Assembly Planning Using Petri Net

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Abstract

An assembly planning is a significant problem for an automatic assembling using robotic manipulators. To cope with this problem, lots of strategies have been proposed. One of the most promising method for this problem is a planning based on the AND/OR graph representation. However, the drawback in the past research is that the mathematical structure of the AND/OR graph is somewhat obscure. In this paper, we present a new assembly planning method using Petri Net graph. Firstly, we model the assembly network by using the Petri Net graph with referring to the conventional AND/OR graph. Here, the AND/OR graph is assumed to be given. Secondly, the state equation of Petri Net, which is a mathematical model of Petri Net graph, is analyzed. From this analysis, it is clarified that the set of a basis solution of a state transition matrix is identical to the set of a solution which corresponds to an actual assembly sequence. This results in the fact that, when we consider an optimization problem which minimize a summation of a weight value of all tasks included in the assembly sequence, we can use a linear programming (LP) technique. This kind of optimization problem has been solved by a heuristic method such as AO^*. However, in case of using AO^*, it is difficult to determine the heuristic function, and, moreover, it is not ensured that we can get the optimal solution. On the contrary, in case of LP technique, the optimal solution can always be found. Finally, we show some numerical examples to certify the validity of the proposed analysis.