The symbolic OBDD scheme for generating mechanical assembly sequences

Abstract

Assembly sequence planning is one of typical combinatorial optimization problems, where the size of parts involved is a significant and often prohibitive difficulty. The compact storage and efficient evaluation of 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, assembly knowledge models of liaison graph and translation function are formulated by OBDDs, and OBDD-based representation of assembly sequences is proposed. A novel OBDD-based procedure was presented to generate all geometrically feasible assembly sequences from the OBDDs of liaison graph and translation relation. This procedure can be used conveniently on the computer and all the feasible sequences can be derived. The great advantage of OBDD-based scheme is that the storage space of OBDD-based representation of feasible assembly sequences does not increase with the part count of assembly dramatically so quickly as that of AND/OR graph does. We developed the prototype tool for generating assembly sequence using Visual C++ and CUDD package, and undertake some experimental tests. It was shown that the OBDD scheme generated feasible assembly sequences correctly and completely.

Synthesizing Design Solutions for Assembling Complex Items on the Basis of Hypergraph Cutting

“…В работе [31] информация о контактах задается в форме графа связей, а геометрические связи описываются в виде совокупности T-функций. Этот граф и множество T-функций рассматриваются как бинарные отношения и описываются при помощи OBD-диаграмм (ordered binary decision diagram).…”

Symbolic OBDD Assembly Sequence Planning Algorithm Based on Unordered Partition with 2 Parts of a Positive Integer

“…Gu, Xu and Yang proposed symbolic OBDD representations for mechanical assembly sequences [6], the experimental results show that the storage space of OBDD based representation of all the feasible assembly sequences is less than that of AND/OR graph do. Gu and Liu developed an symbolic OBDD algorithm for assembly sequence planning which is limited to monotone linear assembly [7]. Gu and Xu presented a novel scheme to integrate constraint satisfaction problem model with OBDD for the assembly sequence planning, but the procedure consumes a lot of time with the problem of backtracking [8].…”

A Novel Symbolic OBDD Algorithm for Generating Mechanical Assembly Sequences Using Decomposition Approach

“…Gu, Xu and Yang proposed symbolic OBDD representations for mechanical assembly sequences [7], the experimental results show that the storage space of OBDD based representation of all the feasible assembly sequences is less than that of AND/OR graph do. Gu and Liu developed an algorithmic procedure using a direct generation approach to generate all feasible assembly sequences by putting together the separated parts into final assembly from the OBDD of liaison graph and translation relation [8], but this procedure leads to the problem of backtracking when an already assembled part is an obstacle for later assembly operations. Xu and Gu presented a novel scheme to integrate constraint satisfaction problem model with the symbolic ordered binary decision diagram for the assembly sequence planning [9], but this procedure also leads to the problem of backtracking.…”