On the localization of symmetric workpieces

Present a geometric theory for efficient and accurate localization of symmetric features. First, show that the configuration space of a symmetric feature can be naturally identified with the homogeneous space SE(3)/G₀ of the Euclidean group SE(3), where G₀ is the symmetry group of the feature. Then, explore the geometric structure of the homogeneous space and present a simple and unifying algorithm for symmetric localization. Finally, give simulation results illustrating several unique features of the algorithm: implementational simplicity, robustness with respect to initial conditions, highly accuracy in computed results, and computational efficiency.