Caging of rigid polytopes via dispersion control of point fingers

Abstract

This dissertation addresses the problem of object caging. The author proposes approaches for designing “cages” by means of imposing simple constraints to control the manipulator. Each designed cage is represented in the form of a finger placement relative to the object and its error tolerance. The error tolerance determines how much the fingers may deform based on a measure. The proposed approaches are based on decomposing the workspace into convex subsets, then constructing a roadmap to identify possible cages for a given system. After a roadmap is constructed, it is possible to query if a finger placement forms a cage or enumerate all the cages efficiently. The approaches can be extended to handle constrained fingers and/or uncertainty in the system.