Most existing control methods for wheeled mobile robot (WMR) are based on the primary assumption that the WMR's center of mass (CM) is known and fixed. This paper presents an adaptive tracking control scheme for an asymmetrically actuated WMR with slipping/skidding dynamics and uncertain/unknown mass center. First, we establish the WMR dynamic model with consideration of the fact that its CM is normally unknown or even shifting due to dynamic loading and/or load shifting. The resultant model also takes into account the impact of slipping/skidding uncertainties. Second, a structurally simple and computationally inexpensive controller is developed to deal with time-varying unknown control gain and parametric/nonparametric uncertainties of WMR, where the asymmetric and nonsmooth input saturation with no a prior knowledge of bounds of input saturation, together with output constraints and actuation/propulsion failures, is addressed.