The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems. Particular examples are systems comprised of multiple agents. When it comes to coordinately control a group of autonomous mobile agents in order to achieve a common task, communication constraints impose limits on the achievable control performance. In this paper we consider a widely studied problem in the robotics and control communities, called consensus or state agreement problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the agreement. Time-invariant communication networks that exhibit particular symmetries are shown to yield slow convergence if the amount of information exchanged does not scale with the number of agents. On the other hand, we show that, randomly time-varying communication networks allow very fast convergence rates. The last part of the paper is devoted to the study of time-invariant communication networks with logarithmic quantized data exchange among the agents. It is shown that, by adding quantized data links to the network, the control performance significantly improves with little growth of the required communication effort.

In a sensor network, in practice, the communication among sensors is subject to: (1) errors or failures at random times; (2) costs; and (3) constraints since sensors and networks operate under scarce resources, such as power, data rate, or communication. The signal-to-noise ratio (SNR) is usually a main factor in determining the probability of error (or of communication failure) in a link. These probabilities are then a proxy for the SNR under which the links operate. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. To consider this problem, we address a number of preliminary issues: (1) model the network as a random topology; (2) establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail; and, in particular, (3) show that a necessary and sufficient condition for both mss and a.s. convergence is for the algebraic connectivity of the mean graph describing the network topology to be strictly positive. With these results, we formulate topology design, subject to random link failures and to a communication cost constraint, as a constrained convex optimization problem to which we apply semidefinite programming techniques. We show by an extensive numerical study that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the asymptotic performance of a non-random network at a fraction of the communication cost.

The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We consider as instance of coordination the consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the consensus. We show that time-invariant communication networks with circulant symmetries yield slow convergence if the amount of information exchanged by the agents does not scale well with their number. On the other hand, we show that randomly time-varying communication networks allow very fast convergence rates. We also show that, by adding logarithmic quantized data links to time-invariant networks with symmetries, control performance significantly improves with little growth of the required communication effort.

Several consensus protocols have been proposed in the literature and their convergence properties studied via a variety of methods. In all these methods, the communication topologies play a key role in the convergence of consensus processes. The goal of this paper is two fold. First, we explore communication topologies, as implied by the communication assumptions, that lead to consensus among agents. For this, several important results in the literature are examined and the focus is on different classes of communication assumptions being made, such as synchronism, connectivity, and direction of communication. In the latter part of this paper, we show that the confluent iteration graph unifies various communication assumptions and proves to be fundamental in understanding the convergence of consensus processes. In particular, based on asynchronous iteration methods for nonlinear paracontractions, we establish a new result which shows that consensus is reachable under directional, time-varying and asynchronous topologies with nonlinear protocols. This result extends the existing ones in the literature and have many potential applications. 1

Abstract — Motivated by the fact that linear controllers can stabilize the rotational motion of a rigid body, we propose in this paper a control strategy that exploits graph theoretic tools for cooperative control of multiple rigid bodies. The control objective is to stabilize the system to a configuration where the rigid bodies will have a common orientation and common angular velocity. The control law respects the limited information each rigid body has with respect to the rest of the team. Specifically, each rigid body is equipped with a control law that is based on the Laplacian matrix of the communication graph, which encodes the limited communication capabilities between the team members. Similarly to the linear case, the convergence of the multi-agent system relies on the connectivity of the communication graph. I.

We consider a formation control system where individual systems are controlled by a path-following design and the path variables are to be synchronized. We first show a passivity property for the path following system and, next, combine this with a passivity-based synchronization algorithm developed in [1]. The passivity approach expands the classes of synchronization schemes available to the designer. This generality offers the possibility to optimize controllers to, e.g., improve robustness and performance. Two designs are developed in the proposed passivity framework: The first employs the path error information in the synchronization loop, while the second only uses synchronization errors. A sampled-data design, where the path variables are updated in discrete-time and the path following controllers are updated in continuous time, is also developed.

Information consensus in sensor networks has received much attention due to its numerous applications in distributed decision making. This paper discusses the problem of a distributed group of agents coming to agreement on a probability vector over a network, such as would be required in a decentralized estimation of state transition probabilities or agreement on a probabilistic search map. Unique from other recent consensus literature, however, the agents in this problem must reach agreement while accounting for the uncertainties in their respective probabilities, which are formulated according to generally non-Gaussian distributions. The first part of this paper considers the problem in which the agents seek agreement to the centralized Bayesian estimate of the probabilities, which is accomplished using consensus on hyperparameters. The second part shows that the new hyperparameter consensus methodology can ensure convergence to the centralized estimate even while measurements of a static process are occurring concurrently with the consensus algorithm. A machine repair example is used to illustrate the advantages of hyperparameter consensus over conventional consensus approaches. I.

This paper analyzes task assignment for heterogeneous air vehicles using a guaranteed conflict-free assignment algorithm, the Consensus Based Bundle Algorithm (CBBA). We extend this recently proposed algorithm to handle two realistic multi-UAV operational complications. Our first extension accounts for obstacle regions in order to generate collision free paths for UAVs. Our second extension reduces task planner sensitivity to sensor measurement noise, and thereby minimizes churning behavior in flight paths. After integrating our enhanced CBBA module with a 3D visualization and interaction software tool, we simulate multiple aircraft servicing stationary and moving ground targets. Preliminary simulation results establish that consistent, conflict-free multi-UAV path assignments can be calculated on the order of a few seconds. The enhanced CBBA consequently demonstrates significant potential for real-time performance in stressing environments. I.

This paper introduces a mathematical model of the behavior of a group of agents and their interactions in a shared environment. We represent environmental spatial constraints that allow us to model range-limited sensing, motion, and communication capabilities of the agents. We derive general sensing, coordination, and motion conditions on the agents that guarantee that a desired distribution of the group of agents will emerge across the environment. We show the impact of group size on the distribution of agents, and consider the emergent distribution for different classes of environments. For more restrictive sensing and motion conditions we then characterize the rate at which the desired distribution is achieved. Finally, we show how this theory is useful in solving a multi-vehicle cooperative surveillance problem and discuss how our theory might be useful in understanding animal distributions in nature. I.

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