New and Improved Manipulation Algorithms for MEMS Arrays and Vibratory PartsFeeders: What Programmable Vector Fields Can (and Cannot) Do --- Part II

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This paper explores how to use programmable vector fields to control flexible planar parts feeders. For a description of these devices and their actuation technology, see our companion paper, Part~I~\cite{BohringerDonaldMacDonald96b}\ifDRAFT{}\else{, also submitted to ICRA}\fi . When a part is placed on our devices, the programmed vector field induces a force and moment upon it. Over time, the part may come to rest in a dynamic equilibrium state. By chaining together sequences of vector fields, the equilibria may be cascaded to obtain a desired final state. By analyzing and constraining the equilibria of programmable vector fields, we can generate and execute plans to orient and sort parts. These plans require no sensing. This paper describes new manipulation algorithms using the tools developed in Part~I~\cite{BohringerDonaldMacDonald96b}. In particular, we improve existing planning algorithms by a quadratic factor, and the plan-length by a linear factor. Using our new and improved strategies, we show how to simultaneously orient and pose any part, without sensing, from an arbitrary initial configuration. We relax earlier dynamic and mechanical assumptions to obtain more robust and flexible strategies. Finally, we consider parts feeders that can only implement a very limited "vocabulary" of vector fields (as opposed to the pixel-wise programmability assumed above). We show how to plan and execute parts-posing and orienting strategies for these devices, but with a significant increase in planning complexity and some sacrifice in completeness guarantees. We discuss the tradeoff between mechanical complexity and planning complexity.

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computer science; technical report


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