Interactive Spacecraft Trajectory Design Strategies Featuring Poincaré Map Topology

Wayne R Schlei, Purdue University

Abstract

Space exploration efforts are shifting towards inexpensive and more agile vehicles. Versatility regarding spacecraft trajectories refers to the agility to correct deviations from an intended path or even the ability to adapt the future path to a new destination—all with limited spaceflight resources (i.e., small ΔV budgets). Trajectory design methods for such nimble vehicles incorporate equally versatile procedures that allow for rapid and interactive decision making while attempting to reduce Δ V budgets, leading to a versatile trajectory design platform. A versatile design paradigm requires the exploitation of Poincaré map topology , or the interconnected web of dynamical structures, existing within the chaotic dynamics of multi-body gravitational models to outline low-Δ V transfer options residing nearby to a current path. This investigation details an autonomous procedure to extract the periodic orbits (topology nodes) and correlated asymptotic flow structures (or the invariant manifolds representing topology links). The autonomous process summarized in this investigation (termed PMATE) overcomes discontinuities on the Poincaré section that arise in the applied multi-body model (the planar circular restricted three-body problem) and detects a wide variety of novel periodic orbits. New interactive capabilities deliver a visual analytics foundation for versatile spaceflight design, especially for initial guess generation and manipulation. Such interactive strategies include the selection of states and arcs from Poincaré section visualizations and the capabilities to draw and drag trajectories to remove dependency on initial state input. Furthermore, immersive selection is expanded to cull invariant manifold structures, yielding low-ΔV or even ΔV-free transfers between periodic orbits. The application of interactive design strategies featuring a dense extraction of Poincaré map topology is demonstrated for agile spaceflight with a simple spacecraft rerouting scenario incorporating a very limited Δ V budget. In the Earth-Moon system, a low-ΔV transfer from low Earth orbit (LEO) to the distant retrograde orbit (DRO) vicinity is derived with interactive topology-based design tactics. Finally, Poincaré map topology is exploited in the Saturn-Enceladus system to explore a possible ballistic capture scenario around Enceladus.

Degree

Ph.D.

Advisors

Tricoche, Purdue University.

Subject Area

Applied Mathematics|Aerospace engineering|Computer science

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