Extended state observer-based adaptive hierarchical sliding mode control for longitudinal movement of a spherical robot

The inner suspension of spherical robot undergoes a kind of typical underactuated vibration when the mobile benchmark performs the longitudinal movement. The inherent vibration deteriorates the control performances such that it is difficult to obtain the satisfactory movement effects. Considered the fact that the state variables of a spherical robot and the uncertain rolling resistance moment are unavailable in practical implementation, an extended state observer is proposed with the aid of which some of the sensors can be replaced and the rolling resistance can be obtained to construct the controllers. Also, an adaptive hierarchical sliding mode control approach is presented based on the extended state observer. The proposed control methodologies can assure the robot rolling performances and realize the effective control of the inner suspension simultaneously. The numerical simulation results demonstrate that the designed closed-loop control system of the spherical robot possesses robust and adaptive capabilities to overcome the uncertain rolling resistance which is significant for a mobile robot in unstructured environment.