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This study addresses the trajectory tracking control problem of electrically driven wheeled mobile robots under non-holonomic constraints in the presence of model uncertainties without velocity measurement. By defining a suitable set of output equations, a new input-output model of wheeled mobile robots is developed, which helps the designer utilise the classic control algorithms of robot manipulators. An observer-based trajectory tracking controller is proposed for the new wheeled mobile robot (WMR) model. Then, in order to reduce the design complexity, the dynamic surface control approach is effectively exploited to propose a tracking controller considering the actuator dynamics. Adaptive robust techniques are also adopted to cope with the parametric and non-parametric uncertainties in the WMR model. A Lyapunov-based stability analysis is utilised to guarantee that tracking and state estimation errors are uniformly ultimately bounded. Simulation results are presented to illustrate the feasibility and efficiency of the proposed controller.