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 efficient algorithms for their evaluation. The theory of limit surfaces offers a purely geometric characterization of micro-scale contacts between actuator and moving object, which can be used to efficiently 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 efficiently 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 stiffness, which is of great advantage for an effective 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.