Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach

TL;DR

This paper introduces a unified nonlinear synchronization framework for formation flying spacecraft, enabling precise coupled translational and rotational control using contraction analysis for stability proofs.

Contribution

It presents a novel decentralized control law that synchronizes both attitude and position of multiple spacecraft in a unified nonlinear framework.

Findings

Achieves global exponential convergence in attitude synchronization.

Enables coupled translational and rotational maneuvers.

Handles highly nonlinear spacecraft dynamics with nonlinearly coupled inertia.

Abstract

This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. While the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of spacecraft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework.