Abstract: 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)/Go of the Euclidean group SE(3), where Go 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.

Key words: Workpiece localization, Coordinate measuring machine, Geometric tolerances, Lie groups, Symmetric features