Nonconservative adaptive practical predefined-time sliding mode tracking of uncertain robotic manipulators

In this article, a nonconservative predefined-time sliding mode control (SMC) scheme and an adaptive practical predefined-time SMC scheme are proposed for trajectory tracking of uncertain robotic manipulators. The nonconservative predefined-time SMCer can achieve strong predefined-time stability of a class of second-order systems without dynamic uncertainties and disturbances. Nonetheless, even in the dynamic uncertainties and disturbances, we show that the studied scheme provides a nonconservative upper bound of settling time. Moreover, considering the unknown coupling uncertainty of the robotic system, adaptive laws are proposed to estimate the upper bound of the coupling uncertainty. Based on the proposed practical predefined-time stability criterion, the designed adaptive practical predefined-time SMCer is shown that the tracking error of the system can converge to a neighborhood of the origin within a predefined time, and the proposed controller weakens the chattering and no prior knowledge of the upper bound of the system uncertainty is required. Several simulation examples are conducted to show the feasibility of the proposed controller, especially evaluating the robustness and the nonconservative settling time.