Extraction and Visualization of Poincaré Map Topology for Spacecraft Trajectory Design
This work addresses the problem of energy-efficient spacecraft trajectory planning for mission designers, offering a domain-specific visualization tool that is incremental in nature.
The paper tackles the challenge of designing low-cost spacecraft trajectories by extracting and visualizing the topology of Poincaré maps in multi-body gravitational systems, revealing novel periodic orbits and invariant manifolds for interactive transfer selection in the circular restricted three-body problem.
Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincaré 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.