Optimal scheduling for satellite refuelling in circular orbits

The necessity of refuelling satellites arises from the idea of abandoning the current practice of replacing an existing satellite with a new one if the existing satellite is depleted of its onboard fuel. Being able to refuel satellites significantly reduces the cost in production, launching, and maintenance. This dissertation focuses on the scheduling issues arising from refuelling or servicing multiple satellites. The problem of refuelling a satellite constellation in a circular orbit in a given total time is considered primarily. Four major results are presented in this context. (1) An improvement has been developed to calculate the minimum-ΔV fixed-time two-impulse rendezvous between two satellites in coplanar circular orbit using multiple-revolution Lambert's solution. In particular, a procedure is developed to quickly pick the minimum-ΔV transfer orbit from multiple candidates. (2) Battin's formulation for solving Lambert's problem is extended so that it can be used to calculate the multiple-revolution solution. The basic idea is to reverse the order of the successive substitution described in Battin's method. (3) A solution to the scheduling problem of refuelling a satellite constellation with a single Refuelling Spacecraft (RSc) is obtained. First, given n satellites in a particular order and a total time, integer programming is used to obtain the minimum cost for the RSc to refuel these n satellites in the given order. A heuristic study is then conducted to determine the best refuelling sequence. It is found that the optimal refuelling sequence can be chosen from the sequences with the minimum total sweep angle. (4) Two variations of the peer-to-peer refuelling problem are studied. One problem assumes that the cost of rendezvous maneuvers between two satellites is negligible, and the other takes into consideration the rendezvous cost. Each of these problems is formulated and solved as a maximum-weight matching problem.