A Theory of Manipulation and Control for Microfabricated Actuator Arrays

This paper investigates manipulation tasks with arrays of microelectromechanical structures (MEMS). We develop a model for the mechanics of microactuators and a theory of sensorless, parallel manipulation, and we describe e cient algorithms for their evaluation. The theory of limit surfaces o ers a purely geometric characterization of micro-scale contacts between actuator and moving object, which can be used to e ciently predict the motion of the object on an actuator array. We develop a theory of sensorless manipulation with microactuator arrays. It is shown how simple actuator control strategies can be used to uniquely align a part up to symmetry. These manipulation strategies can be computed e ciently and do not require 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 low-temperature SCREAM process. They exhibit high aspect ratios and high vertical sti ness, which is of great advantage for an e ective implementation of our theory. Calculations show that arrays of these actuators can generate forces that are strong enough to levitate and move e.g. a piece of paper.