R. H. Wilson, L. E. Kavraki, J.-C. Latombe, and T. Lozano-Perez, “Two-Handed Assembly Sequencing,” International Journal of Robotics Research, vol. 14, no. 4, pp. 335–350, 1995.
This article considers the computational complexity of automat ically determining assembly sequences for mechanical products. Specifically, we address the partitioning problem: given an assembly of rigid parts, identify a proper subassembly that can be removed as a rigid object without disturbing the rest of the assembly. We examine the complexity of the partition ing problem under various types of relative motions allowed for the subassemblies. We show that when arbitrary motions are allowed to separate the two subassemblies, partitioning is NP-complete. We then describe a general framework for reasoning about assembly motions called the interference diagram. In its most general form the interference diagram yields an exponential- time algorithm to partition an assembly. However, two special cases of the interference diagram studied in this article yield polynomial-time sequencing algorithms. The first case occurs when assembly motions are restricted to single translations. The second case considers infinitesimal rigid motions in translation and rotation and yields a superset of all feasible partitionings. These two algorithms have important practical applications in assembly planning.