Hierarchical analysis for determining disconnectedness in a contact formation

Stratification of compliant control requires that we know whether, for any contact configurations under the same contact formation, them exists a CF-compliant motion connecting them. This motivates the question of whether a given CF has disjoint regions of configurations. It is the geometric features of the contacting objects that may cause disjoint regions of contact configurations under the same topological contact formation. In this paper we further analyze such geometric features between two contacting polygons. This paper presents a vocabulary and a hierarchical method that we have found useful in analyzing CFs to determine the connectedness of their regions of CF-compliant configurations. The hierarchical analysis method simplifies the detection of disjoint regions in a CF through a series of tests of increasing complexity on the geometric relations between the two objects in contact under the CF