This work deals with the robust position tracking control problem for an omnidirectional mobile robot. To this aim, four continuous Sliding-Mode Control strategies are presented. The position and orientation of the platform are assumed to be the only available information about the system. To implement the controllers as output-feedback controllers, a High-Order Sliding-Mode Observer is implemented for each output signal. The proposed robust control strategies are able to deal with some classes of external disturbances. The closed-loop stability of each controller is proved by means of Lyapunov functions and homogeneity concepts. Simulations and experiments validate the applicability of the proposed controllers.