基于李雅普诺夫函数的两轮机器人非线性控制设计

Nonlinear control design using Lyapunov function for two-wheeled mobile robots

针对两轮移动机器人提出了一种非线性反馈控制方法,利用系统平衡点稳定和可计算的稳定域来获得渐进稳定的李雅普诺夫函数控制率.使用了标准化和部分反馈线性化方法来简化动力学方程,部分反馈线性化是在动坐标下完成的.为了验证控制率设计的合理性,在一个静态不稳定的两轮移动机器人上进行了垂直位置稳定和速度跟踪的模拟,结果表明:该控制方法控制效果良好,而且需求的控制量较少.

This paper presents a nonlinear feedback control framework for two-wheeled mobile robots. The approach uses a constructive Lyapunov function which allows the formulation of a control law with asymptotic stability of the equilibrium point of the system and a computable stability region. The dynamic equations are simplified through normalization and partial feedback linearization. The latter allows linearizing only the actuated coordinate. Description of the control law is complemented by the stability analysis of the closed loop dynamics of the system. The effectiveness of the method has been illustrated by its good performance and less control demand through simulations conducted for two control tasks：upright position stabilization and velocity tracking for a statically unstable two wheeled mobile robot.