Stable transport of assemblies: Pushing stacked parts

This paper presents a method to determine stable pushing motions for a planar stack of polygonal parts. The approach consists of solving a series of subproblems where each part in the stack is pushing the parts ahead of it The solutions to these subproblems are sets of stable motions, and their intersection is the set of stable motions for the entire stack. The motion of multiple parts depends on the exact locations of the centers of mass and the relative masses of the parts. If either or both of these is unknown, it is still possible to calculate a conservative set of motions guaranteed to be stable by using a center of mass uncertainty region. Local-local controllability is also analyzed for single parts and stacks of parts with uncertain centers of mass.