A Predefined-Time Nonsingular Terminal Sliding Mode Control for Multispace Transport Robot System with Varying Power Reaching Law

This article proposes a predefined-time nonsingular terminal sliding mode controller (PNTSMC) for multispace transport robot system, which is suitable for complex on-orbit assembly tasks. First, a composite Lyapunov function predefined-time stability criterion (CLF-PSC) is proposed to simplify the stability analysis and controller design. Comparing with traditional predefined-time stability criterion, the CLF-PSC offers a simpler form. More importantly, combining with chain rule of the composite Lyapunov function, the CLF-PSC can be composed and decomposed flexibly, which makes it more convenient for application. Second, a unified framework for nonsingular terminal sliding mode surfaces is proposed. By integrating the CLF-PSC with the framework, a general method for predefined-time nonsingular terminal sliding mode surface (PNTSMF) design is presented, which can effectively avoid the singularity problem without violating strict predefined-time stability. In addition, two PNTSMFs are proposed as specific examples. In addition, a predefined-time reaching law with varying power is designed based on the CLF-PSC. Due to that the power can change with the sliding variable, the reaching law can weaken chattering, reduce control input, and strictly guarantee predefined-time convergence. Third, combining the PNTSMF with the reaching law, a predefined-time disturbance observer and a distributed cooperative PNTSMC are designed for the system, which exhibit excellent performance of predefined-time convergence, high precision, chattering suppression, and robustness against disturbances. Finally, simulations are provided to verify the performance of the proposed PNTSMF and PNTSMC.