Spacecraft Relative Motion Dynamics and Control Using Fundamental Solution Constants

TL;DR

This paper introduces a novel method for analyzing and controlling satellite relative motion by expressing the state in terms of fundamental solution constants derived from Lyapunov-Floquet theory, applicable in various periodic dynamical environments.

Contribution

It presents a new approach that uses fundamental solution constants to analyze and control satellite relative motion, offering insights and elegant control strategies in periodic dynamical systems.

Findings

Applicable to any periodic chief orbit environment

Demonstrated in eccentric Keplerian and CR3BP scenarios

Enables control design via variation of fundamental solution weights

Abstract

This paper explores expressing the relative state in the close-proximity satellite relative motion problem in terms of fundamental solution constants. The nominal uncontrolled relative state can be expressed in terms of a weighted sum of fundamental and geometrically insightful motions. These fundamental motions are obtained using Lyapunov-Floquet theory. In the case that the dynamics are perturbed by the action of a controller or by unmodeled dynamics, the weights on each fundamental solution are allowed to vary as in a variation-of-parameters approach, and in this manner function as state variables. This methodology reveals interesting insights about satellite relative motion and also enables elegant control approaches. This approach can be applied in any dynamical environment as long as the chief orbit is periodic, and this is demonstrated with results for relative motion analysis and control in the eccentric Keplerian problem and in the circular restricted three-body problem (CR3BP). Some commentary on extension of the methodology beyond the periodic chief orbit case is also provided. This is a promising and widely applicable new approach to the close-proximity satellite relative motion problem.