Blanchard, Jared T. | Search NASA

NASA NTRS2022

Model Predictive Control in the Three-body Problem Using Invariant Funnels As Terminal Sets

This paper describes a method for augmenting Model Predictive Control techniques using invariant funnels computed in the Circular Restricted Three-Body Problem. We use ellipsoids that roughly approximate the boundary of the invariant funnel as convex terminal sets for a short look-ahead optimization problem at each time step. We apply this method to a hypothetical low-thrust mission to land on Jupiter’s mooon Europa and show that including the invariant funnels as terminal sets reduces the amount of control effort required by almost an order of magnitude.

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NASA NTRS2021

New Tools for Tour Design: Swiss Cheese Plot, Invariant Funnel, and Resonant Encounter Map

We define a new set of tools for tour design introduced in previous work: the”Swiss Cheese Plot,” ”Invariant Funnel,” and ”Resonant Encounter Map.” These tools promise to be useful in designing, analyzing, and navigating low-energy trajectories through multi-body systems. We review and clarify methods for generating the swiss cheese plot and invariant funnels in the Circular Restricted Three-Body Problem. We introduce the resonant encounter map as a graphical representation of the three-body design space, similar to the pork-chop plot for the two-body problem. We also discuss some interesting characteristics of the resonant encounter map and its connection to the invariant manifolds of periodic libration orbit

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