Trajectory tracking control of wheeled mobile robots with skidding and time-varying delay

This paper tackles the problem of trajectory tracking for wheeled mobile robots subject to time-varying input delay and bounded external disturbances. First, we establish a dynamic model for a wheeled mobile robot under sliding and skidding conditions, and determine the maximum allowable input delay that maintains system stability using Razumikhin-type stability analysis without prior knowledge of the variation in delay. The proposed adaptive robust controller combined with super-twisting sliding mode control is resilient to disturbances such as input delay, system uncertainty, and parameter variation. The proposed adaptive law enables real-time modification of switching gain based on tracking error without predefined knowledge of uncertainty bounds. Compared with traditional sliding mode control strategies, the super-twisting algorithm can eliminate chattering phenomenon while combined robust methods further reduce modeling uncertainties' influence on system performance. Finally, we select an appropriate Lyapunov function to analyze and prove uniformly ultimately bounded of the closed-loop system. MATLAB simulation comparison results demonstrate that this approach achieves high tracking accuracy, faster response speed, and robustness.