A game theoretical representation for the rendezvous problem

In this paper, we explore the application of Transferable Utility games, which is one of the many different types of games that make up the class of cooperative games, to the rendezvous problem. We consider an environment with multiple robots, wherein the objective is for them to agree in a decentralized manner on a rendezvous point in a non holonomic environment. The utility functions to be used by the controllers is such that they are shown to converge to a solution that leads all the robots to the objective. The paper also offers a mathematical proof of convergence for the proposed algorithm. Finally, simulations and experiments confirm our results.