Graph invariants for unique localizability in cooperative localization of wireless sensor networks: rigidity index and redundancy index

Rigidity theory enables us to specify the conditions of unique localizability in the cooperative localization problem of wireless sensor networks. This paper presents a combinatorial rigidity approach to measure (i) generic rigidity and (ii) generalized redundant rigidity properties of graph structures through graph invariants for the localization problem in wireless sensor networks. We define the rigidity index as a graph invariant based on independent set of edges in the rigidity matroid. It has a value between 0 and 1, and it indicates how close we are to rigidity. Redundant rigidity is required for global rigidity, which is associated with unique realization of graphs. Moreover, redundant rigidity also provides rigidity robustness in networked systems against structural changes, such as link losses. Here, we give a broader definition of redundant edge that we call the "generalized redundant edge." This definition of redundancy is valid for both rigid and non-rigid graphs. Next, we define the redundancy index as a graph invariant based on generalized redundant edges in the rigidity matroid. It also has a value between 0 and 1, and it indicates the percentage of redundancy in a graph. These two indices allow us to explore the transition from non-rigidity to rigidity and the transition from rigidity to redundant rigidity. Examples on graphs are provided to demonstrate this approach. From a sensor network point of view, these two indices enable us to evaluate the effects of sensing radii of sensors on the rigidity properties of networks, which in turn, allow us to examine the localizability of sensor networks. We evaluate the required changes in sensing radii for localizability by means of the rigidity index and the redundancy index using random geometric graphs in simulations.Comment: 13 pages, 7 figures, to be submitted for possible journal publicatio

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

A distributed optimization framework for localization and formation control: applications to vision-based measurements

Multiagent systems have been a major area of research for the last 15 years. This interest has been motivated by tasks that can be executed more rapidly in a collaborative manner or that are nearly impossible to carry out otherwise. To be effective, the agents need to have the notion of a common goal shared by the entire network (for instance, a desired formation) and individual control laws to realize the goal. The common goal is typically centralized, in the sense that it involves the state of all the agents at the same time. On the other hand, it is often desirable to have individual control laws that are distributed, in the sense that the desired action of an agent depends only on the measurements and states available at the node and at a small number of neighbors. This is an attractive quality because it implies an overall system that is modular and intrinsically more robust to communication delays and node failures

Localizability Optimization for Multi Robot Systems and Applications to Ultra-Wide Band Positioning

RÉSUMÉ: RÉSUMÉ Les Systèmes Multi-Robots (SMR) permettent d’effectuer des missions de manière efficace et robuste du fait de leur redondance. Cependant, les robots étant des véhicules autonomes, ils nécessitent un positionnement précis en temps réel. Les techniques de localisation qui utilisent des Mesures Relatives (MR) entre les robots, pouvant être des distances ou des angles, sont particulièrement adaptées puisqu’elles peuvent bénéficier d’algorithmes coopératifs au sein du SMR afin d’améliorer la précision pour l’ensemble des robots. Dans cette thèse, nous proposons des stratégies pour améliorer la localisabilité des SMR, qui est fonction de deux facteurs. Premièrement, la géométrie du SMR influence fondamentalement la qualité de son positionnement pour des MR bruitées. Deuxièmement, les erreurs de mesures dépendent fortement de la technologie utilisée. Dans nos expériences, nous nous focalisons sur la technologie UWB (Ultra-Wide Band), qui est populaire pour le positionnement des robots en environnement intérieur en raison de son coût modéré et sa haute précision. Par conséquent, une partie de notre travail est consacrée à la correction des erreurs de mesure UWB afin de fournir un système de navigation opérationnel. En particulier, nous proposons une méthode de calibration des biais systématiques et un algorithme d’atténuation des trajets multiples pour les mesures de distance en milieu intérieur. Ensuite, nous proposons des Fonctions de Coût de Localisabilité (FCL) pour caractériser la géométrie du SMR, et sa capacité à se localiser. Pour cela, nous utilisons la Borne Inférieure de Cramér-Rao (BICR) en vue de quantifier les incertitudes de positionnement. Par la suite, nous fournissons des schémas d’optimisation décentralisés pour les FCL sous l’hypothèse de MR gaussiennes ou log-normales. En effet, puisque le SMR peut se déplacer, certains de ses robots peuvent être déployés afin de minimiser la FCL. Cependant, l’optimisation de la localisabilité doit être décentralisée pour être adaptée à des SMRs à grande échelle. Nous proposons également des extensions des FCL à des scénarios où les robots embarquent plusieurs capteurs, où les mesures se dégradent avec la distance, ou encore où des informations préalables sur la localisation des robots sont disponibles, permettant d’utiliser la BICR bayésienne. Ce dernier résultat est appliqué au placement d’ancres statiques connaissant la distribution statistique des MR et au maintien de la localisabilité des robots qui se localisent par filtrage de Kalman. Les contributions théoriques de notre travail ont été validées à la fois par des simulations à grande échelle et des expériences utilisant des SMR terrestres. Ce manuscrit est rédigé par publication, il est constitué de quatre articles évalués par des pairs et d’un chapitre supplémentaire. ABSTRACT: ABSTRACT Multi-Robot Systems (MRS) are increasingly interesting to perform tasks eÿciently and robustly. However, since the robots are autonomous vehicles, they require accurate real-time positioning. Localization techniques that use relative measurements (RMs), i.e., distances or angles, between the robots are particularly suitable because they can take advantage of cooperative schemes within the MRS in order to enhance the precision of its positioning. In this thesis, we propose strategies to improve the localizability of the SMR, which is a function of two factors. First, the geometry of the MRS fundamentally influences the quality of its positioning under noisy RMs. Second, the measurement errors are strongly influenced by the technology chosen to gather the RMs. In our experiments, we focus on the Ultra-Wide Band (UWB) technology, which is popular for indoor robot positioning because of its mod-erate cost and high accuracy. Therefore, one part of our work is dedicated to correcting the UWB measurement errors in order to provide an operable navigation system. In particular, we propose a calibration method for systematic biases and a multi-path mitigation algorithm for indoor distance measurements. Then, we propose Localizability Cost Functions (LCF) to characterize the MRS’s geometry, using the Cramér-Rao Lower Bound (CRLB) as a proxy to quantify the positioning uncertainties. Subsequently, we provide decentralized optimization schemes for the LCF under an assumption of Gaussian or Log-Normal RMs. Indeed, since the MRS can move, some of its robots can be deployed in order to decrease the LCF. However, the optimization of the localizability must be decentralized for large-scale MRS. We also propose extensions of LCFs to scenarios where robots carry multiple sensors, where the RMs deteriorate with distance, and finally, where prior information on the robots’ localization is available, allowing the use of the Bayesian CRLB. The latter result is applied to static anchor placement knowing the statistical distribution of the MRS and localizability maintenance of robots using Kalman filtering. The theoretical contributions of our work have been validated both through large-scale simulations and experiments using ground MRS. This manuscript is written by publication, it contains four peer-reviewed articles and an additional chapter

