Control of changes in formation for a team of mobile robots

Addresses the control of a team of robots navigating in a terrain with obstacles while maintaining a desired formation and changing formations when required. We model the team as a triple consisting of a group element that describes the gross motion of the team, a set of shape variables that describe the relative positions of robots, and a control graph that describes the behaviors of the robots in the formation. We assume that a lead robot is equipped with the appropriate sensors and plans the gross motion (path) for the team. This path is derived from optimal control theory. All other robots are coordinated by continuous controllers that are prescribed by the control graph. Our framework allows us to enumerate the number of control graphs and the possible transitions between them. Further, we describe an algorithm that allows the team of robots to move between any two formations, while avoiding obstacles. We illustrate the methodology with examples involving teams of 5 and 6 robots in the presence of obstacles