A class of nonlinear PID global regulators for robot manipulators

In this paper we propose a class of nonlinear PID global regulators for manipulators which do not include their dynamics in the central law. The structure of this class of global regulators is based on a linear PD feedback, plus an integral action driven by a nonlinear function of the joint position error, and the addition of the gradient of a C¹ artificial potential function satisfying some typical features required by the energy shaping methodology. By using Lyapunov´s direct method and LaSalle´s invariance principle we provide simple explicit conditions on the regulators gains to ensure global asymptotic stability