Extraction and Visualization of Poincar\'e Map Topology for Spacecraft Trajectory Design

TL;DR

This paper introduces algorithms for extracting and visually exploring the topology of Poincaré maps in astrodynamics, aiding spacecraft trajectory design by revealing key dynamical structures like periodic orbits and invariant manifolds.

Contribution

It presents novel algorithmic methods for characterizing and visualizing Poincaré map topology specifically tailored for astrodynamics applications, enhancing trajectory planning tools.

Findings

Revealed new periodic orbits in the CR3BP.

Enabled interactive visualization of invariant manifolds.

Improved trajectory design efficiency using topology insights.

Abstract

Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincar\'e maps to search for a suitable path through the interconnected web of periodic orbits and invariant manifolds found in multi-body gravitational systems. This paper is concerned with the extraction and interactive visual exploration of this structural landscape to assist spacecraft trajectory planning. We propose algorithmic solutions that address the specific challenges posed by the characterization of the topology in astrodynamics problems and allow for an effective visual analysis of the resulting information. This visualization framework is applied to the circular restricted three-body problem (CR3BP), where it reveals novel periodic orbits with their relevant invariant manifolds in a suitable format for interactive transfer selection. Representative design problems illustrate how spacecraft path planners can leverage our topology visualization to fully exploit the natural dynamics pathways for energy-efficient trajectory designs.