This paper proposes a robust H-infinity control design of a single unit differential type Wheeled Mobile Robot. Mobile robots are non holonomic systems as their constraint equations are not integrable. Considering the constraints and combining the kinematics and dynamics of the system, a linearized model is obtained. Taking into account the exogenous inputs in the form of model uncertainties and output disturbances, the augmented plant is formulated. The Hinfinity controller is designed such that the sensitivity of the closed loop system is minimised. The proposed design renders a robust controller such that the closed loop system is internally stable and the effect of disturbances and model uncertainties on some of the outputs is attenuated. Simulation results showing asymptotic stability plot, disturbance response and Robust Stability and Performance margins are found to be satisfactory.