Optimal robotic cell scheduling with controllers using mathematically based timed Petri nets

This paper presents an optimal solution to the robotic cell scheduling problem for robot movement controllers using timed Petri nets (TPNs). The suggested TPN approach is used to generate a mathematical transition model, based on a From/To transition matrix and the properties of the TPN, that considers all possible movements of robots between cell stations. The mathematical model thus obtained is solved to identify the optimal firing sequence of TPN transitions for the considered robotic cell problem to minimize the time elapsed before the firing of the last transition (the cycle time). Finally, the optimal sequence of transitions is used to generate robotic cell controllers and construct the final TPN model. A numerical example is used to demonstrate the proposed approach.