Showing papers by "Brian D. O. Anderson published in 2006"

A Theory of Network Localization

Abstract: 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

Localization in sparse networks using sweeps

Abstract: 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.

Reaching an Agreement Using Delayed Information

Abstract: This paper studies a modified version of the Vicsek's problem, also known as the "consensus problem". Vicsek et al. (1995) consider a discrete-time model consisting of n autonomous agents all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of the headings of its "neighbors". We consider a modified version of the Vicsek's problem in which integer valued delays occur in sensing the values of headings which are available to agents. By appealing to the concept of graph composition, we side-step most issues involving products of stochastic matrices and present a variety of graph theoretic results which explains how convergence to a common heading is achieved

WSN06-4: Online Calibration of Path Loss Exponent in Wireless Sensor Networks

Abstract: The path loss exponent (PLE) is a parameter indicating the rate at which the received signal strength (RSS) decreases with distance, and its value depends on the specific propagation environment. Path loss exponent estimation plays an important role in distance-based wireless sensor network localization, where distance is estimated from the RSS measurements. Path loss exponent estimation is also useful for other purposes like sensor network dimensioning. Existing techniques on PLE estimation rely on both RSS measurements and distance measurements in the same environment to calibrate the PLE. However distance measurements can be difficult and expensive to obtain in some environments. In this paper we propose a novel technique for online calibration of the path loss exponent in wireless sensor networks without using distance measurements. The major contribution of this paper is to demonstrate that it is possible to estimate the PLE using only power measurements and the geometric constraints associated with planarity in a sensor network. This may have a significant impact on wireless sensor network localization.

Precise Localization using Sweeps in Sparse Networks

Abstract: 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. Categories and Subject Descriptors: C.2.1 [Computer Communication Networks]: Network Architecture and Design – Wireless communication; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems General Terms: Algorithms, Performance, Design. Keywords: Localization, Sweeps, Global Rigidity, ControlledMobility

Principles to control autonomous formation merging

Abstract: This paper provides a complete description of possible scenarios of merging two minimally rigid or globally rigid formations to obtain a single minimally rigid or globally rigid formation, respectively, both in /spl Ropf//sup 2/ and /spl Ropf//sup 3/. A strategy is developed based on simplification of the merging problem to a problem of growing a minimally or globally rigid graph. Based on this strategy, three principles are provided to control the merging efficiently and optimally, in the sense of minimizing the number of added edges and the number of vertices incident to these edges. Any possible scenario of merging two given minimally or globally rigid formations can be handled using a combination of these three principles. Although the main results are provided for merging two formations, application of the proposed techniques to merging of more than two formations is briefly discussed as well.

Checking if controllers are stabilizing using closed-loop data

Abstract: Suppose an unknown plant is stabilized by a known controller. Suppose also that some knowledge of the closed-loop system is available and on the basis of that knowledge, the use of a new controller appears attractive, as may arise in iterative control and identification algorithms, and multiple-model adaptive control. The paper presents tests using a limited amount of experimental data obtained with the existing known controller for verifying that introduction of the new controller will stabilize the plant.

Control and information architectures for formations

Abstract: This paper reviews a number of concepts and results relevant to the design of architectures to maintain the shape of a formation of autonomous agents. The paper begins with motivating examples from nature and the manmade world, and emphasises the task of providing satisfactory sensing, communication and control architectures within a formation of autonomous agents. Then some technical tools for characterising and designing architectures are described, largely resting on graph theoretic considerations.

Adaptive Source Localization by Mobile Agents

Abstract: The problem of source localization has assumed increased importance in recent years. Applications include locating the source of a cellular phone signal, sensor localization or satellite localization. In this paper we formulate a continuous time adaptive localization algorithm that permits a mobile agent to estimate the location of a stationary source using only the measured distance from the source. The algorithm is shown to be exponentially asymptotically stable, under a persistent excitation condition that has an intuitively appealing interpretation. Exponential asymptotic stability indicates the ability of the algorithm to track modest movements of the source.

