Motion control of an underactuated spherical robot: A hierarchical sliding-mode approach with disturbance estimation

The inner suspension of a spherical robot undergoes an underactuated state which will be difficult for the underactuated system control, when the robot is rolling ahead. To resolve this underactuated control problem, an adaptive hierarchical sliding mode control scheme is proposed. The spherical robot system is separated as shell subsystem and inner suspension subsystem according to the movement. Then a pair of first layer sliding surfaces is defined for each subsystem, by which the equivalent control law is derived to ensure states of each subsystem approaching to their own sliding mode surface. Based on the first layer sliding surface, a second layer surface is defined correspondingly, through which a total control law is given to make sure that all states can converge to their desired value via Lyapunov stability theorem. Meanwhile, considering the unavoidable and uncertain disturbance in the unstructured exploration environment, an adaptive hierarchical sliding mode control scheme is adopted to estimate the uncertain disturbances in real-time. Finally, the simulation results demonstrate the controller's adaptability and validity.