On the Controllability of an Orbiting Satellite Model with Electromagnetic-only Actuation

TL;DR

This paper establishes conditions under which a satellite with electromagnetic actuation can be controlled in small time, focusing on underactuated magnetorquer-driven rotational dynamics and analyzing controllability properties.

Contribution

It provides the first controllability analysis for a satellite model actuated solely by electromagnetic torques, using Lie algebra and Sussmann's conditions.

Findings

Small-time local controllability is proven under natural mass distribution assumptions.

Linearized system is not controllable near the equilibrium point.

Controllability is established despite underactuation with magnetorquers.

Abstract

This paper presents sufficient conditions for small-time local controllability of a control-affine system that describes the rotational motion of a satellite in a circular orbit. The satellite is modeled as a rigid body subject to electromagnetic actuation. We focus on the underactuated scenario where the control torque is generated solely by magnetorquers. The main contributions of this work include proving small-time local controllability around the relative equilibrium under some natural assumptions on the mass distribution of the rigid body. This result is based on the Lie algebra rank condition and Sussmann's controllability condition. Furthermore, it is shown that the linearized system is not controllable in a neighborhood of the considered equilibrium.