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This research formulates a path-following control problem subjected to wheel slippage and skid and solves it using a logic-based control scheme for a wheeled mobile robot (WMR). The novelty of the proposed scheme lies in its methodology that considers both longitudinal and lateral slip components. Based on the derived slip model, the controller for longitudinal motion slip has been synthesized. Various control parameters have been studied to investigate their effects on the performance of the controller resulting in selection of their optimum values. The designed controller for lateral slip or skid is based on the proposed side friction model and skid check condition. Considering a car-like WMR, simulation results demonstrate the effectiveness of the proposed control scheme. The robot successfully followed the desired circular trajectory in the presence of wheel slippage and skid. This research finds its potential in various applications involving WMR navigation and control.