Network-centric methods for heterogeneous multiagent systems

We present tools for a network topology based characterization of heterogeneity in multiagent systems, thereby providing a framework for the analysis and design of heterogeneous multiagent networks from a network structure view-point. In heterogeneous networks, agents with a diverse set of resources coordinate with each other. Coordination among different agents and the structure of the underlying network topology have significant impacts on the overall behavior and functionality of the system. Using constructs from graph theory, a qualitative as well as a quantitative analysis is performed to examine an inter-relationship between the network topology and the distribution of agents with various capabilities in heterogeneous networks. Our goal is to allow agents maximally exploit heterogeneous resources available within the network through local interactions, thus exploring a promise heterogeneous networks hold to accomplish complicated tasks by leveraging upon the assorted capabilities of agents. For a reliable operations of such systems, the issue of security against intrusions and malicious agents is also addressed. We provide a scheme to secure a network against a sequence of intruder attacks through a set of heterogeneous guards. Moreover, robustness of networked systems against noise corruption and structural changes in the underlying network topology is also examined.Ph.D

Information-theoretic Reasoning in Distributed and Autonomous Systems

The increasing prevalence of distributed and autonomous systems is transforming decision making in industries as diverse as agriculture, environmental monitoring, and healthcare. Despite significant efforts, challenges remain in robustly planning under uncertainty. In this thesis, we present a number of information-theoretic decision rules for improving the analysis and control of complex adaptive systems. We begin with the problem of quantifying the data storage (memory) and transfer (communication) within information processing systems. We develop an information-theoretic framework to study nonlinear interactions within cooperative and adversarial scenarios, solely from observations of each agent's dynamics. This framework is applied to simulations of robotic soccer games, where the measures reveal insights into team performance, including correlations of the information dynamics to the scoreline. We then study the communication between processes with latent nonlinear dynamics that are observed only through a filter. By using methods from differential topology, we show that the information-theoretic measures commonly used to infer communication in observed systems can also be used in certain partially observed systems. For robotic environmental monitoring, the quality of data depends on the placement of sensors. These locations can be improved by either better estimating the quality of future viewpoints or by a team of robots operating concurrently. By robustly handling the uncertainty of sensor model measurements, we are able to present the first end-to-end robotic system for autonomously tracking small dynamic animals, with a performance comparable to human trackers. We then solve the issue of coordinating multi-robot systems through distributed optimisation techniques. These allow us to develop non-myopic robot trajectories for these tasks and, importantly, show that these algorithms provide guarantees for convergence rates to the optimal payoff sequence