Recognizing polygonal parts from width measurements

Automatic recognition of parts is an important problem in many industrial applications. One model of the problem is: given a finite set of polygonal parts, use a set of "width" measurements taken by a parallel-jaw gripper to determine which part is present. We study the problem of computing efficient strategies ("grasp plans"), with the goal to minimize the number of measurements necessary in the worst case. We show that finding a minimum length grasp plan is NP-hard, and give a polynomial time approximation algorithm that is simple and produces a solution that is within a log factor from optimal.