A Distributed Biconnectivity Check

Abstract

Summary. For many distributed autonomous robotic systems, it is important to maintain communication connectivity among the robots. That is, each robot must be able to communicate with each other robot, perhaps through a series of other robots. Ideally, this property should be robust to the removal of any single robot from the system. In this work, we define a property of a team's communication graph that ensures this property, called biconnectivity. We present a distributed algorithm to check if a team of robots is biconnected, prove its correctness, and analyze it theoretically. IntroductionMany 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 [1,2], 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 space and underwater exploration, search and rescue, and cleaning robots.We say that robot R 1 is connected to robot R 2 if there is a series of robots, each within communication range of the previous, which can pass a message from R 1 to R 2 . In order for the team to stay connected, it must be the case that every robot is connected to each other robot either directly or via two distinct paths that don't 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.In previous work, we developed algorithms for multirobot surveillance under the assumption that each pair of robots could communicate directly [2]. This communication assumption enabled the robots to negotiate to achieve an efficient task division,

Stability and Vulnerability of Bird Flocking Behaviour: A Mathematical Analysis

“…To model the vulnerable of flocking topology, we can use the definition of articulation point in a graph G as described in (Ahmadi and Stone 2006). A bird that is modeled as a node i ∈ V of a connected flocking topology G is called an articulation point if a reduced graph G R ⊂ G is not connected.…”

“…Mathematically, this node is then defined as articulation points. Regarding this H A Y AT I Journal of Biosciences property, the graph which has no articulation points is called biconnected graph (Ahmadi and Stone 2006).…”

Decentralized fault diagnosis for heterogeneous multi-agent systems

“…In particular, the problem of maintaining connectivity in the presence of failures is considered. While connectivity maintenance has been widely studied in the last few years [10], [11], [12], [13], fault tolerance has been recently considered in some works, ensuring the biconnectivity property in a multi-agent system [14], [15], [16], [17], [18]. In the second case, faults are detected and isolated, and the system can be subsequently reconfigured.…”

Decentralized biconnectivity conditions in multi-robot systems

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