Many of the most fundamental examples in probability involve the pose statistics of coins and dice as they are dropped on a flat surface. For these parts, the probability assigned to each stable face is justified based on part symmetry, although most gamblers are familiar with the possibility of loaded dice. In industrial part feeding, parts also arrive in random orientations. We consider the following problem: given part geometry and parameters such as center of mass, estimate the probability of encountering each stable pose of the part. We describe three estimators for solving this problem for polyhedral parts with known center of mass. The first estimator uses a quasistatic motion model that is computed in time O(n log n) for a part with n vertices. The second estimator has the same time complexity but takes into account a measure of dynamic stability based on perturbation. The third estimator uses repeated Monte Carlo experiments with a mechanics simulation package. To evaluate these estimators, we used a robot and computer vision system to record the pose statistics based on 3595 physical drop experiments with four different parts. We compare this data to the results from each estimator. We believe this is the first paper to systematically compare alternative estimators and to correlate their performance with statistically significant experiments on industrial parts.
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