Essentially decision free Petri nets for real-time resource allocation

Qualitative properties of Petri nets (such as liveness and safeness) are useful in discrete manufacturing applications since they correspond to consistent, deadlock-free control logic. In this paper we introduce the qualitative property of essentially decision free (EDF) places in Petri nets (PNs) to represent the absence of unresolved (nonunique) resource allocation conditions. We show that a previously developed method for PN synthesis of on-line control logic may lead to ambiguous resource allocation conditions which are exhibited in the PN model us non-EDF places. Using the theory of place-invariants, we develop a procedure for identifying non-EDF places in the synthesized logic. The procedure is illustrated for an example of assigning robots to tasks in a flexible assembly cell. For this example, allocation ambiguities are systematically resolved by introducing logical NOT conditions in the PN model.