Analysis and prediction of the behavior of one class of multiple foraging robots with the help of stochastic Petri nets

Performance evaluation of multi-agent robotic systems requires a great amount of simulations in order to check the emergence of the required collective behavior. The paper proposes to model such systems by the stochastic Petri nets formalism. In this way, it is shown how to use the powerful tools of Markov chains analysis for computing quickly the evolution of the states of the multi-agent system and of the environment. A simple example illustrates the presentation, and the theoretical results are compared to simulations. It concerns an homogeneous population of Tom-Thumb robots collecting samples situated in some unknown places (mines) and bringing them to a home base. The Markovian model, which is able to provide the system's state at any time, is solved very quickly, while the simulations are long and tedious when the performance must be evaluated as a function of various parameters: number of robots, of mines, of samples, etc.