On algebraic and graph structural properties of assembly Petri net

Abstract

Assembly planning is a significant problem for automatic assembling using robotic manipulators. An assembly planning method using a Petri net is presented. The assembly network is modeled by using the Petri net with reference to the conventional and/or net. The state shift equation of the Petri net, which is a mathematical model of the net, is analyzed. From this analysis, it is clarified that the set of a basis solution of a state shift matrix is an actual assembly sequence. When considering an optimization problem which minimizes a summation of a weight value of all tasks included in the assembly sequence, a linear programming (LP) technique can be used. Some numerical examples to certify the validity of the proposed analysis are shown.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>