This paper addresses the control of a team of nonholonomic mobile robots navigating in a terrain with obstacles while maintaining a desired formation and changing formations when required, using graph theory.We model the team as a triple, (g, r, H), consisting of a group element that describes the gross position of the lead robot, a set of shape variables g that describe the relative positions of robots, and a control graph H that describes the behaviors of the robots in the formation. Our framework enables the representation and enumeration of possible control graphs and the coordination of transitions between any two formations
