A General Formulation of Under-Actuated Manipulator Systems

Abstract

This paper discusses a general formulation both in kinematics and dynamics for under-actuated manipulator systems, represented by a free- joint manipulator, a free-floating manipulator, a flexible-base manipulator and a flexible-arm ma- nipulator. We highlight the fact that a concept, originally developed for a particular system, is ap- plicable to the others as well because the dynamic equations of all four systems show common char- acteristics. Examples of such concepts are the generalized Jacobian matrix and the generalized inertia tensor which were originally developed for a free-floating manipulator, and also the reaction null-space concept, which was introduced for a free-floating and a flexible-base manipulator. We show also that the differences of the four systems are essentially due to the integrability conditions.