Optimal low-thrust hyperbolic rendezvous for Earth-Mars missions

Earth-Mars cycling spacecraft have been proposed as a valuable option for the future exploration of Mars. Cycler mission architectures consider the use of a large space vehicle that cycles continuously between Earth and Mars, describing a near-ballistic path that includes flybys at the two planets. While this large spacecraft can be equipped with the life support system appropriate for a long interplanetary flight with a crew, taxi vehicles of reduced size are sufficient to ensure the connection between the interplanetary vehicle and each planet. This research addresses the determination of the optimal low-thrust transfer trajectories for a pair of taxi vehicles aimed at transferring a crew or an inert payload from and toward a large Earth-Mars cycling spacecraft. The problem is solved through the indirect heuristic method, which uses the necessary conditions for optimality together with a heuristic technique, i.e. the particle swarm algorithm. The use of the indirect heuristic approach for low-thrust paths may be affected by hypersensitivity with respect to the initial values of the costate. This phenomenon is mitigated through a judicious choice of the equations of motion that govern the spacecraft dynamics. The solution method proposed in this work proves to be effective and very accurate, and leads to determining the minimum-time low-thrust paths for a pair of taxi vehicles traveling from and toward a large cycling spacecraft.