Adaptive Hierarchical Sliding Mode Control Based on Extended State Observer for Underactuated Robotic System

In order to stabilize underactuated robotic systems with external disturbances, an adaptive hierarchical sliding mode control strategy based on extended state observer is proposed. The extended state observer is designed to estimate the joint states and lumped disturbance composed of matched and unmatched disturbances. The underactuated robotic system is divided into two subsystems. For each subsystem, a sub-sliding mode surface is constructed to obtain the first layer sliding mode surface and the second layer sliding mode surface is derived from the first layer sliding mode surface. Then the hierarchical sliding mode controller is designed with the estimated state obtained from the observer to compensate the lumped disturbance and an adaptive law is designed to adjust the switching gain. The stability of the system is proved by Lyapunov theory and the effectiveness of the proposed control strategy is verified by comparative simulations. With the proposed control, the tracking performance of the underactuated robotic system is effectively improved and the convergence time of the system is reduced.