This article tackles the trajectory tracking problem for a non-holonomic wheeled mobile robot (WMR) with non-random and random disturbances. A nonlinear disturbance observer with extended Kalman filter (NDEKF) is designed to observe the velocity and the non-random disturbance of the WMR. An error feedback controller and a kinematic controller are proposed to achieve the disturbance compensation and perfect position tracking. The mean square exponential boundedness for the estimation error of NDEKF is presented. Applying the Lyapunov stability theory, it is proved that the velocity and position tracking error of the double closed-loop system are uniformly ultimately asymptotically stable. Finally, numerical simulations demonstrate the validity of the presented methodology.

本文解决了具有非随机和随机干扰的非完整轮式移动机器人（WMR）的轨迹跟踪问题。设计了带有扩展卡尔曼滤波器（NDEKF）的非线性干扰观测器，以观测WMR的速度和非随机干扰。提出了一种误差反馈控制器和运动控制器，以实现干扰补偿和完美的位置跟踪。给出了NDEKF估计误差的均方指数有界性。应用李雅普诺夫稳定性理论，证明了双闭环系统的速度和位置跟踪误差最终是一致渐近稳定的。最后，数值模拟证明了所提出方法的有效性。