Optimal Rendezvous Trajectories Initialized with Analytical Radial Thrust Solutions

This paper presents a methodology to generate optimal guidance solutions initialized by analytically-computed trajectories for the orbit rendezvous problem with a continuously thrusting chaser and a passive target. First, radial thrust based rendezvous trajectories are analytically computed in terms of elliptic integrals. Although these analytical radial thrust solutions are suboptimal, they are cheap-to-compute and satisfy all the requisite boundary conditions for the rendezvous problem. Then, the main contribution of this work is presented: a novel continuation strategy that maps the radial thrust solution to initial co-states for the harder-to-compute optimal control problem. Finally, a trade study comparing time-of-flight and total fuel used to complete a rephasing maneuver is conducted and reveals a descending stair-step like behavior in fuel consumption as time-of-flight is increased.