Linear Quadratic Differential Game Formulation for Leaderless Formation Control

The leaderless formation control problem for a multi-robot system with double integrator dynamics is studied. The interaction dynamics among robots and the formation objective are added together and expressed in terms of individual cost functions. The problem is posed as a linear quadratic differential game. For the non cooperative mode of play, the open-loop Nash equilibrium solution of the formation control differential game problem is discussed. It is shown that the existence of a unique Nash equilibrium solution for the formation problem, whose cost functions are Mayer type, depends on the invertibility of a matrix introduced. A triangle formation is tested to justify the models and the results.