Semi-centralized control for multi robot formation

Multi-robot formation control enables robots to cooperate as a working group in completing complex tasks. Given a formation to reach, each robot may first choose a position in the formation. Apart from arranging each robot with a fixed position, we may have more reasonable arrangement to minimize the moving cost while reaching the formation. To solve the problem, we formulate an optimization problem and give a solution by the Hungarian method. The moving cost of our proposed method is compared with others by simulation. As an extension, we discuss controlling of transformation between different formations. A theorem is given here confirming that our proposed strategy to choose center of the new formation may minimize the moving cost. Our work can improve the performance of multi-robot formation control and guide the system design.