Formation Flying with Single Input

Abstract

A new formulation of formation flying in a circular orbit where the control input is limited to radial direction is considered. The control input is of pulse type and the performance index is the total velocity change required for formation acquisition. If the input is restricted to radial direction, the system becomes uncontrollable. We show that formation flying associated with periodic solutions of the Hill-Clohessy-Wiltshire equations are achievable even when the control input is restricted to radial or alongtrack direction. Suboptimal feedback controllers are designed with the help of null controllability with vanishing energy of the Hill-Clohessy-Wiltshire equations. The L1-norm of the control input for limited case are compared to that of full input case.