Swiss Cheese Plot Trajectory Mapping for Low-Fuel Spacecraft Navigation
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Solution Overview
Problem
Current methods for navigating and landing on secondary bodies, such as moons and asteroids, face challenges in finding robust and error-resistant orbits, particularly at high latitudes, and are inefficient in fuel usage due to the complexity of resonant orbits in multi-body systems like the Earth-Moon and Outer Planets environments.
Innovation Solution
The use of novel navigation methods involving a generalized Poincaré Map called the 'Swiss Cheese Plot', 'Invariant Funnel', and 'Resonant Encounter Map' to plot low-energy trajectories under CR3BP conditions, allowing for the identification of resonant orbits and autonomous navigation in three- and four-body systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional navigation methods are used for landing on secondary bodies, then the mission can be completed, but the navigation risks are high and fuel consumption is excessive
Solution Approach 1:
The patent transforms the navigation problem by changing the parameter space from direct trajectory control to energy-based orbital parameter selection. By using the Jacobi constant and Delaunay variables to parameterize orbits, the system identifies resonant orbits that naturally minimize fuel consumption while maintaining high navigation reliability through mathematical guarantees of orbital stability.
Solution Approach 2:
The patent replaces traditional mechanical navigation control systems with a mathematical mapping system. The Swiss Cheese Plot and Resonant Encounter Map provide a geometric-mechanical substitution where orbital intersections in phase space automatically determine safe, fuel-efficient trajectories without requiring active control interventions.
2Use of energy by moving object
If resonant orbits are used for capture and landing, then fuel consumption is reduced, but the difficulty of finding suitable orbits increases
Solution Approach 1:
The patent adds a dimensional transformation by mapping three-dimensional orbital trajectories onto two-dimensional surfaces of section. The Swiss Cheese Plot and Resonant Encounter Map project complex 3D resonant orbit structures into 2D phase space representations, making them visually identifiable and computationally tractable while preserving all essential orbital characteristics.
Solution Approach 2:
The patent performs preliminary identification of resonant orbits through pre-computed maps before actual mission execution. By预先 calculating and storing the Swiss Cheese Plot and Resonant Encounter Map for the specific planet-moon system, the navigation problem is reduced to simple map reading and parameter matching during the actual mission, dramatically reducing real-time computational difficulty.
3Adaptability or versatility
If high latitude landing sites on moons are targeted, then scientific exploration value increases, but the complexity of finding resonant orbits increases significantly
Solution Approach 1:
The patent creates a universal mapping methodology that works for any planet-moon system and any landing site latitude. The Swiss Cheese Plot and Resonant Encounter Map frameworks are system-agnostic and can be applied to Europa, Enceladus, or any other moon with high latitude targets, providing a unified approach that handles all latitudes through the same mathematical machinery rather than requiring separate solutions for different cases.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
These methods significantly reduce navigation risks and fuel consumption by providing robust and efficient flight paths for capture, flyby, and landing missions, enabling exploration and development of celestial bodies and applications in Cislunar space, asteroid mining, and defense against hazards.
Implementation Method 1
The resonant orbits between the Earth and Moon can be used for the transport of cargo; they can be identified using the Swiss Cheese map and the Global Resonant Encounter Maps
Data Source
AI summary
Systems and methods are described for computing a trajectory of an object in space to a secondary body (M2) in orbit around a primary body to land on, or capture into orbit, or flyby M2 in a Three-Or-More Body Problem. A special plotting of sampled vectors from M2 are integrated backward using a Poincaré Map to form a “Swiss Cheese plot” to find a nominal trajectory. A funnel-like set of trajectories can be constructed along the nominal trajectory for navigation purposes. A global resonant encounter map over a sphere around M2 can be constructed to provide trajectories to, for example, flyby any point near M2, capture into orbit over any point about M2, land on any point on M2. Besides space exploration, there are many applications to the development of Cislunar space commercialization and colonization including asteroid capture and mining.