Characterization of the minimum warning time for low-thrust collision avoidance maneuvers

International audience ; Owing to the exponential increase of tracked objects in the LEO and GEO regions, the number of alerts for potential collisions is continuously increasing. Satellites equipped with low-thrust propulsion need to maneuver for a finite, possibly large, time to reduce the risk of collision to a safe threshold. This study offers a characterization of minimal requirements for such time in the context of the fast encounter between a low-thrust actuated satellite and a non-cooperative object. We first introduce a state vector consisting of the time of closest approach and the orbital elements of the primary at this time, and we deduce its equations of motion. Necessary conditions of optimality are then disclosed, and an approximate solution is proposed, which does not require to solve a shooting problem, but it is obtained by means of a backward integration from the safe set for any initial state in the proximity of the advertised collision. A thorough analysis of the optimal synthesis of this solution is proposed with special focus on the computation of the cut and conjugate loci.