离轴式拖车移动机器人的任意路径跟踪控制

Arbitrary path following control of off-axle tractor-trailer mobile robot

中文关键词  离轴式拖车移动机器人  坐标变换  任意路径跟踪  Lyapunov方法

英文关键词  off-axle tractor-trailer mobile robot  coordinate transformation  arbitrary path following  Lyapunov methods

中文摘要

      离轴式拖车移动机器人属于非完整系统, 当车头线速度随时间变化且过零变号时, 难以用一个控制器实现系统对期望路径的跟踪. 本文研究离轴式拖车移动机器人系统的任意路径跟踪问题. 首先由系统和虚拟小车的运动学方程得到误差状态模型, 线性化后用坐标变换将其化为标准型, 然后基于Lyapunov方法构造出一种跟踪控制律. 只要车头的运动线速度有界且不趋于零, 其导数有界, 则所设计的控制律就可以保证系统跟踪任意的期望路径, 且跟踪误差最终一致有界, 最终界的大小与期望路径的曲率变化率成比例. 当期望路径的曲率变化率为零或趋于零时, 所设计的控制律可以保证拖车移动机器人指数收敛到期望路径. 仿真结果证实了控制律的有效性.

英文摘要

      The tractor-trailer mobile robot with off-axle hitching is a classical nonholonomic system. It is difficult to use one controller to achieve path following when the linear velocity of the tractor is time-varying and sign changeable. This paper investigates the arbitrary path following problem of off-axle tractor-trailer robots with time-varying and sign changeable linear velocity. The error state model is first derived from the kinematic equations of the system and the virtual vehicle. The coordinate transformation is used to convert the simplified linearized error model to a normal form, and then a path-following control law is constructed via Lyapunov methods. Assume that the linear velocity of the tractor is bounded, not convergent to zero, and its derivative is bounded, then the designed control law guarantees that the tractor-trailer system is able to follow an arbitrary desired path. The size of the ultimate bound is proportional to the derivative of curvature. Moreover, asymptotic exponential convergence of the tractor-trailer to the desired path is achieved when the derivative of curvature is zero or convergent to zero. Simulation results show the effectiveness of the proposed control scheme.