Elementary operations for the reorganization of minimally persistent formations

Abstract: In this paper we study the construction and transformation of two-dimensional minimally persistent graphs Persistence is a generalization to directed graphs of the undirected notion of rigidity In the context of moving autonomous agent formations, persistence charac- terizes the efficacy of a directed structure of unilateral distances constraints seeking to preserve a formation shape Analogously to the powerful results about Henneberg sequences in minimal rigidity theory, we propose different types of directed graph operations allowing one to sequen- tially build any minimally persistent graph (ie persistent graph with a minimal number of edges for a given number of vertices), each intermediate graph being also minimally persistent We also consider the more generic problem of obtaining one minimally persistent graph from another, which corresponds to the on-line reorganization of an autonomous agent formation We show that we can obtain any minimally persistent formation from any other one by a se- quence of elementary local operations such that minimal persistence is preserved throughout the reorganization process

Localization of Sensor Networks Using Sweeps

Abstract: The sensor network localization problem with distance information is to determine the positions of all sensors in a network given the positions of some sensors and the distances between some pairs of sensors. We present a specialized localization algorithm and identify the graph properties of some classes of networks that can be localized by the algorithm. We also give an important application of our algorithm in creating formations in multi-agent systems.

Agreeing Asynchronously: Announcement of Results

Abstract: This paper formulates and solves a continuous-time version of the widely studied Vicsek consensus problem in which each agent independently updates its heading at times determined by its own clock. It is not assumed that the agents' clocks are synchronized or that the "event" times between which any one agent updates its heading are evenly spaced. Heading updates need not occur instantaneously. Using the concept of "analytic synchronization" together with several key results concerned with properties of "compositions" of directed graphs, it is shown that the conditions under which a consensus is achieved are essentially the same as those applicable in the synchronous discrete-time case provided the notion of an agent's neighbor between its event times is appropriately defined.

A two-degree-of-freedom H∞ control design method for robust model matching

Abstract: SUMMARY We propose an H1 controller design method which achieves a closed-loop transfer function equal or otherwise sensibly close to a desired transfer function, viz. a model reference design. The proposed controller design method inherits the model reference feature of the internal model control design method and incorporates the weighting scheme of the H1 loop-shaping. It utilizes Youla–Kucera parameterization in a two-degree-of-freedom scheme to achieve robust model reference and high performance design while ensuring a sensible robust stability margin, and can be readily applied to the generic class of LTI systems (SISO, MIMO, stable, unstable). Copyright # 2006 John Wiley & Sons, Ltd.

Merging Multiple Formations: A Meta-Formation Prospective

Abstract: This paper considers the problem of merging of more than two (minimally) rigid formations which do not have any common agent to obtain a single (minimally) rigid formation in Rfr2 and Rfr3. Following previously developed strategies for sequential merging of two rigid formations, a new set of enhanced merging operations is developed. They can be performed in a formalized meta-formation framework, where the individual rigid formations are considered as meta-vertices and they can be merged into a meta-formation. These operations for growing meta-formations offer a level of control to the merging quality and optimality, in the sense of minimizing the number of meta-edges (that is, edges between different meta-vertices) required. It is also proved that all minimally rigid meta-formations in Rfr2 can be obtained by successively merging two or more meta-vertices using the proposed set of meta-operations

Rigidity and Persistence of Meta-Formations

Abstract: This paper treats the problem of the merging of formations, where the underlying model of a formation is graphical. We first analyze the persistence of meta-formations, which are formations obtained by connecting several persistent formations. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations, persistence characterizes the efficacy of a directed structure of unilateral distance constraints seeking to preserve a formation shape. We derive then, for agents evolving in a two- or three-dimensional space, the conditions under which a set of persistent formations can be merged into a persistent meta-formation, and give the minimal number of interconnections needed for such a merging. We also give conditions for a meta-formation obtained by merging several persistent formations to be persistent.

Information Architecture and Control Design for Rigid Formations

Abstract: Formations of robots, underwater vehicles and autonomous airborne vehicles are progressively being deployed to tackle problems of surveillance, bush fire control, and the like. Much formation behavior mimics the behavior of formations of living organisms, such as birds and fish. This paper reviews a number of concepts and results relevant to the design of control schemes and information architectures to maintain the shape of a formation of autonomous agents. The task of providing satisfactory sensing, communication and control architectures within a formation of autonomous agents is emphasized and elaborated in the paper. The paper provides a set of technical tools for characterizing and designing information architectures, which largely rest on graph theoretic considerations, as well as a control scheme exemplifying a class of decentralized controllers for maintaining the shape of a formation.

