A Game Theoretic Approach to Regular Polygon Formation Control of Mobile Robots

In this paper we consider the regular polygon formation control problem of a mobile multi-robot system via a Nash Equilibrium (NE) seeking approach. We aim to steer the mobile robots towards the Nash equilibrium of a suitably defined virtual static game. In this game, the actions are the desired final positions of the robots and the cost functions include terms that penalize positions which are not vertices of a regular polygon with fixed center, while also taking into account deviations from their starting positions. As a result, the unique NE of the game defines a formation which is close to that of a regular polygon. Distributed adaptive control laws are then designed for seeking the NE of the aforementioned game. Simulation results verify the validity of the proposed methodology.