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

TLDR

Manipulation problems such as assembly and grasping have been studied separately, each framed as solving inequalities from unidirectional mechanical contacts, yet the inherent intractability of these inequalities remains a major challenge. This work introduces a unified kinematic and static analysis framework for manipulative tasks performed through mechanical contacts. The authors formulate manipulation problems using a coherent representation and develop systematic procedures based on polyhedral convex cone theory, implemented computationally for tasks like grasping, fixturing, and hybrid position/force control. The computational implementation successfully solves these diverse manipulation problems, illustrating the method’s effectiveness and general applicability.

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.