A Globally Stable PD Controller for Bilateral Teleoperators

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In a recent scheme, with delayed derivative action [Lee and Spong, <emphasis emphasistype="italic">IEEE Trans. Robot.</emphasis>, vol. 22, no. 2, pp. 269--281, Apr. 2006], it is claimed that a simple proportional derivative (PD) scheme yields a stable operation. Unfortunately, the stability proof hinges upon unverifiable assumptions on the human and contact environment operators, namely, that they define <formula formulatype="inline"><tex>${\cal L}_\infty$</tex></formula>--stable maps <emphasis emphasistype="italic">from velocity to force</emphasis>. In this short paper, we prove that it is indeed possible to achieve stable behavior with simple PD-like schemes---even without the delayed derivative action---under the classical assumption of passivity of the terminal operators. </para>