Algorithms for Sensorless Manipulation Using a Vibrating Surface
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We describe a programmable apparatus that uses a vibrating surface for sensorless, nonprehensile manipulation, where parts are systematically positioned and oriented without sensor feedback or force closure. The idea is to generate and change the dynamic modes of a vibrating surface. Depending on the node shapes of the surface, the position and orientation of the parts can be predicted and constrained. The vibrating surface creates a two-dimensional force vector field. By chaining together sequences of force fields, the equilibrium states of a part in the field can be successively reduced to obtain a desired final state. We describe efficient polynomial-time algorithms that generate sequences of force fields for sensorless positioning and orienting of planar parts, and we show that these strategies are complete. Finally we consider parts feeders that can only implement a finite set of force fields. We show how to plan and execute strategies for these devices. We give numerical examples and experiments. and discuss tradeoffs between mechanical complexity and planning complexity.
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