Paper abstract

 Title:  A General Stability Test for Multiply Contacted Objects in 
          a Potential Field, with Example Applications to Planar Objects Under
          Gravity
 Authors:  Richard Mason, Elon Rimon, and Joel Burdick

 In:  (submitted)  IEEE Transactions on Robotics and Automation , December 1996.

ABSTRACT:

This paper develops a general test for determining the stability of an object, B, in frictionless contact with bodies A_1, ... ,A_k, in the presence of gravity, or any other force arising from a potential field. For a small number of contacts, the stability of B depends on the surface normals and surface curvatures of the contacting bodies. For a sufficiently large number of contacts, the surface normals alone determine the stability of B. In addition, the stability test includes as a parameter the location of B's center of mass. We use this feature of the test to study in detail the stability of planar objects in the presence of gravity. Using the stability test, we find the set of center of mass locations which keep B in stable equilibrium for a given contact geometry. In a companion paper, we present an extension of this work to three-dimensional objects. This extension has applications in areas such as grasping, fixturing, and robot locomotion.