基于Lyapunov方法和快速终端滑模的轨迹跟踪控制

Trajectory tracking control based on Lyapunov method and terminal sliding mode

针对移动机器人的运动学模型,提出一种具有全局渐近稳定性的跟踪控制器。该跟踪控制器的设计分为两部分:第一部分是采用全局快速终端滑动模态的思想设计了角速度的控制律,用来渐近镇定移动机器人跟踪的前向角误差;第二部分是采用Lyapunov方法设计了线速度的控制律,用来渐近镇定移动机器人跟踪的平面坐标误差。采用Lyapunov稳定性定理,证明了移动机器人在满足这些控制律条件下,实现了对参考轨迹的全局渐近跟踪。实验结果表明移动机器人能够有效地跟踪期望轨迹,有利于在实际应用中推广。

In view of the kinematic model of mobile robot,a tracking controller of global asymptotic stability was proposed.The design of tracking controller was divided into two parts： The first part designed the control law of angular velocity by using global fast terminal sliding mode in order to asymptotically stabilize the tracking error of the heading angle;the second part designed the control law of linear velocity by using the Lyapunov method in order to asymptotically stabilize the tracking error of the planar coordinate.By combining Lyapunov stability theorem and two control laws,the mobile robot can track the desired trajectory in a global asymptotic sense when the angular velocity and the linear velocity satisfy these control laws.The experimental results show that the mobile robot can track desired trajectory effectively.It is helpful for promoting the practical application.