Locally controllable manipulation by stable pushing

When a polygonal object is pushed with line contact along an edge, the push is called stable if the object remains fixed to the pusher. The object is small-time locally controllable by stable pushing if, by switching among pushing edges, it can be pushed to follow any path arbitrarily closely. Because the pushes are stable by the frictional mechanics, pushing plans can be executed without position feedback of the object. In this paper we derive a necessary and sufficient condition for a polygon to be small-time locally controllable by stable pushing: the pushing friction coefficient must be nonzero and the set of feasible pure forces (forces applied through a polygon edge and passing through the center of friction) must positively span the plane. We interpret this condition in terms of the polygon shape, the location of the center of friction, and the pushing friction coefficient, allowing us to characterize classes of polygons with this fundamental “maneuverability” property.