This paper presents an electrohydraulic series elastic manipulator (ESEM) system containing a novel variable stiffness actuator (VSA) and a hybrid robust control. The ESEM includes a series elastic manipulator (SEM), an adjustable stiffness mechanism (ASM), and an electrohydraulic servo system (EHS). Thus, the ESEM can benefit from the advantages of the EHS, such as high-power density and a high torque-to-weight ratio. Besides, the ESEM system can use the advantages of the VSA to give the system a suitable dynamic in unknown environments as well as low energy consumption for cyclic tasks. The proposed VSA adjusts the stiffness by changing the position of the springs along the ball screw. This system can provide fast stiffness regulation in a much broader range. However, the variant characteristics of the VSA, and nonlinearities and uncertainties in the EHS, such as friction, leakages, and dependence of bulk modulus on temperature, are major challenges for the control design. The new design of a backstepping adaptive fuzzy sliding mode control (BAFSMC) is addressed in this study. It is developed via sliding mode control, backstepping technique, and an adaptive fuzzy scheme. The controller is separated into two control loops for the mechanical dynamics and the hydraulic dynamics. The SMC is embedded for each loop to reduce the system's order and to ensure that the system's state variables reach and stay on the sliding surface. The adaptive fuzzy scheme is used to replace the robust term in the control effort of the conventional SMC to get rid of the chattering phenomenon and to deal with uncertainties in the mechanical and hydraulic subsystems. The Lyapunov approach and backstepping technique are used to prove the robustness and stability of the controlled system and to derive the adaptive laws. On the other hand, a fuzzy input shaping (FIS) scheme which combines an input shaping technique (IST) and a fuzzy logic system, was proposed to minimize the residual vibration at the end effector robustly over the expected operating range of the VSA system. Numerical experiments and comparisons with some existing algorithms are presented to illustrate the theoretical results and show the efficiency of the proposed controller.
