A solution for the goal position assignment in formation problem

This paper is focused on the development of one methodology to assign the corresponding goal position for a group of vehicles in a proper manner, starting from any initial configuration and one established formation shape. The assignment methodology will guarantee that the formation will be reached in a minimum period of time and without collision risk. Hungarian algorithm was used as combinatorial optimization algorithm, and this methodology requires a cost matrix. In order to show the optimal behavior of the proposed cost matrix, three approaches of cost matrix were evaluated. Simulations of quad-rotor formations were carried out to analyze approaches behavior, the formation was based on potential functions and the control law for each vehicle was based on nested saturation.