A stable self-organizing fuzzy PD control for robot manipulators

In this paper we propose a Self-Organizing Fuzzy Proportional Derivative (SOF-PD) tracking controller for robot manipulators, which exploits the simplicity and robustness of the simple PD control and enhances its benefits. This proposed controller has a gain-scheduling structure, in which, based on the position error, a SOF system performs the gains tuning of a simple PD controller in the feedback loop. The SOF system is a fuzzy system in which the inference rules are continuously updated according to two performance index tables designed for adjusting – in a separated way – the P and D gains. The tuning of the gains is performed independently for each joint. By using the Lyapunov theory, it is shown that, for an arbitrary bounded desired trajectory, uniform ultimate boundedness of the tracking errors is guaranteed by selecting suitable maximum and minimum allowed PD gain values. This stability result can be generalized to others varying gains schemes for PD tracking control, in which the gains are bounded functions of the tracking errors. Experimental results in a two degrees of freedom robotic arm show the superiority of the proposed approach over the classic PD control, in terms of the position errors.