Formation flying along a circular orbit with pulse control

This paper is concerned with formation flying along a circular orbit. The control input is of pulse type and the performance index is the total velocity change required for formation acquisition. For the in-plane motion, optimal three-pulse strategies which use control acceleration only in the flight direction are given under the condition that the difference of orbit size is relatively larger than that of drift velocity. If the inputs are restricted to the radial direction, only formation reconfiguration is possible and optimal two-pulse strategies are given. For the out-of-plane motion, the existence of optimal single pulse strategies is shown. Formation flying with feedback control is also considered. For the in-plane motion, suboptimal feedback controllers are designed with the help of null controllability with vanishing energy of the Hill-Clohessy-Wiltshire equations. Feedback controls restricted to flight direction are also designed, and the total velocity changes are compared with those of full control. Simulation results for a formation reconfiguration problem are given both for optimal open loop strategies and feedback controls.