Feedback linearization approach to distributed feedback manipulation

This report formulates the problem of a distributed planar manipulation realized by shaping a spatially continuous force field. It also suggests a control strategy based on feedback linearization. Force fields derived from potential fields are considered. The potentials are ``shaped'' by a set of spatially discrete ``actuators`` such as electrodes in the case of dielectrophoresis, electromagnets in the case of planar magnetic manipulators, or linear piezoelectric actuators in the case of deformable flat surfaces. The actuators form arrays. Distinguished feature of such force fields is that the contribution from an individual actuator usually affects the situation in the neighboring zones too, but usually not in too remote zones. As an idealization, the spatial domain is considered unbounded, which enables examination of asymptotic behavior of the manipulation scheme.