Global terminal sliding‐mode control for the synchronization problem of uncertain bilateral teleoperation system with time‐varying delays

Abstract In this paper, an adaptive global terminal sliding‐mode control is developed for a nonlinear bilateral teleoperation system with time‐varying delays, external disturbances, and uncertainties. By selecting a time‐varying sliding‐mode manifold, a finite‐time sliding‐mode control algorithm is proposed to guarantee the suppression of the reaching phase associated with the conventional sliding‐mode control. This implies that the robustness is guaranteed throughout to entire response of the system. Meanwhile, the chattering phenomenon and the energy consumption are significantly reduced. Furthermore, in order to enhance the tracking performance in practical situations, adaptive tuning laws are developed to estimate the unknown upper bounds of the lumped uncertainties. Hence, the proposed approach has several merits, namely, fast response, accurate synchronization, and strong robustness with respect to large uncertainties and disturbances. The stability of the system in closed‐loop and the boundedness on the internal dynamics are proved by Lyapunov stability theory. Illustrative simulations were conducted to show the effectiveness of the proposed controller.