Proposing a Novel Fixed-Time Non-singular Terminal Sliding Mode Surface for Motion Tracking Control of Robot Manipulators

This article proposes a new fixed-time non-singular terminal sliding mode (FxNTSM) surface for synthesizing the tracking control algorithm of robotic manipulators. The new sliding mode surface has no singularity, improved convergence speed. It contains dynamic coefficients that can be adapted to control errors that drive the system states quickly converge to the equilibrium point within bounded convergence time regardless of initial system states. The settling time of the sliding motion phase is fully calculated in both cases, including the initial state of the system is far/near the equilibrium stability point. A novel finite-time NTSMC (FnNTSMC) is formed from a combination of the proposed sliding surface and auxiliary reaching control law (ARCL). Due to the advantages of the proposed sliding surface and mentioned reaching control law, therefore, the novel finite-time control system provides superior characteristics such as high tracking accuracy, improved fast convergence, and robustness to cope with the lumped uncertainties. The fixed time/finite-time stability and convergence of the control method are validated by using the Lyapunov criteria. Computer simulations applied to a 3-DOF robotic manipulator are presented to verify the effectiveness and outstanding properties of the proposed control method.