This brief proposes a novel solution to the trajectory tracking control problem for input-constrained differential-drive robots. In particular, we develop a robust set-based receding horizon tracking scheme capable of dealing with state-dependent input constraints arising when the vehicle’s dynamics are approached by a standard feedback linearization (FL) technique. First, offline, we characterize the worst case input constraint set and compute an admissible, although not optimal, controller. Then, online, we leverage the knowledge of the robot’s orientation to enlarge the constraint set in a receding horizon fashion and, consequently, improve the tracking performance. Recursive feasibility and constraints’ fulfillment are formally proven. The approach’s effectiveness is experimentally validated on a Khepera IV differential-drive robot by comparing the control performance with several competitor schemes.