Trajectory tracking of under-actuated nonlinear dynamic robots: Adaptive fuzzy hierarchical terminal sliding-mode control

In recent years, underactuated nonlinear dynamic systems trajectory tracking, such as space robots and manipulators with structural flexibility, has become a major field of interest due to the complexity and high computational load of these systems. Hierarchical sliding mode control has been investigated recently for these systems; however, the instability phenomena will possibly occur, especially for long-term operations. In this paper, a new design approach of an adaptive fuzzy hierarchical terminal sliding-mode controller (AFHTSMC) is proposed. The sliding surfaces of the subsystems construct the hierarchical structure of the proposed method; in which the top layer includes all of the subsystems’ sliding surfaces. Moreover, terminal sliding mode has been implemented in each layer to ensure the error convergence to zero in finite time besides chattering reduction. In addition, online fuzzy models are employed to approximate the two nonlinear dynamic system’s functions. Finally, a simulation example of an inverted pendulum is proposed to confirm the effectiveness and robustness of the proposed controller.