Orbital Logistics: Optimal Planning to Service Multiple Satellites in LEO through Mixed Integer Linear Programming and Q-law

This paper addresses the problem of finding the optimal visiting sequence and trajectory for a servicer satellite that has to visit multiple client satellite once, minimizing fuel spent and satisfying the Keplerian dynamics and low-thrust propulsion system constraints. The cost of each transfer is evaluated through two different cost functions: an approximated analytical cost function based on Edelbaum’s theory and a more accurate Q-law cost function. The optimal sequence is found by using an Exhaustive Search algorithm and a Mixed Integer Linear Programming. Computational time and accuracy of the methods are compared. In all cases the global optimum is obtained. In particular, the implementation of the Q-law cost function in the Mixed Integer Linear Programming context provides the optimal sequence for a large dataset while maintaining accurate trajectory estimation.