Optimal hyperbolic rendezvous trajectories for cycler missions

Cycler mission architectures are based on the joint use of a large spacecraft that cycles continuously between Earth and Mars, and small taxi vehicles, aimed at connecting each planet with the cycling vessel. The latter describes a hyperbolic path relative to the Earth. This work considers the problem of optimizing the trajectory of the taxi leading to rendezvous with the cycler. Propellant minimizing transfers have been found for both impulsive (short-duration, high-thrust) and low-thrust hyperbolic rendezvous. For the impulsive case, two, three, or four velocity changes are proven to be optimal for performing the rendezvous. If the time of flight can be large, the most fuel efficient rendezvous path is composed of four velocity impulses, and ends at the farthest allowed point along the cycler hyperbola. The optimal low-thrust rendezvous trajectory is found as well, using nonsingular equinoctial elements, in conjunction with the indirect heuristic method.