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 flexible planar parts feeders such as massively parallel microactuator arrays or transversely vibrating (macroscopic) plates. These new automation designs promise great flexibility, speed, and dexterity—we believe they may be employed to position, 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 field induces a force and moment upon it. Over time, the part may come to rest in a dynamic equilibrium state. By chaining sequences of force fields, the equilibrium states of a part in the field may be cascaded to obtain a desired final state. The resulting strategies require 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 building the M-CHIP (Manipulation CHIP), a massively parallel array of programmable micromotion pixels. Both the M-CHIP and other microarray devices, as well as macroscopic devices such as transversely vibrating plates, may be programmed with vector fields, and their behavior predicted and controlled using our equilibrium analysis. We demonstrate lower bounds (i.e., impossibility results) on what the devices cannot do, and results on a classification of control strategies yielding design criteria by which well-behaved manipulation strategies may be developed. We provide sufficient conditions for programmable fields to induce well-behaved equilibria on every part placed on our devices. We define composition operators to build complex strategies from simple ones, and show the resulting fields are also well behaved. We discuss whether fields 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 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 trade-off between mechanical complexity and planning complexity.