Controllability of Keplerian Motion with Low-Thrust Control Systems

TL;DR

This paper investigates the controllability of satellite Keplerian motion using low-thrust systems, demonstrating controllability for orbital transfers and conditions for de-orbit and insertion problems with numerical methods.

Contribution

It establishes controllability conditions for low-thrust control of Keplerian motion, including state constraints and numerical computation of thrust limits.

Findings

Controllability holds for any positive maximum thrust in orbital transfer.

Controllability depends on a threshold thrust for de-orbit and insertion problems.

Numerical methods are provided to compute the critical thrust value.

Abstract

In this paper, we present the controllability properties of Keplerian motion controlled by low-thrust control systems. The low-thrust control system, compared with high or even impulsive control system, provide a fuel-efficient means to control the Keplerian motion of a satellite in restricted two-body problem. We obtain that, for any positive value of maximum thrust, the motion is controllable for orbital transfer problems. For two other typical problems: de-orbit problem and orbital insertion problem, which have state constraints, the motion is controllable if and only if the maximum thrust is bigger than a limiting value. Finally, two numerical examples are given to show the numerical method to compute the limiting value.