水下滑翔机李雅普诺夫稳定性分析

Lyapunov stability analysis of the underwater glider

水下滑翔机作为一种新型的水下机器人利用了水平固定翼将净重力转换为前进驱动力,从而降低了水下机器人的功耗,在海洋科学研究、环境监测、资源探测和军事侦察等方面都具有广阔的应用前景。为了得到实际水下滑翔机稳定性与设计参数和控制参数之间的关系,将已建立的水下滑翔机一般数学模型应用于具体的实际水下滑翔机上。在此基础上将模型线性化,结合李雅普诺夫稳定性第一定理和第二定理,分析出水下滑翔机定常运动的动态稳定性随设计参数(初稳性高)和控制参数(姿态调节控制量)变化的规律。为水下滑翔机器人的设计和控制提供理论依据。

As a novel underwater robot,the underwater glider converts net gravity to driving force forward with the horizontal fixed-wing,thereby reducing the power consumption of the underwater robot. The underwater glider has broad application prospects in marine scientific research,environmental monitoring,resource exploration and military reconnaissance,etc. In order to ascertain the relationship between design parameters,control parameters and stability of actual underwater gliders,the general mathematical model that had been established was applied to a specific underwater glider in practice and then linearized. Stability was judged by Lyapunov first and second theorems. The law in which stability varies with design parameters（ initial metacentric height） and control parameters（ attitude adjustment parameters） was obtained,providing a theoretical basis for design and control of underwater gliders.