Superposition Methods for Distributed Manipulation Using Quadratic Potential Force Fields

Planar quadratic potential fields are useful for distributed manipulation because they are readily analyzable and naturally produce predictable equilibria. This generally simplifies implementation, since feedback and control may not be necessary. Traditionally, to dynamically produce moving fields for complex manipulation tasks, these fields had to be realized by highly capable, but redundant, actuator arrays. This paper suggests a new method: using simpler devices to generate basic component fields, and superposing these fields to produce desired fields with similar degrees of freedom. This approach is particularly useful for naturally produced force fields which do not allow the dynamic moving and changing of a field, but allow for superposition, and thus, can be spatially combined to produce the desired net behaviors. A vector representation of these fields is developed and applied to two problems: how to place the fields in space to span the maximum possible configuration space; and how to generate an optimal solution to generate a desired field by a superposition of a fixed field arrangement with minimal effort from each field. We experimentally validated these methods using airflow fields based on phenomenological and time superposition. Finally, we use superposition to simplify trajectory following, by blending proportions of two fields over time and by superimposing a set of component fields, each responsible for compensating a particular dynamic term