What programmable vector fields can (and cannot) do: force field algorithms for MEMS and vibratory plate parts feeders

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.