Robust Trajectory Tracking for Omnidirectional Mobile Robots with Input Time Delay: An ADRC Approach

In this article, the problem of control of the kinematic model of an omnidirectional robot with time delay in the control input is tackled through an Active Disturbance Rejection Control (ADRC) with a disturbance predictor-based scheme, which consists in predicting the generalized forward disturbance input in order to cancel it and then using a feedforward linearization approach to control the system in trajectory tracking tasks. The novelties of the scheme are to demonstrate that using the proposed extended state disturbance estimation leads to a forward estimation following the Taylor series approximation, and, to avoid using additional pose predictions, a feedforward input as an exact linearization approach is used, in which the remaining dynamics can be lumped into the generalized disturbance input. Thus, the use of extended states in prediction improves the robustness of the predictor while increasing the prediction horizon for larger time delays. The stability of the proposal is demonstrated using the second method of Lyapunov, which shows the closed-loop estimation/tracking ultimate bound behavior. Additionally, numerical simulations and experimental tests validate the robustness of the approach in trajectory-tracking tasks.