PD control with desired gravity compensation of robotic manipulators: a review
International Journal of Robotics Research
Control Theory of Nonlinear Mechanical Systems
Control Theory of Nonlinear Mechanical Systems
Robot Dynamics and Control
Stable fuzzy self-tuning PID control of robot manipulators
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
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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.