欠驱动船舶的光滑时变指数镇定

Smooth time-variant exponential stabilization for underactuated surface vessels

船舶水平面运动的欠驱动特性使船舶运动控制的研究具有了新的内涵．本文在船舶水平面运动的运动学及动力学模型基础上,将其演化为二阶系统方程组．针对其欠驱动的特性,借助微分同胚变换及控制输入变换将其转化为两个子系统,分别设计状态反馈控制律,从而得到了原系统的具有指数收敛速率的时变光滑反馈镇定律,实现闭环系统所有状态全局指数收敛至平衡点．该方法可用于欠驱动船舶动力定位或自动泊位控制．最后的仿真试验验证表明本方法是有效的．

The underactuated characteristic of surface vessel motion in horizontal plane creates new direction in the research field of ship steering. Based on the kinematic and dynamic equations of surface vessel in horizontal plane, a set of second-order dynamic equations are given. Due to its underactuated characteristic, two sub-systems are obtained based on the diffeomorphism transformation and input transform. The state feedback control laws to form a smooth time-varying feedback stabilization law with exponentially convergence rate for original system are then derived. The proposed smooth time-varying feedback stabilization law guarantees all the states of original system to converge to the equilibrium point exponentially. The stabilization law could be used in the cases of dynamic positioning and auto-mooring for underactuated vessels. Finally, the effectiveness of the proposed method is illustrated by simulation tests.