Biconnected structure for multi-robot systems

Many applications of distributed autonomous robotic systems can benefit from, or even may require, the team of robots staying within communication connectivity. For example, consider the problem of multirobot surveillance (Ahmadi & Stone 2006), in which a team of robots must collaboratively patrol a given area. If any two robots can directly communicate at all times, the robots can coordinate for efficient behavior. This condition holds trivially in environments that are smaller than the robots' communication range. However in larger environments, the robots must actively maintain physical locations such that any two robots can communicate -- possibly through a series of other robots. Otherwise, the robots may lose track of each others' activities and become miscoordinated. Furthermore, since robots are relatively unreliable and/or may need to change tasks (for example if a robot is suddenly called by a human user to perform some other task), in a stable multirobot surveillance system, if one of the robots leaves or crashes, the rest should still be able to communicate. Some examples of other tasks that could benefit from any pair of robots being able to communicate with each other, are multi-robot exploration, search and rescue, and cleaning robots. We say that robot R1 is connected to robot R2 if there is a series of robots, each within communication range of the previous, which can pass a message from R1 to R2. It is not possible to maintain connectivity in the face of arbitrary numbers of robot departures: if there are any two robots that are not within communication of one another and all other robots simultaneously depart, the system becomes disconnected. Thus we focus on the property of remaining robust to any single failure under the assumption that the team can readjust its positioning in response to a departure more quickly than a second departure will occur. In order for the team to stay connected, even in the face of any single departure, it must be the case that every robot is connected to each other robot either directly or via two distinct paths that do not share any robots in common. We call this property biconnectivity: the removal of any one robot from the system does not disconnect the remaining robots from each other.