The complexity of sensing by point sampling

In assembly tasks it is often necessary to recognize parts arriving via a conveyor belt or a parts feeder at some robot work cell. Generally the parts feeder will have reduced the number of possible poses of the parts to a small nite set. In order to distinguish between the remaining poses of the parts some simple sensing or probing operation may be used. In this paper we consider the problem of nding the minimum number of sensing points required to distinguish between a nite set of polygonal shapes. For instance, we might imagine embedding a series of point light detectors in a feeder tray. Then we would be interested in the question \What is the minimum number of light detectors that can fully distinguish between all the possible shapes?" Or we might imagine a set of mechanical probes that touches the feeder at a nite number of predetermined points. Then we would ask \What are the minimum number of probing points and where should the probes be located in order to distinguish all the possible shapes?" We address these questions in this paper.