In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discrete-time model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its \neighbors." In their paper, Vicsek et. al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models.

Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with latticetype nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multi-vehicle formations.

We discuss an old distributed algorithm for reaching consensus that has received a fair amount of recent attention. In this algorithm, a number of agents exchange their values asynchronously and form weighted averages with (possibly outdated) values possessed by their neighbors. We overview existing convergence results, and establish some new ones, for the case of unbounded intercommunication intervals.

This note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for information consensus. The note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs across some time intervals has a spanning tree frequently enough as the system evolves. Simulation results show the effectiveness of our update schemes.

Abstract — The problem is studied of achieving a specified formation among a group of mobile autonomous agents by distributed control. If convergence to a point is feasible, then more general formations are achievable too, so the focus is on convergence to a point (the agreement problem). Three formation strategies are studied and convergence is proved under certain conditions. Also, motivated by the question of whether collisions occur, formation evolution is studied. I.

This paper considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for consensus of information. That the union of a collection of interaction graphs across some time intervals has a spanning tree frequently enough as the system evolves is shown to be a necessary and sufficient condition for information consensus under dynamically changing interaction topologies. Simulation results show the effectiveness of our results.

We consider the problem of classifying among a set of M hypotheses via distributed noisy sensors. The sensors can collaborate over a communication network and the task is to arrive at a consensus about the event after exchanging messages. We apply a variant of belief propagation as a strategy for collaboration to arrive at a solution to the distributed classification problem. We show that the message evolution can be re-formulated as the evolution of a linear dynamical system, which is primarily characterized by network connectivity. We show that a consensus to the centralized MAP estimate can almost always reached by the sensors for any arbitrary network. We then extend these results in several directions. First, we demonstrate that these results continue to hold with quantization of the messages, which is appealing from the point of view of finite bit rates supportable between links. We then demonstrate robustness against packet losses, which implies that optimal decisions can be achieved with asynchronous transmissions as well. Next, we present an account of energy requirements for distributed detection and demonstrate significant improvement over conventional decentralized detection. Finally, extensions to distributed estimation are described. 1

In this paper, we propose discrete-time and continuous-time consensus update schemes motivated by the discrete-time and continuous-time Kalman filters. With certainty information encoded into each agent, the proposed consensus schemes explicitly account for relative confidence / reliability of information states from each agent in the team. We show mild sufficient conditions under which consensus can be achieved using the proposed consensus schemes in the presence of switching interaction topologies.

This paper investigates the consensus problem for a team of agents with inconsistent information, which is a core component for many proposed distributed planning schemes. Kalman filtering approaches to the consensus problem have been proposed, and they were shown to converge for strongly connected networks. However, it is demonstrated in this paper that these previous techniques can result in biased estimates that deviate from the centralized solution, if it had been computed. A modification to the basic algorithm is presented to ensure the Kalman Filter converges to an unbiased estimate. The proof of convergence for this Modified Distributed Kalman Consensus algorithm to the unbiased estimate is then provided for both static and dynamic communication networks. These results are demonstrated in simulation using several simple examples.

Accurately synchronized clocks are crucial for many applications in sensor networks. Existing time synchronization algorithms provide on average good synchronization between arbitrary nodes, however, as we show in this paper, close-by nodes in a network may be synchronized poorly. We propose the Gradient Time Synchronization Protocol (GTSP) which is designed to provide accurately synchronized clocks between neighbors. GTSP works in a completely decentralized fashion: Every node periodically broadcasts its time information. Synchronization messages received from direct neighbors are used to calibrate the logical clock. The algorithm requires neither a tree topology nor a reference node, which makes it robust against link and node failures. The protocol is implemented on the Mica2 platform using TinyOS. We present an evaluation of GTSP on a 20-node testbed setup and simulations on larger network topologies.