TABLE OF CONTENTS When we began working in MEMS in 1991, it was not immediately clear what fundamental algorithmic or computational problems arose in this new area. Even after obtaining our first results on the theory of programmable force vector fields in 1993 [22], the received view in the community was that the chief computational issues in MEMS arose in (1) design, and (2) simulation. Indeed, it is these problems that motivated our initial efforts (see, e.g., [5, 6, 8, 7]): in 1990, Ralph Merkle of Xerox PARC and Kris Pister of Berkeley urged us to apply our results on the design and simulation [33] of snap fasteners to MEMS [51].
At that time, work on force fields for manipulation had been limited to the artificial potential fields first developed by Khatib, Koditschek, and Brooks. [3] While potential fields have been widely used in robot control [42, 43, 56, 53], micro-actuator arrays present us with the ability to explicitly program the applied force at every point in a vector field. Whereas previous work had developed control strategies with artificial potential fields, our fields are non-artificial (i.e., physical). Artificial potential fields require a tight feedback loop, in which, at each clock tick, the robot senses its state and looks up a control (i.e., a vector) using a state-indexed navigation function (i.e., a vector field). In contrast, physical potential fields employ no sensing, and the motion of the manipulated object evolves open-loop (for example, like a particle...
