Time, Petri nets, and robotics

Based on the Petri net (PN) theory a particular class of condition/event nets called Ω, suitable for modeling repetitive workcell tasks, is defined. Nets ∈Ω are either deterministic or exhibit a restricted kind of conflict called choice among alternatives. It is shown how the repetitive behavior of such a net may be studied by decomposing this conflict into deterministic components associated with mutually exclusive alternatives. A unified description of the important temporal extensions of PN theory is presented, with emphasis on formal analysis. The PN notion of coverability is extended in the temporal sense and it is demonstrated that, for nets ∈Ω, the period of repetition (cycle time) can be directly computed from the durations associated with the individual operations, once the decomposition into components is performed. When the durations are specified in the form of minimum and maximum values, this period of repetition may be described by optimistic and pessimistic bounds. A typical assembly example adapted from work with a multirobot workcell testbed is also presented to illustrate two forms of temporal analysis