Symbolic OBDD representations for mechanical assembly sequences

Assembly sequence planning is one typical combinatorial optimization problem, where the size of parts involved is a significant and often prohibitive difficulty. The compact storage and efficient evaluation of all the feasible assembly sequences is one crucial concern. Ordered binary decision diagram (OBDD) is a canonical form to represent and manipulate the Boolean functions efficiently, and appears to give improved results for large-scale combinatorial optimization problems. In this paper, subassemblies, assembly states and assembly tasks are represented as Boolean characteristic functions, and the symbolic OBDD representation of assembly sequences is proposed. In this framework, the procedures to transform directed graph and AND/OR graph into OBDDs are presented. The great advantage of OBDD-based scheme is that the storage space of OBDD-based representation of all the feasible assembly sequences does not increase with the part count of assembly dramatically so quickly as that of both directed graph and AND/OR graph do. We undertake many experimental tests using Visual C++ and CUDD package. It was shown that the OBDD scheme represented all the feasible assembly sequences correctly and completely, and outperforms either directed graph or AND/OR graph in storage efficiency.