CONTROL FOR CIRCULAR FORMATION INITIALIZATION WITH COLLISION AVOIDANCE

Basically the formation initialization task is a rendezvous. The first part of this paper presents how to state formations in terms of keplerian elements deviations. From this we then show how the rendezvous can be replaced by a transfer task. For this transfer we consider an injection impulse from the rocket upper stage whose amplitude is free, and we focus on the optimization of this maneuver, the formation phase angle and the transfer maneuvers in order to minimize the fuel consumption and to bound the collision risk. Two methods which allow to minimize the fuel consumption are presented: first the Variation Of Parameters approach for which a simple one impulse is described. Then we move on to the Primer Vector approach and we find that the formation initialization falls into a particular case of the theory. Afterwards the collision risk is assessed with an analytical distances analysis and shows that the injection impulse permits to bound the collision risk. Then impulse uncertainties are introduced and two control methods are presented: the second one shows that the inter spacecraft distance can be kept within non critical bounds.