Low-Thrust Propulsion and Drift Orbit Optimization for Multi-Client Servicing Missions in Low Earth Orbit

This paper presents a general approach to solve multi-client space logistics path optimization problems in the case of low-thrust propulsion. The methodology accounts for key time-dependent factors, including orbital perturbations (secular J2 and drag), eclipse propulsion constraints, and servicer fuel mass depletion. A low-thrust transfer strategy, consisting of three phases (thrust-coast-thrust), is employed, utilizing a drift orbit to correct the difference in Right Ascension of the Ascending Node. The drift orbit parameters are optimized by using a Non-Linear Programming algorithm to minimize the fuel cost associated with the transfer while satisfying maximum time of flight constraint. An optimization is conducted for all possible transfers (three-element targeting) between the satellites of a dataset on a two-dimensional discrete grid of initial servicer mass and departure time. This procedure creates two four-variable matrices representing the cost of each possible visitation in terms of fuel consumption and time of flight. The matrices are then interpolated to efficiently solve a general path optimization problem by using a genetic algorithm. Two test cases are analyzed for datasets consisting of 12 and 20 satellites in Low Earth Orbit, respectively. The first addresses an optimal open tour problem where the servicer must visit all satellites once while minimizing total fuel consumption. The second addresses an on-orbit refueling problem where the servicer must refuel as many satellites as possible. The mission scenario is generalized to consider a priority index associated with each client; servicing time and fuel mass constraints are also taken into account.