Primitive operations for the construction and reorganization of minimally persistent formations

Abstract: In this paper, we study the construction and transformation of twodimensional persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations, persistence characterizes the efficacy of a directed structure of unilateral distances constraints seeking to preserve a formation shape. Analogously to the powerful results about Henneberg sequences in minimal rigidity theory, we propose different types of directed graph operations allowing one to sequentially build any minimally persistent graph (i.e. persistent graph with a minimal number of edges for a given number of vertices), each intermediate graph being also minimally persistent. We also consider the more generic problem of obtaining one minimally persistent graph from another, which corresponds to the on-line reorganization of an autonomous agent formation. We prove that we can obtain any minimally persistent formation from any other one by a sequence of elementary local operations such that minimal persistence is preserved throughout the reorganization process.

Use of meta-formations for cooperative control

Abstract: This paper reviews a number of very recent results in rigid graph theory and their extension for directed graphs to persistence theory, with an application focus on the cooperative control of formations. Particular attention is paid to issues related to the merging of formations, where the internal structure of each of the individually merging formations is, to the maximum extent possible, downplayed in the calculation. The meta-formation framework is then introduced in light of merging process for its construction. The ideas also have application to sensor network localization, where there is potential to make great computational saving.

Minimal multirealization of MIMO linear systems

Abstract: This note explores the minimal multirealization problem, which is the determination of a minimal degree, parameter-dependent, state variable description to express a finite set of linear multivariable systems. The form of the parameter-dependent state variable description is selected as a feedback form to implement "state sharing" and "bumpless transfer," which are possible ways to improve poor transient responses for switching control. The problem is solved by finding a special kind of minimal multiplier for a finite set of polynomial matrices.

Sequential Localization of Networks

Abstract: The sensor network localization problem with distance information is to determine the positions of all sensors in a network given the positions of some sensors and the distances between some pairs of sensors. The sensors whose positions are given are said to be anchors. Knowing the positions of sensors is essential in many network algorithms such as geographic routing and coverage. The sensor network localization problem is solvable if and only if the network is “localizable”. A network in R is said to be localizable if there exists exactly one position in R corresponding to each non-anchor sensor such that the given inter-sensor distances are satisfied. The authors of [1] use rigidity theory to give the necessary and sufficient conditions for a network to be localizable. However, the process of localizing a network has been shown to be NP-hard even when the network is known to be localizable [2]. This leaves us to consider the more refined question of what kinds of localizable networks can we efficiently localize? This has been investigated in [3] and we extend the results of that paper. While some ingenious heuristics-based schemes have been proposed [4], [5], [6], [7], we are interested in provably correct localization algorithms and the kinds of networks that can be efficiently localized by them. In the following we will give a localization algorithm that consists of a finite number of steps to be carried out sequentially. We will also give some classes of networks that can be efficiently localized by the algorithm. In the process, we will raise a number of graph theoretic questions related to rigidity theory. The resolution of these questions can in turn help us shed light on which networks can be efficiently and provably correctly localized. This is another indication that the sensor network localization problem and rigidity theory are intricately related. We begin by giving some terms and definitions to be used in the exposition which follows. A configuration p = {p1, . . . , pn} in d-dimensional space is a set of n points in R labelled p1, . . . , pn. A configuration p is said to be generic if the coordinates of points in p are algebraically independent over the rationals. Two configurations p = {p1, . . . , pn} and q = {q1, . . . , qn} of n points are congruent if for all i, j ∈ {1, . . . , n}, the distance between pi and pj is equal to the distance between qi and qj . A point formation of n points at a configuration p = {p1, . . . , pn} consists of p and a simple undirected graph G with vertex set V = {1, . . . , n}, and is denoted by (G, p). If (i, j) is an edge in G, then we say the length of edge (i, j) in the point formation (G, p) is the distance between pi and pj . A point formation (G, p) is globally rigid in R if p and q are congruent configurations in R whenever (G, p) and (G, q) have the same edge lengths. A graph G is said to be generically globally rigid in R if (G, p) is globally rigid in R whenever p in R is generic. Since almost all configurations are generic, we have that (G, p) is globally rigid in R for almost all configurations p in R if G is generically globally rigid in R. A graph that is generically globally rigid in R is said to be minimally generically globally rigid in R if the removal of any edge causes the graph to not be generically globally rigid in R. A sensor network with n sensors is modelled by a point formation (G, p), where each sensor corresponds to exactly one vertex of G, and vice versa, with (i, j) being an edge of G if i and j are distinct and the distance between the corresponding sensors is known, and p = {p1, . . . , pn} where pi is the position of the sensor corresponding to vertex i. We say that G is the graph of the network, and p is the configuration of the network. Vertex v of G is called an anchor vertex if the sensor corresponding to v is an anchor, and a sensor vertex otherwise. Since almost all configurations are generic, we have that the configurations of networks are almost always generic. Henceforth, we will only consider networks with generic configurations. It is known that if the configuration of a network in R is generic, then the network is localizable if and only if it has at least 3 non-collinear anchors and the graph of the network is generically globally rigid in R. A graph is said to be a trilateration graph with trilateration ordering v1, . . . , vn if its vertices can be relabelled as v1, . . . , vn so that the subgraph induced by v1, v2, v3 is complete and each vi with i > 3 is adjacent to at least three distinct vertices vj which “precede” it in the ordering, where by precede we mean j < i [1]. It is shown in [1] that trilateration graphs are generically globally rigid in R. A graph is a bilateration graph with bilateration ordering

