This paper provides a solution for the stabilization of a nonholonomic wheeled mobile robot which is affected by additive input disturbances. The solution is based on the supervisory control framework, finite-time stability and robust multi-output regulation. A supervisor and two controls are designed with the objective to stabilize the first output (in the input-to-output stability sense) while the second output has to be kept under a threshold. The results is then applied to the case of the unicycle mobile robot which has to reach a position (i.e. stabilization) avoiding eventual obstacle during the task (i.e. keeping the second output under a threshold). The effectiveness of the solution is proved mathematically, supported by simulation results and finally tested on a wheeled mobile robot in a real scenario.