A Globally Stable PD Controller for Bilateral Teleoperators

In a recent scheme, with delayed derivative action [Lee and Spong, IEEE Trans. Robot., 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 L_infin-stable maps from velocity to force. 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.