Adaptive fuzzy global coupled nonsingular fast terminal sliding mode control of n-rigid-link elastic-joint robot manipulators in presence of uncertainties

Abstract

This paper presented a high-speed and low power consumption adaptive fuzzy global coupled nonsingular fast terminal sliding mode control (NFTSMC) to the position tracking control of the n-rigid-link elastic-joint robot manipulators (RMs) in the presence of the uncertainties. To the applying the proposed scheme to the system that is in the category of the under-actuated mechanical systems, first, the dynamic equations are divided into two subsystems in such a way that they are coupled together using an intermediate variable. Then, a fuzzy approximator in fuzzy global coupled NFTSMC is proposed to eliminate the singularity, increase the tracking speed, and reduce the amplitude of the chattering phenomenon in the control input signal. Finally, to estimate the boundary of the system uncertainties, an adaptive fuzzy global coupled NFTSMC with only one adaptive law is proposed which able to overcome the uncertainties effect, eliminate the chatting phenomenon and reduce the amplitude of the control input to an actual limit. The computational complexity of the fuzzy parts is extremely low. The mathematical proof guarantees the global finite-time asymptotic stability of the closed-loop control system under fuzzy and adaptive fuzzy global coupled NFTSMC in the presence of the uncertainties. The effectiveness of the proposed scheme is demonstrated by the qualitative and quantitative studies for the simulation and practical implementation on the two-link and single-link elastic-joint RMs, respectively.