Adaptive Approximation Sliding-Mode Control of an Uncertain Continuum Robot with Input Nonlinearities and Disturbances

This paper develops an adaptive nonsingular fast terminal sliding-mode control (ANFTSMC) scheme for the continuum robot subjected to uncertain dynamics, external disturbances, and input nonlinearities (e.g., actuator deadzones/faults). Concretely, a function approximation technique (FAT) is utilized to estimate unknown robot dynamics and actuator deadzones/faults online. Furthermore, a disturbance observer (DO) is devised to make up for unknown external disturbances. Then, an ANFTSMC scheme combined with FAT and DO is developed, to expedite the restoration of the stability for the continuum robot. The proposed ANFTSMC not only can retain the benefits of traditional terminal sliding-mode control (TSMC), containing easy enforcement, quick response, and robustness to uncertainties but also dispose of the latent singularity for traditional faster TSMC designs. Afterward, the simulation results show that the proposed controller can effectively improve the trajectory tracking accuracy of the continuum robot, and the tracking root-mean-square errors are 0.0115 and 0.0128 rad. Finally, the effectiveness of ANFTSMC scheme is validated by experiments.