**Abstract**

2D Ballbot is an actual under-actuated system with second-order nonholonomic velocity constraints and input coupling case where only control input is employed to control two outputs of the system. Controlling such a system is not easy because it faces many changelings including nonlinearities, external disturbances, and uncertainties. This study proposed a robust control system for a Ballbot mobile robot. The proposed control scheme is constructed using the hierarchical sliding mode control technique. The kinematics and dynamics of the Ballbot are derived. A Lyapunov function is used to prove the stability of the closed-loop control system. The stabilizing and transferring problems are investigated through several simulations and experiments by using the actual Ballbot platform.

**Keywords:** sliding mode control, Ballbot, under-actuated system, Lyapunov analysis, stabilizing and transferring
