Optimal Low-Thrust Station Keeping Maneuvers to Maintain Desired Osculating Keplerian Orbital Elements

Station keeping (SK) is often a vital part of a spacecraft’s mission profile. If a given mission allows, SK strategies focused on maintaining orbital geometry rather than a full spacecraft state can offer significant fuel savings, though these methods have received limited attention. In this work, an automated method to solve the minimum-fuel point-to-orbit SK problem with an indirect formulation is introduced, utilizing a parameterization of the final state derived from the commonly-used transformation between Cartesian state and Keplerian orbital elements. A particle swarm optimization costate initialization scheme is used to find minimum-fuel transfers in a three-step solution process, including (i) finding the required minimum time-of-flight, (ii) solving the energy-optimal transfer problem, and (iii) transitioning the energy-optimal solution to that of the fuel-optimal problem. The method is demonstrated through simulation of a spacecraft performing point-to-orbit SK on a slightly inclined, near-circular geosynchronous orbit.