Stably Supported Rotations of a Planar Polygon with Two Frictionless
Contacts
Tamara Abell and Michael Erdmann Proceedings of the 1995 IEEE/RSJ International Conference on
Intelligent Robots and System, Pittsburgh, Pennsylvania,
pp. 411-418.
Abstract
In this paper, we explore the use of stable support in robotic
manipulation. Stable support describes any contact configuration which
balances a known applied force and is stable with respect to small
perturbations in the handled object's pose. Specifically, we address the
problem of manipulating a planar polygonal object in a fixed gravitational
field, stably supported by two frictionless contacts. Representing each
contact configuration as a force focus point defined by the
intersection of the lines of action of the contact forces, we derive geometric
regions of permissible force focus points for contacts on each pair of polygon
edges. Each permissible force focus point maps to a unique configuration of
the object and contacts in stable equilibrium. In turn, paths in the space of
permissible force focus points map to real space motions of the contact points
which induce quasi-static rotations of the object. We also present two graph
search based strategies for planning hand-offs between pairs of contacts, thus
enabling larger rotations than can be executed by a single contact pair.
Finally, we describe an implementation of one of these planners