ON THE SYMMETRICAL LOCALIZATION PROBLEM

Accurate and efficient localization of symmetric features plays an imp ortant role in dimensional inspection of machined parts and machining of partially finished workpieces. In this paper, we present a geometri c theory for efficient and accurate localization of symmetric features . First, we show that the configuration space of a symmetric feature c an be naturally identified with the homogeneous space SE(3)/G(o) of th e Euclidean group SE(3), where G(o) is the symmetry group of the featu re. Then, we explore the geometric structure of the homogeneous space and present a simple and unifying algorithm for symmetric localization . Finally, we give simulation results illustrating several unique feat ures of the algorithm: 1) implementational simplicity; 2) robustness w ith respect to initial conditions; 3) high accuracy in computed result s; 4) computational efficiency.