A correction is given to a previously published result concerned with the relationship between a suitably defined matrix seminorm for consensus analysis and a coefficient of ergodicity.

For the purposes of this paper, “gossiping” is a distributed process whose purpose is to enable the members of a group of autonomous agents to asymptotically determine, in a decentralized manner, the average of the initial values of their scalar gossip variables. This paper discusses several different deterministic protocols for gossiping which avoid deadlocks and achieve consensus under different assumptions. First considered is$T$-periodic gossiping which is a gossiping protocol which stipulates that each agent must gossip with the same neighbor exactly once every$T$time units. Among the results discussed is the fact that if the underlying graph characterizing neighbor relations is a tree, convergence is exponential at a worst case rate which is the same for all possible$T$-periodic gossip sequences associated with the graph. Many gossiping protocols are request based which means simply that a gossip between two agents will occur whenever one of the two agents accepts a request to gossip placed by the other. Three deterministic request-based protocols are discussed. Each is guaranteed to not deadlock and to always generate sequences of gossip vectors which converge exponentially fast. It is shown that worst case convergence rates can be characterized in terms of the second largest singular values of suitably defined doubly stochastic matrices.

Determining node positions is essential for many next-generation network functionalities. Previous localization algorithms lack correctness guarantees or require network density higher than required for unique localizability. In this paper, we describe a class of algorithms for fine-grained localization called Sweeps. Sweeps correctly finitely localizes all nodes in bilateration networks. Sweeps also handles angle measurements and noisy measurements. We demonstrate the practicality of our algorithm through extensive simulations on a large number of networks, upon which it consistently localizes one-thousand-node networks of average degree less than five in less than two minutes on a consumer PC.

In this paper, we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.

Knowing the positions of the nodes in a network is essential to many next generation pervasive and sensor network functionalities. Although many network localization systems have recently been proposed and evaluated, there has been no systematic study of partially localizable networks, i.e., networks in which there exist nodes whose positions cannot be uniquely determined. There is no existing study which correctly identifies precisely which nodes in a network are uniquely localizable and which are not. This absence of a sufficient uniqueness condition permits the computation of erroneous positions that may in turn lead applications to produce flawed results. In this paper, in addition to demonstrating the relevance of networks that may not be fully localizable, we design the first framework for two dimensional network localization with an efficient component to correctly determine which nodes are localizable and which are not. Implementing this system, we conduct comprehensive evaluations of network localizability, providing guidelines for both network design and deployment. Furthermore, we study an integration of traditional geographic routing with geographic routing over virtual coordinates in the partially localizable network setting. We show that this novel cross-layer integration yields good performance, and argue that such optimizations will be likely be necessary to ensure acceptable application performance in partially localizable networks.

We provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.

In the near future, the advent of large-scale networks of mobile agents autonomously performing long-term sensing and communication tasks will be upon us. However, using controlled node mobility to improve communication performance is a capability that the mobile networking community has not yet investigated. In this paper, we study mobility as a network control primitive. More specifically, we present the first mobility control scheme for improving communication performance in such networks. Our scheme is completely distributed, requiring each node to possess only local information. Our scheme is self-adaptive, being able to transparently encompass several modes of operation, each respectively improving power efficiency for one unicast flow, multiple unicast flows, and many-to-one concast flows. We provide extensive evaluations on the feasibility of mobility control, showing that controlled mobility can improve network performance in many scenarios. This work constitutes a novel application of distributed control to networking in which underlying network communication serves as input to local control rules that guide the system toward a global objective.

This article addresses the visual servoing of a rigid robotic manipulator under fixed camera configuration. The control goal is to move the robot end-effector to a visually determined target position by using a vision system equipped with two fixed cameras. A general image-based controller is proposed to achieve "precise" positioning in the absence of measurement noise. Based on the "epipolar constraint", we have shown that the overall closed-loop system using redundant image features, is exponentially stable provided that the camera model imprecision is small.

Most of the work in robotic manipulation and visual servoing has emphasized how to specify and perform particular tasks. Recent results have formally shown what tasks are possible with uncalibrated imaging systems. This paper extends those results by characterizing in a constructive manner the set of tasks which can be performed with different types of uncalibrated camera models. The tasks resulting structure provides a principle foundation both for a specification language and for automatic execution monitoring in uncalibrated environments.

Over the last several years, there has been an increasing appreciation of the impact of control architecture on the accuracy of visual servoing systems. In particular, it is generally acknowledged that so-called image-based methods provide the highest guarantees of accuracy on inaccurately calibrated hand-eye systems. Less clear is the impact of the control architecture on the set of tasks which the system can perform. In this article, we present a formal analysis of control architectures for hand-eye coordination. Specifically, we first state a formal characterization of what makes a task performable under three possible encoding methods. Then, for the specific case of cameras modeled using projective geometry, we relate this characterization to notions of projective invariance and demonstrate the limits of achievable performance in this regard.

This article describes the theory and implementation of a system that positions a robot manipulator using visual information from two cameras. The system simultaneously tracks the robot end-effector and visual features used to define goal positions. An error signal based on the visual distance between the end-effector and the target as defined and a control law that moves the robot to drive this error to zero is derived. The control law has been integrated into a system that performs tracking and stereo control on a single processor with no special purpose hardware at real-time rates. Experiments with the system have shown that the controller is so robust to calibration error that the cameras can be moved several centimeters and rotated several degrees while the system is running with no adverse effects.>