An asymptotically stable joint PD controller for robot arms with flexible links under gravity

Abstract

The authors present a simple joint PD (proportional plus derivative) control scheme for robots with flexible links which guarantees global asymptotic stability of a desired constant arm configuration in the presence of gravity. A structural assumption about link elasticity is required and a mild condition on the proportional gain is derived. The proof of global asymptotic instability goes through a classical Lyapunov argument. The control law does not require any feedback from the deflection variables and is composed of a linear term plus a nominal feedforward term.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>