Stably supported rotations of a planar polygon with two frictionless contacts

Explores 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, the authors 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, the authors 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. The authors 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, the authors describe an implementation of one of these planners.