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

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.

Source: arXiv:2602.10961v1 - http://arxiv.org/abs/2602.10961v1 PDF: https://arxiv.org/pdf/2602.10961v1 Original Link: http://arxiv.org/abs/2602.10961v1