What Programmable Vector Fields Can ( and Cannot ) Do : Force Field Algorithms for MEMS and Vibratory Plate Parts

Programmable vector elds can be used to control a variety of exible planar parts feeders. These devices can exploit exotic actuation technologies such as arrayed, massively-parallel microfabricated motion pixels or transversely vibrating (macroscopic) plates. These new automation designs promise great exibil-ity, speed, and dexterity|we believe they may be employed to orient, singulate, sort, feed, and assemble parts. However, since they have only recently been invented , programming and controlling them for manipulation tasks is challenging. When a part is placed on our devices, the programmed vector eld induces a force and moment upon it. Over time, the part may come to rest in a dynamic equilibrium state. We demonstrate lower bounds (i.e., impossibility results) on what the devices cannot do, and results on a classiication of control strategies yielding design criteria by which well-behaved manipulation strategies may be developed. We suggest suf-cient conditions for programmable elds to induce well-behaved equilibria on every part placed on our devices. We deene composition operators to build complex strategies from simple ones, and show the resulting elds are also well-behaved. We discuss whether elds outside this class can be useful and free of pathology. Using these tools, we describe new manipulation algorithms. 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 connguration. We relax earlier dynamic and mechanical assumptions to obtain more robust and exible strategies. Finally, we consider parts feeders that can only implement a very limited \vocabulary" of vector elds. We discuss the tradeoo between mechanical complexity and planning complexity. (a) (c) (b) Figure 1: Sensorless sorting using force vector elds: Parts of diierent sizes are rst centered and subsequently separated depending on their size.