Analytical Formulation for Light and Fast Low-Thrust Guidance Design to Perform Multi-Target On-Orbit Servicing

A new analytical formulation is presented to approach low-thrust trajectories design, in the framework of a guidance law definition for an automated spacecraft to rendezvous and serve multiple active targets. The formulation exploits polar coordinates, avoiding the need of either Keplerian or equinoctial elements. To minimize the low thrust maneuver cost to approach the targets an integer number of revolutions is imposed together with a constant transversal thrust to focus on orbital energy gain for phasing. The here proposed analytical formulation is the basis of a first algorithm, fast and straightforward, well-suited for preliminary global cost assessment in multiple targets rendezvous scenarios. A second algorithm, numerically settled, is also presented, to further optimize the attainable guidance profile trajectories which may open the door to enhanced guidance strategies. The combination of the two offers on one side a good initial guess which helps containing the computational cost of the numerical search for optimal guidance, ensuring, on the other hand, fast and reliable solutions. Performance and results are discussed on the study case of a single spacecraft to serve multiple GEO satellites without loss of generality.