Adaptive Non-Singular Terminal Sliding Mode Trajectory Tracking Control of Robotic Manipulators Based on Disturbance Observer Under Unknown Time-Varying Disturbance

We address the problems in the trajectory tracking control of a multi-joint robotic arm, including uncertainty in the internal modeling of its significant external unknown time-varying disturbances. With the control objective of tracking the desired trajectories of each joint stably and accurately, this paper proposes an adaptive non-singular terminal sliding mode control method based on a nonlinear disturbance observer (NDO). In order to speed up the convergence of the tracking error and avoid the singular value problem existing in the traditional terminal sliding mode (TSM), a non-singular terminal sliding mode (NTSM) surface is proposed in this paper. Given the system modeling uncertainty and external unknown time-varying disturbances, a nonlinear disturbance observer is used to observe the total set disturbance for feed-forward compensation. Secondly, the switching gain adaptive law is used to estimate the observation error of the total set disturbance and allow for the online adjustment of the switching gain weights. A robust gain adaptive law is also designed to reconverge quickly to the non-singular sliding mode surface when transient significant disturbances shock the system’s state variables out of the sliding phase. A simulation analysis of the spatial two-link robotic arm is carried out in Simulink. The results show that the adaptive non-singular terminal sliding mode control strategy based on the nonlinear disturbance observer proposed (PNDOANTSM) in this paper can reduce the average steady-state errors of robotic arm joints 1 and 2 by 36.58%, 38.40%, 44.68%, and 42.86%, compared with those observed in switching term adaptive law non-singular terminal sliding mode control based on a nonlinear disturbance observer (NDOANTSM) and non-singular terminal sliding mode control based on a nonlinear disturbance observer (NDONTSM). This paper provides a practical and feasible trajectory tracking control method for multi-joint robotic arms.