Shape-Based Algorithm for the Automated Design of Low-Thrust, Gravity Assist Trajectories

Given the benefits of coupling low-thrust propulsion with gravity assists, techniques for easily identifying candidate trajectories would be extremely useful to mission designers. The computational implementation of an analytic, shape-based method for the design of low-thrust, gravity-assist trajectories is described. Two-body motion (central body and spacecraft) is assumed between the flybys, and the gravity-assists are modeled as discontinuities in velocity arising from an instantaneous turning of the spacecraft’s hyperbolic excess velocity vector with respect to the flyby body. The method is augmented by allowing coast arcs to be patched with thrust arcs on the transfers between bodies. The shape-based approach permits not only rapid, broad searches over the design space, but also provides initial estimates for use in trajectory optimization. Numerical examples computed with the shape-based method, using an exponential sinusoid shape, are presented for an Earth‐Mars‐Ceres rendezvous trajectory and an Earth‐Venus‐Earth‐Mars‐Jupiter flyby trajectory. Selected trajectories from the shape-based method are successfully used as initial estimates in an optimization program employing direct methods.