Smart speakers and robots become ever more prevalent in our daily lives. These agents are able to execute a wide range of tasks and actions and, therefore, need systems to control their execution. Current state-of-the-art such as (deep) reinforcement learning, however, requires vast amounts of data for training which is often hard to come by when interacting with humans. To overcome this issue, most systems still rely on Finite State Machines. We introduce Petri Net Machines which present a formal definition for state machines based on Petri Nets that are able to execute concurrent actions reliably, execute and interleave several plans at the same time, and provide an easy to use modelling language. We show their workings based on the example of Human-Robot Interaction in a shopping mall.