Formation control of multi-vehicle systems using cooperative game theory

In this work the issue of team cooperation in a multi-vehicle system is discussed in the form of a formation problem, and control signals are designed for the vehicles in a framework of cooperative game theory. Considering each vehicle as a player, its individual cost as the payoff function, and its control input as the decision that it has to make, a differential game is defined. By using the concept of Pareto optimality and minimizing a team cost function, the common goal of all the agents i.e. forming and maintaining the team´s predefined formation is reached. The information structure of the team has a leader-follower configuration and therefore the formation is formulated as a tracking problem. Both methods of open-loop and feedback information differential games are presented in the control design discussion. Finally, the simulation results of an illustrative example show that in addition to being able to accomplish the formation mission, compared to the Nash equilibrium´s non-cooperative game approach, a more improved team formation error is obtained using this cooperative game method.