ESO-Based Adaptive Backstepping Sliding Mode Control of a Multi-DoF Deep-Sea Hydraulic Manipulator

The accurate control of multiple degree-of-freedom (Multi-DoF) deep-sea hydraulic manipulator (DHMs) is often challenging due to their strong nonlinearities, uncertainties, and coupling characteristics. To address these issues, an adaptive extended state observer-based adaptive backstepping sliding mode control (AESO-ABSMC) strategy is proposed, which does not require velocity measurements. First, a velocity-free adaptive law is designed to handle parameter uncertainties. Second, two adaptive extended state observers (AESOs) are developed to estimate and compensate for lumped disturbances and to estimate the unmeasured velocity state. Specifically, the adaptive law is integrated into the AESO design to avoid the coupling between parameter adaption and state estimation, thereby reducing the burden on the AESO. Combines the adaptive law and AESO, an AESO-ABSMC controller is designed that does not require velocity information and possess stronger robustness against disturbances. Additionally, the novel adaptive reaching law (NARL) is adopted in the controller, which can not only improve the performance, but solve the contradiction between accelerating the suppression of traditional SMC chattering and fast convergence. Theoretical analysis confirms the asymptotic stabilization of the system and the boundedness of the tracking error. Comparative experiments on the Multi-DoF DHM demonstrate the effectiveness of the proposed control method.