This paper presents a method to determine whether an assembly of planar parts will stay assembled as it is pushed over a support surface. For a given pushing motion, an assembly is classified into one of three categories: (P = possible): any force necessary to preserve the assembly can be generated by the pushing contacts; (I = impossible): pushing forces cannot preserve the assembly; and (U = undecided): pushing forces may or may not be able to preserve the assembly. This classification is made based on the solution of linear constraint satisfaction problems. If the part-part and part-pusher contacts are frictionless, motions labeled P are guaranteed to preserve the assembly. The results are based on bounds on the possible support friction acting on individual parts in the face of indeterminacy in the distribution of support forces. Experimental results supporting the analysis are given

This paper presents a method to determine whether an assembly of planar parts will stay assembled as it is pushed over a support surface. For a given pushing motion, an assembly is classified into one of three categories: (P = possible) any force necessary to assure stability of the assembly can be generated by the pushing contacts; (I = impossible) stability of the assembly is impossible; and (U = undecided) pushing forces may or may not be able to stabilize the assembly. This classification is made based on the solution of linear constraint satisfaction problems. If the pushing contacts are frictionless, motions labeled P are guaranteed to preserve the assembly. The results are based on bounds on the possible support friction acting on individual parts in the face of indeterminacy in the distribution of support forces. Experimental results supporting the analysis are given.

Throwing and catching parts, similar to vibratory agitation, promises to be a powerful manipulation technique, but is analytically complicated by equations of motion involving friction and impacts. However, one can show that some simple part manipulators exhibit limit set behavior, where the parts enter a set that is invariant under the mapping that corresponds to the throwing action. We show that by analyzing limit sets directly we can design parts and their environment so that part feeding or assembling naturally emerges from the dynamics. We include experiments validating both these approaches and a discussion of future work.

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.

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.