Kinematics and Statics of Manipulation Using the Theory of Polyhedral Convex Cones and Their Application to the Plannning of Manipulative Operations.

Abstract

A systematic approach to the kinematic and static analysis of manipulative operations performed through mechanical contacts is presented. A variety of manipulation problems, including assembly and grasps, have been treated separately in different streams of robotics research. All of the problems are treated as problems to solve a certain class of inequalities resulting from the unidirectional nature of mechanical contacts. One of the fundamental difficulties in the analysis of manipulative operations is the intractable nature of inequalities.In this paper, we establish an underpinning mathematical tool for dealing with a variety of manipulative operations 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 is applied to a variety of manipulation problems including grasping, fixturing, assembly, and admittance control.