This paper presents a fault-tolerant trajectory tracking control scheme for nonholonomic wheeled mobile robots (NWMRs) by integrating a Sliding Mode Controller (SMC) with a High-Order Integral-Chain Differentiator (HOICD). The proposed structure directly estimates velocity from position signals, eliminating the need for direct velocity sensing and enhancing robustness against actuator faults and modeling uncertainties. The estimation error is embedded into the sliding surface to accelerate convergence and improve transient response. Lyapunov-based analysis guarantees closed-loop stability. Simulation results demonstrate that the proposed SMC-HOICD controller achieves superior tracking accuracy, faster convergence, and stronger robustness compared to conventional methods under actuator efficiency degradation and external disturbances.