首次为存在干扰力的飞行器提供稳定性理论证明。
Stability Analysis of Geometric Control for a Canonical Class of Underactuated Aerial Vehicles with Spurious Forces
- 构建通用模型，用李雅普诺夫方法证明悬停点局部指数稳定。
- 揭示控制力矩引发的非最小相位特性是传统分析失效主因。
- 适合研究无人机控制理论或鲁棒控制的学者参考。
标准几何控制依赖力-力矩解耦假设，但在许多飞行平台中，控制力矩会自然产生干扰力，导致该假设失效。尽管针对这类耦合系统已有实验验证，但其稳定性尚无严格理论证明。本文填补这一空白，首次对一类受干扰力影响的浮体刚体系统提供正式稳定性分析。通过引入典型模型并构造基于李雅普诺夫的证明，确立了悬停平衡点的局部指数稳定性。关键在于，分析明确处理了阻碍标准级联论证应用的结构难题——尤其是由干扰力引起的非最小相位行为。
原文摘要 · Abstract (English)
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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