Closed Relative Trajectoriesfor Formation Flying with Single-Input Control

Abstract EN

We study the problem of formation shape control under the constraints on the thrust direction.

Formations composed of small satellites are usually subject to serious limitations forpower consumption, mass, and volume of the attitude and orbit control system (AOCS).

Ifthe purpose of the formation flying mission does not require precise tracking of a given relativetrajectory, AOCS of satellites may be substantially simplified; however, the capacity ofAOCS to ensure a bounded or even periodic relative motion has to be studied first.

We considera formation of two satellites; the deputy one is equipped with a passive attitude controlsystem that provides one-axis stabilization and a propulsion system that consists of one or twothrusters oriented along the stabilized axis.

The relative motion of the satellites is modeled bythe Schweighart-Sedwick linear equations taking into account the effect of J2 perturbations.

Weprove that both in the case of passive magnetic attitude stabilization and spin stabilization forall initial relative positions and velocities of satellites there exists a control guaranteeing theirperiodic relative motion.