Open-loop orientability of objects on actuator arrays

An actuator array is a form of distributed manipulation where an object being transported and manipulated rests on a large number of supporting actuators. On a discrete array employing an open-loop field, some size and shape objects may have unstable equilibria due to this discreteness. The functional relationship between object dimensions relative to array spacing and rotational stability is examined, and a map of this function is generated. The geometry behind this relationship is also examined, and analytical expressions for the boundaries between stable and unstable regions in the map are derived