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

2026-02-11

AI Summary

Standard geometric control relies on the decoupling assumption between forces and torques; however, in underactuated aerial vehicles, control torques often induce parasitic forces that violate this assumption and lack theoretical stability guarantees. This work addresses such systems by constructing a general rigid-body aerial vehicle model and integrating geometric control theory with Lyapunov-based analysis to overcome the analytical challenges posed by non-minimum-phase characteristics. For the first time, it provides a rigorous proof of local exponential stability for the hover equilibrium of underactuated aerial vehicles subject to parasitic forces, thereby filling a critical theoretical gap in the stability analysis of these coupled dynamical systems.

Technology Category

• Multiagent Systems: Multiagent Systems under Uncertainty
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: Behavior Learning & Control

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

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.

Problem

• geometric control
• underactuated aerial vehicles
• spurious forces
• stability analysis
• non-minimum-phase

Innovation

• geometric control
• spurious forces
• non-minimum-phase
• Lyapunov stability
• underactuated aerial vehicles