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

• URL: http://arxiv.org/abs/2602.10961v3
• Date: Thu, 19 Feb 2026 09:46:15 GMT
• Title: Stability Analysis of Geometric Control for a Canonical Class of Underactuated Aerial Vehicles with Spurious Forces
• Abstract summary: This work provides the first formal stability analysis for a generic class of floating rigid bodies subject to spurious forces.<n>We explicitly address the structural challenges - specifically the induced non-minimum-phase behavior - that prevent the application of standard cascade arguments.
• Score: 2.951722617674417
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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