A General Formulation of Under-Actuated Manipulator Systems

This paper discusses a general formulation both in kinematics and dynamics for under-actuated manipulator systems, represented by a freejoint manipulator, a free-floating manipulator, a flexible-base manipulator and a flexible-arm manipulator. We highlight the fact that a concept, originally developed for a particular system, is applicable to the others as well because the dynamic equations of all four systems show common characteristics. 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.