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Due to their complicated dynamics and underactuated nature, spherical robots require advanced control methods to reveal all their manoeuvrability features. This paper considers the path tracking control problem of a spherical robot equipped with a 2-DOF pendulum. The pendulum has two input torques that allow it to take angles about the robot’s transverse and longitudinal axes. Due to mechanical technicalities, it is assumed that these angles are immeasurable. First, a neural network observer is designed to estimate the pendulum angles. Then a modified sliding mode controller is proposed for the robot’s tracking control in the presence of uncertainties. Next, the Lyapunov theorem is utilized to analyse the overall stability of the proposed scheme, including the convergence of the observer estimation and the trajectory tracking errors. Finally, simulation results are provided to indicate the effectiveness of the proposed method in comparison with the other available control approaches.