An approach for optimal goal position assignment in vehicle formations

In this paper one methodology to solve the goal position assignment (GPA) problem is developed, this is, to assign the corresponding goal position (desired position) for a group of vehicles, knowing the initial positions and the established formation shape. By using this GPA methodology, it can be guaranteed that the formation will be reached in a minimum period of time and with lower collision risk compared with the other possible combinations of pairs "vehicles-goal position". Hungarian algorithm was used as combinatorial optimization algorithm, which requires a cost matrix, therefore it is shown the way to compute the cost matrix to obtain the best GPA. In order to show the optimal behavior of the proposed cost matrix, three approaches of cost matrix were evaluated in simulations of quad-rotor formations. Also, the optimal behavior of the proposed GPA is proved with numerical values of some defined parameters to determine optimal performance. The formation control was based on potential functions, while the control law for each vehicle was based on nested saturation.