Statistical Analysis of the Role of Invariant Manifolds on Robust Trajectories

Abstract

As low-thrust space missions increase in prevalence, it is becoming increasingly important to design robust trajectories against unforeseen thruster outages or missed thrust events. Accounting for such events is particularly important in multibody systems, such as the cislunar realm, where the dynamics are chaotic and the dynamical flow is constrained by pertinent dynamical structures. Yet the role of these dynamical structures in robust trajectory design is unclear. This paper provides the first comprehensive statistical study of robust and non-robust trajectories in relation to the invariant manifolds of resonant orbits in a circular restricted three-body problem. For both the non-robust and robust solutions analyzed in this study, the optimal subset demonstrates a closer alignment with the invariant manifolds, while the overall feasible set frequently exhibits considerable deviations. Robust optimal trajectories shadow the invariant manifolds as closely as the non-robust optimal trajectories, and in some cases, demonstrate closer alignment than the non-robust solutions. By maintaining proximity to these structures, low-thrust solutions are able to efficiently utilize the manifolds to achieve optimality even under operational uncertainties.