Optimal Multi-Client Trajectory Planning for A Low-Thrust Servicing Satellite in the Presence of Perturbations

This paper presents a general method to solve space logistics trajectory optimization problems in the case of low-thrust propulsion. The problem of multiple orbital transfers is considered for a servicing satellite that must visit a set of client satellites only once. A near-optimal distance metric based on the Q-law feedback controller is adopted in order to quantify the cost of the transfer of the servicing satellite between each pair of client-satellite orbits. This distance metric is evaluated for a discrete set of departure orbits, arrival orbits, initial servicer masses, i.e., mass before the transfer, and departure times. A four-dimensional array representing the overall cost is then constructed, and its elements are interpolated in order to efficiently solve the tour-optimization problem using genetic algorithms, particle swarm optimization, and simulated annealing. Both minimum-time and minimum-fuel problems are considered. The proposed method accounts for the following time-dependent factors: secular J2 perturbations, eclipse power constraints, and fuel mass depletion. The proposed method is tested on a case study involving 20 client satellites with low eccentricity and low inclination, between medium Earth orbit and geosynchronous Earth orbit, and with randomly distributed right ascension of the ascending node and argument of perigee. The efficiency and accuracy of the proposed approach are assessed by comparing the results to solutions found by a direct optimization method.