Experiments in the Use of Stable Limit Sets for Parts Handling

Throwing and catching parts promises to be a powerful manipulation technique, but is analytically complicated by equations of motion involving friction and impacts. Traditional control techniques would suggest that one should directly consider the equations of motion and design inputs that produce a unique fixed point. Such analysis can be anywhere from tedious to intractable. However, one can show that some simple part manipulators exhibit limit set behavior, where the parts enter a set that is invariant under the mapping that corresponds to the throwing action. We show here that analyzing limit sets rather than the equations of motion provides a more user friendly method of analysis, yielding tractable methods for understanding and designing part manipulators. These methods are additionally related to the study of self-assembly, and we are able to "nearly" self-assemble parts. In particular, we use a experimental setup to investigate methods to throw parts into a stable assembly using binary feedback.