A Theory of Manipulation and Controlfor

This paper investigates manipulation tasks with arrays of mi-croelectromechanical structures (MEMS). We develop a model for the mechanics of microactuators and a theory of sensorless, parallel manipulation, and we describe eecient algorithms for their evaluation. The theory of limit surfaces ooers a purely geometric characterization of micro-scale contacts between actuator and moving object, which can be used to eeciently predict the motion of the object on an actuator array. We develop a theory of sensor-less 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 eeciently 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 stiiness, which is of great advantage for an eeective 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.