Operational Phase Basins in Multi-Gravity-Assist Trajectories: A Predictive Framework for Low-Sensitivity Mission Design

High-sensitivity multi-gravity-assist (MGA) trajectories remain difficult to design because small launch dispersions, maneuver execution errors, and flyby targeting errors can lead to large downstream deviations, forcing mission designers to rely on expensive global scans and repeated high-fidelity verification. This work introduces a two-layer hierarchical design framework that combines global candidate discovery with a rigorous analytic criterion for identifying robust operational phase basins in interplanetary trajectory space. The approach is illustrated on the B2 basin for the Earth–Venus– Earth–Jupiter sequence. The proposed framework rests on four coupled conditions: co-linear energy pumping at planetary flyby, radial aphelion matching to the target orbit, phase alignment at arrival, and low local sensitivity with respect to the launch epoch. A local variational model is used to derive curvature and sensitivity coefficients that predict basin width and operational robustness a priori, without exhaustive Lambert scanning. We validate our framework across two distinct mission architectures: Earth–Venus– Earth–Jupiter (VEEGA) and Earth–Mars–Earth–Jupiter (EMEGA). Our high-fidelity numerical experiments in a full DE440 N-body environment confirm that B2 phase basins persist under complex perturbations and the transition from patched-conic to fully perturbed dynamics, with only minor shifts in the basin center and local curvature parameters. Rare-event validation is performed using Monte Carlo sampling and Importance Sampling, enabling reliable estimation of atmospheric-entry and keyholerelated failure probabilities in the tail of the uncertainty distribution. The resulting basin B2 reduces the 99% trajectory-correction budget by a factor of 4–5 relative to a baseline route and increases sphere-of-influence (SOI) capture success from 18.4% to 99.8% under the tested uncertainty model. These results indicate that phase basins can serve as predictive, low-sensitivity navigation corridors, enabling a shift from bruteforce trajectory search to analytically guided mission design and assurance.