Distributed non-singular terminal sliding-mode control for a synchronized motion of a Cartesian and a robotic manipulator

This study presents the design of a decentralized terminal sliding-mode (TSM) controller to solve the trajectory tracking problem of a composite robotic device made up of two-dimensional Cartesian and multiple-degree-of-freedom robotic manipulators. The dynamics of the proposed composite robotic device satisfy a standard Lagrangian structure affected by the modeling uncertainties related to the internal interconnection between joint motion and external perturbations. The set of adaptive gains included in the controller implies enforcing the finite-time convergence of the tracking error (TE) to an invariant region considering the state bounds describing the restricted motion of all joints. The application of the barrier Lyapunov stability analysis theory addresses the previously known state constraints for both devices, considering the inclusion of a time-varying gain that guarantees the ultimate boundedness of the TE even with the presence of the effect of external perturbations. The suggested controller was evaluated using a virtual representation of the composite robotic device, which showed better tracking performance (while the restrictions were satisfied) than the performances obtained with the traditional linear state feedback and first-order sliding-mode controllers with restrictions. Analyzing the mean square error and its integral confirmed the benefits of using the adaptive barrier control to satisfy the TSM form.