Algorithms for sensorless manipulation using a vibrating surface

We describe a programmable apparatus that uses a vibrating surface for sens orless, nonprehensile manipulation, where parts are systematically position ed and oriented without sensor feedback or force closure. The idea is to ge nerate and change the dynamic modes of a vibrating surface. Depending on th e node shapes of the surface, the position and orientation of the parts can be predicted and constrained. The vibrating surface creates a two-dimensio nal force vector field. By chaining together sequences of force fields, the equilibrium states of a part in the field can be successively reduced to o btain a desired final state. We describe efficient polynomial-time algorith ms that generate sequences of force fields for sensorless positioning and o rienting of planar parts, and we show that these strategies are complete. F inally we consider parts feeders that can only implement a finite set of fo rce fields. We show how to plan and execute strategies for these devices. W e give numerical examples and experiments, and discuss tradeoffs between me chanical complexity and planning complexity.