Minimum-Fuel On-Orbit Servicing via A Search Algorithm*

On-Orbit Servicing (OOS) represents a viable strategy toward a sustainable and extended exploitation of the Low-Earth-Orbit (LEO) environment. The design of OOS missions requires optimizing both the scheduling of visited objects and the transfer trajectory between each pair of orbits, resulting in the great complexity of the global mission planning problem. This research considers a servicing spacecraft equipped with a high-thrust propulsion system, required to perform multiple orbit transfers to visit several Resident Space Objects (RSOs) in a given time frame with minimum fuel consumption. The proposed method leverages a two-stage approach: (i) first, the optimal transfers are computed for all pairs of orbits and discretized dates, and the associated overall velocity changes are stored in a cost matrix; (ii) then, the problem of visiting all RSOs is cast as a search problem, and the solution space is explored through an A* algorithm. The transfer strategy exploits intermediate drift orbits to increase the differential precession due to the J2 harmonic of the Earth’s gravitational potential. Moreover, the A* procedure leverages a heuristic function based on a modified version of the Held–Karp algorithm, which is proven to be admissible and consistent, meaning that the optimal solution is always reached. The proposed strategy is integrated within a flexible architecture, where operational constraints on phasing and servicing activities can be enforced as well. Finally, the methodology at hand is successfully applied to a case study from the literature involving three successive missions, in charge of visiting 5 RSOs each. Different discretization grids are considered, and the results are compared in terms of overall velocity change and computational time.