This paper contributes to the design of a robust control strategy for the trajectory tracking problem in perturbed unicycle mobile robots. The proposed strategy comprises the design of a robust control law, which is based on an Integral Sliding-Mode Control (ISMC) approach together with an interval predictor-based state-feedback controller and a Model Predictive Control (MPC) scheme. The robust controller deals with some perturbations in the kinematic model, and with state and input constraints that are related to restrictions on the workspace and saturated actuators, respectively. The proposed approach guarantees the exponential convergence to zero of the tracking error. Furthermore, the performance of the proposed approach is validated through some simulations.