Computing Cages for Capturing 2D Bodies

Dr. Elon Rimon, Mechanical Engineering, Technion University, Haifa, Israel

This talk is concerned with the following *caging problem*. We wish 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. There are many applications to this problem, such as blind grasping by robot hands and automatic fixturing during part machining.

We 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, we show that the hand's configuration at which the cage is broken corresponds to a frictionless equilibrium grasp. This allows us 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.

Finally, we present a graphical technique for rendering the caging set, and we show cage computation results based on data collected by a vision system.

(This paper was presented at the 1996 IEEE Int. Conference on Robotics and Automation, where it was nominated for best paper.)