Part Orientation with One or Two Stable

Programmable vector elds are an abstraction to represent a new class of devices for distributed, non-prehensile manipulation for applications in parts feeding, sorting, positioning, and assembly. Unlike robot grippers, conveyor belts, or vibratory bowl feeders, these devices generate force vector elds in which the parts move until they may reach a stable equilibrium pose. Recent research in the theory of programmable force elds has yielded open-loop strategies to uniquely position, orient, and sort parts. These strategies typically consist of several elds that have to be employed in sequence to achieve a desired nal pose. The length of the sequence depends on the complexity of the part. In this paper, we show that unique part poses can be achieved with just one eld. First, we exhibit a single eld that positions and orients any laminar part (with the exception of certain symmetric parts) into two stable equilibrium poses. Then we show that for any laminar part there exists a eld in which the part reaches a unique stable equilibrium pose (again with the exception of symmetric parts). Besides giving an optimal upper bound for unique parts positioning and orientation, our work gives further evidence that programmable vector elds are a powerful tool for parts manipulation. Our second result also leads to the design of \universal parts feeders", proving an earlier conjecture about their existence. We argue that universal parts feeders are relatively easy to build, and we report on extensive simulation results which indicate that these devices may work very well in practice. We believe that the results in this paper could be the basis for a new generation of eecient, open-loop, parallel parts feeders.