Geometry-based part grouping for assembly planning

One way to find an optimal plan is to enumerate all plans and evaluate a quality metric for each plan. However it is well known that N parts can have up to O(2^N) assembly plans. Reducing N by grouping parts has been proposed earlier but to our knowledge has not been formally defined. In this paper we define two types of groups in terms of part geometry using the nondirectional blocking graph and binary adjacency matrices defined by Wilson and Latombe (1994). We give a polynomial time algorithm for identifying serial and parallel groups. We tested the algorithm on two planar assemblies where it reduced plan time by a factor of 4