Statistical Analysis of the Role of Invariant Manifolds on Robust Trajectories

TL;DR

This study investigates how invariant manifolds influence the design of robust low-thrust space trajectories in chaotic multibody systems, revealing that optimal solutions often align closely with these structures to maintain efficiency under uncertainties.

Contribution

It provides the first comprehensive statistical analysis of the relationship between invariant manifolds and robust trajectory solutions in a three-body problem context.

Findings

Optimal trajectories align closely with invariant manifolds.

Robust solutions can sometimes align more closely than non-robust ones.

Maintaining proximity to manifolds enhances trajectory robustness.

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.