Transfer function approximation and identification using magnitude and phase criteria

Abstract: In this paper, we show how convex optimization can be used for model reduction and identification of transfer functions. Two different methods are presented. In the first method magnitude functions are matched, and in the second method phase functions are matched. The weighted error bounds have direct interpretation in a Bode diagram. Both methods are suitable to engineers working with Bode diagrams. Furthermore, we see that transfer functions that have similar magnitude or phase functions also have a small relative H-infinity error under some minimum phase assumptions. The error bounds come from bounds associated with the Hilbert transform operator restricted in its application to rational transfer functions. Two examples are included to illustrate the results. Keywords— Model approximation, model reduction, system identification, magnitude, phase, Hilbert transform, semidefinite programs, KYP lemma, sum of squares decomposition, LMI

Synthesis of parameter-dependent controllers yielding affine-in-parameters characteristic polynomials

Abstract: The problem considered is that of designing a parameter-dependent linear controller for a parameter-dependent linear plant, where the parameter may be time-varying. The set of controllers considered is restricted to those which ensure the closed-loop characteristic polynomial is affine in the parameter. This allows stability results for the case when the parameter is time-varying to be inferred from stability properties applying for time-frozen values of the parameter. The proposed design procedures and conditions for a parameter-dependent controller design are illustrated on a practical design problem.

LMI-based gain scheduled controller synthesis for a class of linear parameter varying systems

Abstract: Times Cited: 0 Francis, BA Smith, MC Willems, JC Workshop on Control of Uncertain Systems Apr 21-22, 2006 Univ Cambridge, St Johns & Gonville & Caius Coll, Cambridge, ENGLAND

Reaching a Consensus in the Face of Measurement Delays

Abstract: An oil spill skimmer is disclosed. The skimmer is designed to be arranged quickly on an oil-spilled area upon an oil spill accident, thereby quickly recovering oil from water while restricting a spread of oil over a wide area. In the skimmer, upper and lower housings are arranged in the top and bottom of the skimmer, with a plurality of anteflex wings being regularly arranged in a space formed between the two housings. A power chamber is concentrically positioned inside the lower housing and acts as a main buoyancy chamber of the skimmer. In the operation of the skimmer, an oil slick and an oil-water mixture are introduced into the interior of the lower housing through associated suction pipes while being pumped by associated pumps, thus individually forming a jet allowing the skimmer to be rotatable. In addition, an external blade, mounted to the outside end of one anteflex wing, allows the skimmer to eccentrically rotate and move around within an oil-spilled area when the skimmer rotates due to the jet. In the lower housing, oil is separated from water by a plurality of separation panels capable of separating the oil from the water using a difference in volume ratio between the oil and the water.