In Proceedings of the 12th IEEE International Conference on Robotics and Automation (ICRA), Minneapolis, Minnesota, Apr. 1996, pp. 1581-1587.

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Complexity Measures for Assembly Sequences

by Michael H. Goldwasser, Jean-Claude Latombe, and Rajeev Motwani

Abstract: Our work examines various complexity measures for two-handed assembly sequences. For many products there exists an exponentially large set of valid sequences, and a natural goal is to use automated systems to select wisely from the choices. Since assembly sequencing is a preprocessing phase for a long and expensive manufacturing process, any work towards finding a ``better'' assembly sequence is of great value when it comes time to assemble the physical product in mass quantities.

We take a step in this direction by introducing a formal framework for studying the optimization of several complexity measures. This framework focuses on the combinatorial aspect of the family of valid assembly sequences, while temporarily separating out the specific geometric assumptions inherent to the problem. With an exponential number of possibilities, finding the true optimal cost solution is non-trivial. In fact in the most general case, our results show that even finding an approximate solution is hard. Furthermore, we can show several hardness results, even in simple geometric settings. Future work is directed towards using this model to study how the original geometric assumptions can be reintroduced to prove stronger approximation results.

Also see article in International Journal of Computational Geometry and Applications.
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Michael Goldwasser