Global stability without motion planning may be worse than local tracking

In this paper we study a three-dimensional (3D) US Navy crane. We present an extension to the 3D case of previous results of the authors concerning the crane´s stabilization by a simple PD controller using only motor position measurements. Two variants are studied: a PD controller using the equilibrium end-point position as a reference and the same controller where this constant reference is replaced by a flatness based trajectory finishing at the same point. The first one is proved to be globally stabilizing, whereas the second one´s stability is only proved to be local. However simulation show the superiority of the latter over the former.