Programmable force fields for distributed manipulation, with applications to MEMS actuator arrays and vibratory parts feeders

Programmable force vector fields can be used to control a variety of flexib le planar parts feeders such as massively parallel microactuator arrays or transversely vibrating (macroscopic)plates. These new automation designs pr omise great flexibility, speed and dexterity-we believe they may be employe d to position, orient, singulate, sort, feed, and assemble parts. However s ince they have only recently been invented programming and controlling them for manipulation tasks is challenging. When apart 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 seq uences of force fields, the equilibrium states of a part in the field may b e cascaded to obtain a desired final state. The resulting strategies requir e no sensing, and enjoy efficient planning algorithms This paper begins by describing new experimental devices that can implement programmable force fields. In particular; we describe our progress in buil ding the M-CHIP (Manipulation CHIP), a massively parallel array of programm able micromotion pixels. Both the M-CHIP and other microarray devices, as w ell as macroscopic devices such as transversely vibrating plates, may be pr ogrammed with vector fields, and their behavior predicted and controlled us ing our equilibrium analysis. We demonstrate lower bounds (i.e., impossibil ity results) on what the devices cannot do, and results on a classification of control strategies yielding design criteria by which well-behaved manip ulation strategies may be developed. We provide sufficient conditions for p rogrammable fields to induce well-behaved equilibria on every part placed o n our devices. We define composition operators to build complex strategies from simple ones, and show the resulting fields are also well behaved We di scuss whether fields outside this class can be useful and free of pathology . Using these teals, we describe new manipulation algorithms. In particular w e improve existing planning algorithms by a quadratic factor; and the plan length by a linear factor: Using our new and improved strategies, we show h ow to simultaneously orient and pose any part, without sensing,from an arbi trary initial configuration. Wk relax earlier dynamic and mechanical assump tions 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, bur with a significant increase in planning c omplexity and some sacrifice in completeness guarantees. We discuss the tra de-off between mechanical complexity and planning complexity.