In this paper we present a low dimensional adaptive neural network controller for robot manipulators with fast convergence of tracking error. Its novelty lies in the low dimensional network, smooth control input and very fast convergence that reduce the computational cost that face the problem of over parameterization. The control strategy is based on a second order sliding surface which drives the controller and the online computation of weights with a chattering-free control output. Furthermore, a time base generator induces wellposed finite time convergence of tracking errors for any initial condition. We validate our approach including experimental results obtained in a planar 2 dgf manipulator.
Owing to the fact that desired tasks are usually defined in operational coordinates, inverse and direct kinematics must be computed to obtain joint coordinates and Cartesian coordinates, respectively. However, in order to avoid the ill-posed nature of the inverse kinematics, Cartesian controllers have been proposed. Considering that Cartesian controllers are based on the assumption that the Jacobian is well known, an uncertain Jacobian will produce a non-exact localization of the end-effector. In this paper, we present an alternative approach to solve the problem of Cartesian tracking for free and constrained motion subject to Jacobian uncertainty. These Cartesian schemes are based on sliding PID controllers where the Cartesian errors are mapped into joint errors without any knowledge of robot dynamics. Sufficient conditions for feedback gains and stability properties of the estimate inverse Jacobian are presented to guarantee stability. Experimental results are provided to visualize the real-time stability properties of the Cartesian proposed schemes.
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