A globally stable PD-NP-I<sup>NP-D</sup> regulator for robot manipulators

Abstract

This paper deals with the position control of robot manipulators with uncertain and varying-time payload. Proposed is a simple class of robot regulators consisting of a linear PD feedback plus a bounded nonlinear term of position errors plus an integral action driven by an NP-D controller, where the nonlinear terms are shaped by a continuous bounded nonlinear function of position errors. By using Lyapunov's direct method and LaSalle's invariance principle, the simple explicit conditions on the regulator gains to ensure global asymptotic stability are provided. The theoretical analysis and simulation results show that: an attractive feature of our scheme is that PD-NP-I <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NP-D</sup> controller has the faster convergence, better flexibility and stronger robustness with respect to uncertain and varying-time payload, and then the optimum response can be achieved by a set of control parameters in the whole control domain, even under the case that the payload is changed abruptly.