leader-fixed frame when a particular boundary condition is satisfied, which is exploited as a nominal controller to take into account the input directional constraints. Due to the singular avoidance of the nominal controller, the additional inputs can be analytically obtained. The effect on the follower trajectory due to the additional inputs is compensated by setting a virtual target orbit, and thus the successful formation reconfiguration is still guaranteed. Some numerical simulation results verify the effectiveness of the proposed method and compare the energy efficiency.