On some structural properties of general manipulation systems

This chapter analyses the geometric and structural characteristics involved in the control of rather general manipulation systems, consisting of multiple cooperating linkages, interac- ting with a reference member of the mechanism (the “object”) by means of contacts on any available part of their links. Object grasp and manipulation by the human hand is taken as a paradigmatic example for this class of manipulators, while classical mechanisms (including closed kinematic chains) can be shown to fit easily in this framework. We present an analytical formulation of the kinematics and dynamics of such systems. Moreover, we report on some recent results on the analysis and control of these mechanisms, based on a geometric analysis of a local approximation of system dynamics. Notwithstanding the local nature of the latter study, it provides a very insightful view of the problem, along with control techniques that achieve interesting performance.