Recursive terminal sliding mode based control of robot manipulators with a novel sliding mode disturbance observer

This paper investigates the high-precision sliding mode based tracking control of robot manipulators with uncertain dynamics and external disturbances. Different from most currently used fast nonsingular terminal sliding mode surfaces (FNTSMs) which use linear sliding mode (LSM) to avoid singularity, a new recursive terminal sliding mode surface (RTSM) is firstly constructed with a recursive structure to avoid the singularity problem in this paper. The RTSM can improve convergence precision and speed near the equilibrium point compared with FNTSMs. Then a sliding mode based controller has been designed to stabilize the closed-loop system. To cope with model uncertainties, frictions and external disturbances, a novel adaptive sliding mode disturbance observer (ASMDO) has been constructed, which can estimate lumped uncertainties and feed them to the controller to achieve disturbance-rejection control. Compared with traditional disturbance observer with asymptotic stability, the observation error of ASMDO can be driven into a sufficiently small set centered on zero within a predefined fixed time, which means fast observation speed and high observation accuracy. The upper bounds of uncertainties and their derivatives are not needed in observer design. Abundant simulations and experiments also verified the effectiveness and superior properties of the proposed scheme.