This paper presents a unique ESO-based fuzzy sliding-mode controller (FSMC-ESO) for a 3-DOF serial-parallel hybrid humanoid arm (HHA) for the trajectory tracking control problem. The dynamic model of the HHA is obtained by Lagrange method and is nonlinear in dynamics with inertia uncertainty and external disturbance. The FSMC-ESO is based on the combination of the sliding-mode control (SMC), extended state observer (ESO) theory, and fuzzy control (FC). The SMC is insensitive to both internal parameter uncertainties and external disturbances. The motivation for using ESO is to estimate the disturbance in real-time. The fuzzy parameter self-tuning strategy is proposed to adjust the switching gain on line according to the running state of the system. The stability of the system is guaranteed in the sense of the Lyapunov stability theorem. The effectiveness and robustness of the designed FSMC-ESO are illustrated by simulations. 1. Introduction The 3-DOF serial-parallel hybrid humanoid arm (HHA) [1, 2] is composed of a 2-DOF parallel mechanism and a 1-DOF serial mechanism, as shown in Figure 1, can be used in humanoid robots or automated production lines. Because of the special structure, the HHA combines the characteristics of series and parallel robot and is discovered in high speed and high positioning accuracy. The special structure introduces complexity in kinematics, dynamic equations, and coupling of the system and places greater demands on control methods. Figure 1: The prototype of 3-DOF forearm. Since HHA is a very complicated multiple-input multiple-output (MIMO) nonlinear system with time-varying, strong-coupling characteristics, the design of robust controllers which is suitable for real-time control of HHA is one of the most challenging tasks, especially when HHA within inertia uncertainty and external disturbance. Advanced controller of robotic is a hot field in robotic research in recent years. Various advanced control strategies, either model-based control or model-free control, have been researched to improve the motion performance of the robotics [3–9]. The current trend of control approaches focuses on integrating conventional control techniques (e.g., adaptive control [6, 7] and sliding-mode control [3–6]) with intelligent schemes (e.g., fuzzy theory [7, 8] and neural network [5]) in order to improve the performance of classical controllers. About the control theory, the sliding-mode control is a useful and effective control scheme and is an efficient method to deal with uncertainties, time varying properties, nonlinearities, and bounded
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