Performance analysis of localization algorithms

Workpiece localization, with novel applications such as workpiece setup, refixturing and dimensional inspections, is a problem of permanent importance in manufacturing. Using the popular least square formulation, several geometric algorithms have been developed for workpiece localization over the last few years. In this paper, we analyze and compare the performance of three localization algorithms based on the following criteria: (a) robustness with respect to variations in initial conditions; (b) accuracy of computed results; and (c) computational efficiency. We develop an approach for improving the robustness of the algorithms for workpieces with sculptured surfaces for which the region of convergence is typically small. Based on simulation results, we also discuss sensitivity of the algorithms with respect to the number of measurement points and give a lower bound on this number for recovering a Euclidean transformation with certain accuracy.