Caging 2D bodies by 1-parameter two-fingered gripping systems

This paper is concerned with the following caging problem. One wishes to surround an object B by a multi-fingered hand such that B has some freedom to move but still cannot escape the "cage" formed by the fingers. The authors introduce a new notion of caging set, which is based on the configuration-space representation of the free motions of the hand-system with respect to B. Using stratified Morse theory, the authors show that the hand's configuration at which the cage is broken corresponds to a frictionless equilibrium grasp. This allows the authors to formulate a technique for computing the caging set of a 2-fingered hand whose opening is controlled by a single parameter. The technique generalizes to 1-parameter gripping systems having higher number of fingers.