On the discrete symmetric localization problem

Workpiece localization has many applications in manufacturing automation. Symmetric localization plays an important role in it, since many commonly used features in engineering design are symmetric. In this paper, we discuss some new problems in symmetric localization. We find that multiple solutions exist even for localizing a cube, while it was known that a unique solution should be found. Then, we re-explore the symmetry subspaces for symmetric features. After that, we find that some symmetric features have different configuration spaces from those known before. This is actually the cause of the problem. A symmetric localization algorithm and simulation results are given to fix the existing problems.