Backstepping funnel control for prescribed performance of robotic manipulators with unknown dead zone

In this paper, a backstepping funnel control (BFC) is proposed to achieve a prescribed tracking performance for robotic manipulator systems with unknown input dead zone. According to the differential mean value theorem, the dead zone inverse compensation approach is avoided by representing the dead zone as a linear time-varying system. Without constructing the complex barrier Lyapunov function, a new constraint variable is employed and the tracking error will be forced to fall into prescribe boundaries. A simple sigmoid neural network is utilized to approximate the system uncertainties and the calculation of derivative terms generated by the recursive steps of traditional backstepping control can be avoided. With the proposed scheme, no prior knowledge is required on the bound of input dead zone, and the convergence of the position tracking error is guaranteed via the Lyapunov synthesis. Comparative simulation examples are given to illustrate the effectiveness of the proposed method.