Statistical Analysis of the Role of Invariant Manifolds on Robust Trajectories

As low-thrust space missions grow in prevalence, it is becoming increasingly important to design low-thrust trajectories with robustness against unforeseen thruster outages or missed thrust events. Accounting for such anomalies is particularly important in chaotic multibody systems, such as the cislunar realm, where pertinent dynamical structures constrain the dynamical flow. Yet it remains unclear how these dynamical structures influence robust trajectory design. This paper provides the first comprehensive statistical comparison between nonrobust and robust trajectories in relation to the invariant manifolds of resonant orbits in a circular restricted three-body problem. For both the nonrobust and robust solution categories, the optimal subset exhibits stronger alignment with the invariant manifolds, whereas the broader feasible set can sometimes deviate significantly. On average, the robust optimal trajectories shadow the invariant manifolds as closely as the nonrobust optimal trajectories and, in some instances, exhibit even stronger alignment than their nonrobust counterparts. By maintaining proximity to these invariant manifolds, the robust low-thrust solutions are able to efficiently leverage the global dynamical flow to achieve optimality even under operational uncertainties.