Formation Flight of Earth Satellites on Low-Eccentricity KAM Tori
Abstract
The problem of Earth satellite constellation and formation flight is investigated in the context of Kolmogorov-Arnold-Moser (KAM) theory. KAM tori are constructed utilizing Wiessel's Low-Eccentricity Earth Satellite Theory, allowing numerical representation of the perturbed tori describing Earth orbits acted upon by geopotential perturbations as sets of Fourier series. A maneuvering strategy using the local linearization of the KAM tangent space is developed and applied, demonstrating the ability to maneuver onto and within desired torus surfaces. Constellation and formation design and maintenance on KAM tori are discussed, along with stability and maneuver error concerns. It is shown that placement of satellites on KAM tori results in virtually no secular relative motion in the full geopotential to within computational precision. The effects of maneuver magnitude errors are quantified in terms of a singular value decomposition of the modal system for several orbits of interest, introducing a statistical distribution in terms of torus angle drift rates due to mismatched energies. This distribution is then used to create expectations of the steady-state station-keeping costs, showing that these costs are driven by operational and spacecraft limitations, and not by limitations of the dynamics formulation. A non-optimal continuous control strategy for formations based on Control Lyapunov Functions is also outlined and demonstrated in the context of formation reconfiguration.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 24, 2016
- Accession Number
- AD1054145
Entities
People
- Christopher T. Craft
Organizations
- Air Force Institute of Technology