This article develops an event-triggered model-predictive control (EMPC) strategy to realize trajectory tracking and obstacle avoidance for a wheeled mobile robot (WMR) subject to input constraints and external disturbances. In the EMPC strategy, a potential field is introduced in the cost function to guarantee a smooth path for the WMR. An event-triggered mechanism is designed to reduce the computational load of solving an optimal control problem (OCP). Moreover, an adaptive prediction horizon is utilized to further achieve computation reduction. Both recursive feasibility of the OCP and practical stability of the resulting closed-loop system are analyzed for the WMR with the input constraints and the external disturbances. Simulation results are provided to demonstrate the effectiveness and superiority of the proposed EMPC strategy.