Kinematics and Statics of Manipulation Using the Theory of Polyhedral Convex Cones

Abstract

A new approach to the kinematic and static analysis of ma nipulative tasks performed through mechanical contacts is presented. A variety of manipulation problems, including as sembly and grasps, have been treated separately in robotics research. All of the problems are treated as ways to solve a certain class of inequalities resulting from the unidirectional nature of mechanical contacts. One of the fundamental diffi culties in the analysis of manipulative tasks is the intractable nature of inequalities. In this article, we establish an underpinning mathematical tool for dealing with a variety of manipulative tasks that are governed by unidirectional constraints. First, we introduce a coherent representation for formulating various manipulation problems. Second, we develop several procedures based on the theory of polyhedral convex cones to solve these problems in a systematic and straightforward manner. The method is then implemented on a computer and applied to a variety of manipulation problems, including grasping, fixturing, and hybrid position/force control.