This paper investigates the trajectory tracking control for a mobile robot under nonholonomic constraints. To address those constraints and the system’s MIMO nature, a backstepping-based Sliding Mode Controller (SMC) is designed at the kinematic level to ensure the system’s asymptotic stability. Complementing this, two Proportional-Integral-Derivative (PID) controllers manage the lower-level velocity control. Compared with two alternative methods from existing literature, the SMC excels notably in time and energy efficiency, albeit at a slightly reduced accuracy. The factors contributing to this accuracy variation are thoroughly discussed. Finally, experimental results are presented to demonstrate the overall performance of the proposed method.