Chapter 1 on Some Structural Properties of General Manipulation Systems 1.1 Introduction

Abstract

This chapter analyses the geometric and structural characteristics involved in the control of rather general manipulation systems, consisting of multiple cooperating linkages, interacting 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 t 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. In the past three decades, research on the geometric approach to dynamic systems theory and control has achieved important results, which made that approach a powerful and thorough tool in the analysis and synthesis of linear systems ((1], 17]). Among the successes of the geometric approach, it must be counted the contribution to the development of a nonlinear systems theory, stemming from and generalizing on deeply geometric ideas ((6]). On the other hand, in the same years, mechanical systems used in industry and developed in research labs also evolved quite quickly. Robotics is one notable case of such evolution. In response to the stepping{up of requirements on the control of mechanical systems engendered by the tightening of performance speciications, the increase in number of degrees{of{ freedom, and the introduction of interacting robotic limbs (as e.g. in pairs of cooperating

Cite this paper

@inproceedings{Bicchi1997Chapter1O, title={Chapter 1 on Some Structural Properties of General Manipulation Systems 1.1 Introduction}, author={Antonio Bicchi and Domenico Prattichizzo}, year={1997} }