An estimate of the Domain of attraction for the PID regulator of manipulators

This paper deals with the problem of estimation of the domain of attraction for the linear Proportional Integral Derivative (PID) regulator of robot manipulators. We first recall a simple semiglobal asymptotic stability analysis, which is one of the simplest found in the literature; then, based on such analysis we obtain an estimate of the domain of attraction in terms of the PID controller gains, allowing to know, in an explicit way, the radius of such an estimate of the region of attraction. To the best of the authors' knowledge, for the classical linear PID regulator of robot manipulators, this is the first paper that explicitly parameterizes the range of attraction of the goal position in terms of the proportional, derivative and integral gain matrices. As a consequence, we also propose a tuning procedure which allows to ensure asymptotic stability for a given initial conditions. Finally, as a way of testing this tuning procedure in a real application, we accomplish some experiments in a direct-drive robot arm.