Programmable vector fields can be used to control a variety of flexible planar parts feeders. 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. We demonstrate lower bounds on what the devices cannot do, and results on a classification of control strategies. We suggest 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, and improve existing planning algorithms by a quadratic factor, and the plan-length by a linear factor. 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. We discuss the trade-off between mechanical complexity and planning complexity.

This paper investigates manipulation tasks with arrays of microelectromechanical structures (MEMS). We develop a geometric model for the mechanics of microactuators and a theory of sensorless, parallel manipulation, and we describe efficient algorithms for their evaluation. The theory of limit surfaces offers a purely geometric characterization of microscale contacts between actuator and moving object, which can be used to efficiently predict the motion of the object on an actuator array. It is shown how simple actuator control strategies can be used to uniquely align a part up to symmetry without sensor feedback. This theory is applicable to a wide range of microactuator arrays. Our actuators are oscillating structures of single-crystal silicon fabricated in a IC-compatible process. Calculations show that these actuators are strong enough to levitate and move, for example, a piece of paper.>