Optimal Scheduling for Servicing Multiple Satellites in a Circular Constellation

Abstract

This paper studies the scheduling of servicing multiple satellites in a circular orbit. Specifically, one servicing spacecraft (SSc) is considered to be initially on the circular orbit of the satellites to be serviced. The SSc then rendezvous with each satellite of the constellation and services it until all satellites are visited. The total time is assumed to be given. A minimum-∆V two-impulse maneuver is used for each rendezvous. The objective is to find the best sequence with the minimum total ∆V to service all satellites in the constellation. Two problems are considered. In the first case, the SSc returns to its starting circular orbital slot. In the second case, the SSc is not required to return to its starting orbital slot. These two servicing scheduling problems are formulated as combinatorial optimization problems, and are solved in a two-step process. First, the optimal time distribution problem is solved using integer programming, which yields the minimum cost maneuver for the SSc to visit the satellites in a given order. Then the optimal sequence problem is solved by a heuristic study. It is shown that integer programming is an effective scheme in solving the optimal time distribution problem. The notion of the sweep angle is introduced for each rendezvous segment as the smaller angle along the circular arc between the SSc and the next satellite to rendezvous. The Total Sweep Angle (TSA) for a servicing sequence is defined as the sum of the sweep angles for all rendezvous segments. The heuristic study shows that the best servicing sequence is always among the group of sequences that assume the minimum TSA. Specifically, for the case when the SSc returns to its starting orbital slot, the best servicing sequence is sequential (orbit-wise or counter-orbit-wise). For the case when the SSc does not return to its original orbital slot, the best sequence is sequential or partially sequential, depending on the satellite distribution on the constellation. The group of sequences with the minimum TSA are completely identified.