Control of a flexible robot arm

Abstract

A flexible robot arm, supported at a prismatic joint so that the length of (the relevant part of) the rod is variable, is modelled. The variation in the length of the arm is taken to be the control action. The principal results are exact controllability for the consideration of purely longitudinal vibrations (wave equation) and the existence of optimal controls in the more practically interesting case of transverse vibrations (Euler-Bernoulli beam equation). In each case, a free boundary problem is considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>