Skip to Main Content
This work 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 subproblem an 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 stocks of parts with uncertain centers of mass. Once parts have been brought together in an automated assembly sequence, they typically must be repositioned to complete fastening or welding operations. This can be done with powerful robots capable of grasping and carrying the assembly and may involve a unique fixture to maintain the assembly during transport. A cheaper and more flexible alternative is to use a less powerful robot that can push the assembly along a horizontal surface without the aid of fixtures. This work presents a graphical method that produces conservative bounds on the pushing motions that guarantee the stability of a linear assembly (i.e., a stock of parts) during the push. The main application is in motion planning for assembly sequencing but the results could also he useful, for example, for mobile robots pushing multiple boxes in a warehouse. The method can be made robust to uncertainty in The mass properties of the parts, such as boxes with unknown contents. It is limited to linear stacks of parts where each part pushes no more than one other part In future work, we plan to devise a method to compute stable pushing motions for arbitrary assemblies of parts.