A Uniform Bound for the Jacobian of the Gravitational Force Vector for a Class of Robot Manipulators

Abstract

In this paper, we study the boundedness of the Jacobian of the gravitational force vector of serial link robot manipulators with respect to the generalized coordinate vector. The uniform bound of this matrix plays an important role in the stability analysis and design of many control systems. In order to insure the existence of a uniform bound, it is typically assumed that manipulators under consideration have only revolute joints. We therefore propose a larger class of manipulators, referred to as class BD manipulators, for which a uniform bound exists. This bound can easily be computed using basic link parameters including the link masses, the Denavit-Hartenberg link parameters, and the link center of mass locations.