Log-linear Dynamic Inversion for Thrusting Spacecraft on SE2(3)

TL;DR

This paper introduces a novel control law for thrusting spacecraft based on the Lie group SE2(3), demonstrating that error dynamics can be effectively linearized and controlled within this geometric framework.

Contribution

It shows that spacecraft error dynamics are nearly group affine on SE2(3) and can be linearized using dynamic inversion, advancing geometric control methods for spaceflight.

Findings

Error dynamics are nearly group affine on SE2(3)

Dynamic inversion effectively bounds nonlinearity

Numerical validation confirms theoretical predictions

Abstract

We demonstrate that the error dynamics of a thrusting spacecraft are nearly group affine on the $SE_2(3)$ Lie group, and the nonlinearity can be bounded, or removed with the application of a dynamic inversion control law. A numerical example validates the results by showing agreement between the error predicted by the log-dynamics and the error obtained from classical integration of trajectories using Newtonian dynamics. The result clarifies how thrusting spacecraft dynamics fit within the invariant systems framework.