A Natural Saturating Extension of the PD-With-Desired-Gravity-Compensation Control Law for Robot Manipulators With Bounded Inputs

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper proposes a natural saturating extension of the proportional-derivative (PD) with desired gravity compensation (PD<emphasis emphasistype="boldital">d</emphasis>gc) control law for the global regulation of robot manipulators with bounded inputs. Compared with other algorithms previously proposed under the same analytical framework, it proves to be advantageous in several senses. First, it involves a single saturation function at each joint. Second, it does not need to discriminate the terms that shall be bounded, since these are simply all of them included within the only saturation involved at every joint. Experimental results show the effectiveness of the proposed scheme. As far as the authors are aware, no such type of natural saturating extension (i.e., involving only one saturation function at each joint, where all the terms of the controller are embedded) to the bounded input case had been previously proposed for the PD<emphasis emphasistype="boldital">d</emphasis>gc scheme. Furthermore, it is shown how the proposed approach may be conceived within the framework of the energy shaping plus damping injection methodology. </para>