In this paper, a nonsingular fixed-time terminal sliding mode control (NFTSMC) strategy based on a fixed-time adaptive sliding mode disturbance observer (FASMDOB) is proposed for a space robot in the presence of dynamic uncertainties and external disturbance. Firstly, based on fixed-time theory, a novel FASMDOB is designed to mitigate the impacts of the lumped disturbance including dynamic uncertainties and external disturbance, improving the robustness of the control system and utilizing an adaptive technique to reduce chattering. Additionally, compared to finite-time disturbance observers (FTDOB), FASMDOB converges estimation errors to zero within a fixed time, regardless of the information about the initial states of the system. Next, a nonsingular fixed-time terminal sliding mode (NFTSM) surface is developed for the following control system design. By replacing the high-order fractional term with a piecewise function, the singularity problem in conventional terminal sliding mode control is effectively avoided. Combining FASMDOB and NFTSM surface, a FASMDOB-based NFTSMC strategy is developed, which guarantees the fixed-time convergence of the sliding mode surface and tracking errors. Notably, the proposed NFTSMC method utilizes the arctangent function to construct the reaching law, improving the performance of the control system. Lastly, based on Lyapunov theory, the fixed-time stability of the proposed control system is rigorously proven. With several comparative simulations being conducted, the feasibility and effectiveness of the proposed FASMDOB-based NFTSMC strategy are verified and highlighted.
Yang et al. (Sat,) studied this question.