Optimal scheduling of GEO debris removing based on hybrid optimal control theory

Abstract The scheduling of debris removing in a coplanar GEO orbit is studied in this paper. Specifically, the servicing spacecraft is considered to be initially on the circular orbit of the debris to be removed, and it should rendezvous with each debris, remove them to the graveyard orbit and finally return to its initial location. The minimum-cost, two-impulse phasing maneuver is used for each rendezvous. The objective is to find the best sequence with the minimum total Δ v to service all debris in the constellation. Considering this mission as a hybrid optimal control problem, a mathematical model is proposed. Based on the analysis and numerous experiments, two heuristic laws of the problem are found out: (1) when targets are sparsely distributed (i.e. each phase angle between the targets is larger than certain threshold), the optimal sequence is the counter-orbit-wise one starting from either the closest leading or the closest lagging target; (2) in general cases, the optimal sequence is the combination of the counter-orbit-wise segments in which each phase angle is larger than a threshold. Then a Rapid Method (RM) is presented based on these laws. It can be concluded from the experiments that the RM is effective and efficient in dealing with this problem especially for the cases with numerous targets.