Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function

David Cruz-Ortiz, Isaac Chairez, Alexander Poznyak

Research output: Contribution to journalArticlepeer-review


This study introduces a design of robust finite-time controllers that aims to solve the trajectory tracking of robot manipulators with full-state constraints. The control design is based on the construction of a distributed state constraint non-singular terminal sliding mode (CNTSM). The CNTSM design includes the gain self-adapting tuning method, which can ensure finite-time convergence to the sliding surface aside from the states to its corresponding reference trajectories. The implementation of the time-varying gain ensures the fulfillment of the accurate tracking for the references while the position and velocity constraints are satisfied permanently. A barrier Lyapunov function is proposed to develop the finite-time stability analysis of the designed controllers. The CNTSM realization uses the tracking error as well as its estimated derivative, which is calculated using a variant of adaptive super-twisting algorithm operating as robust differentiator. The proposed CNTSM is numerically evaluated on a two-link RM with uncertain inertia and Coriolis matrices. Simulation and experimental results evidence the efficiency of the CNTSM controller demonstrating a better tracking performance while the full-state constraints are satisfied in counterpart with the classical non-singular terminal sliding mode which is not able to keep such restrictions.

Original languageEnglish
JournalISA Transactions
StateAccepted/In press - 2021


  • Barrier Lyapunov function
  • Robotic manipulator
  • State constraints and state dependent adaptive gain
  • Terminal sliding mode control


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