According to a given performance criteria, perfect tracking is defined as the performance of zero tracking error in finite time. It is evident that robotic systems, in particular those that carry out compliant task, can benefit from this performance since perfect tracking of contact forces endows one or many constrained robot manipulators to interact dexterously with the environment. In this article, a dynamical terminal sliding mode controller that guarantees tracking in finite-time of position and force errors is proposed. The controller renders a dynamic sliding mode for all time and since the equilibrium of the dynamic sliding surface is driven by terminal attractors in the position and force controlled subspaces, robust finite-time convergence for both tracking errors arises. The controller is continuous; thus chattering is not an issue and the sliding mode condition as well the invariance property are explicitly verified. Surprisingly, the structure of the controller is similar with respect to the infinite-time tracking case, i.e., the asymptotic stability case, and the advantage becomes more evident because terminal stability properties are obtained with the same Lyapunov function of the asymptotic stability case by using more elaborate error manifolds instead of a more complicated control structure. A simulation study shows the expected perfect tracking and a discussion is presented.
Parra-Vega, V., Rodriguez-Angeles, A., & Hirzinger, G. (2001). Perfect position/force tracking of robots with dynamical terminal sliding mode control. Journal of Robotic Systems, 18(9), 517-532. https://doi.org/10.1002/rob.1041