Stability Analysis of Geometric Control for a Canonical Class of Underactuated Aerial Vehicles with Spurious Forces

TL;DR

This paper provides the first rigorous stability analysis for a class of underactuated aerial vehicles affected by spurious forces, using a Lyapunov-based approach to establish local exponential stability.

Contribution

It introduces a canonical model and develops a Lyapunov proof addressing structural challenges like non-minimum-phase behavior in stability analysis.

Findings

Established local exponential stability of hovering equilibrium

Addressed structural challenges preventing standard cascade arguments

Provided a formal stability certification for systems with spurious forces

Abstract

Standard geometric control relies on force-moment decoupling, an assumption that breaks down in many aerial platforms due to spurious forces naturally induced by control moments. While strategies for such coupled systems have been validated experimentally, a rigorous theoretical certification of their stability is currently missing. This work fills this gap by providing the first formal stability analysis for a generic class of floating rigid bodies subject to spurious forces. We introduce a canonical model and construct a Lyapunov-based proof establishing local exponential stability of the hovering equilibrium. Crucially, the analysis explicitly addresses the structural challenges - specifically the induced non-minimum-phase behavior - that prevent the application of standard cascade arguments.