Multifinger Caging Using Dispersion Constraints

An object is caged by a formation of fingers when it is blocked by the fingers from moving arbitrarily far away. Although some objects such as those with opposing concave sections can be caged by only two fingers, many other objects require at least three. Rectangles and 3-D convex objects without a supporting plane, for example, require at least four. This paper focuses on multifinger squeezing caging in which the positions of fingers obey dispersion constraints. In particular, we present an algorithm for computing all initial finger placements at which the object can be caged in an aforementioned manner. An implementation of the proposed algorithm is described along with implementation results both in 2-D and 3-D.