Tolga Eren

A Theory of Network Localization

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

Rigidity, computation, and randomization in network localization

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.

A FRAMEWORK FOR MAINTAINING FORMATIONS BASED ON RIGIDITY

In this paper, a framework for maintaining formations of large number of mobile autonomous vehicles based on rigidity is proposed. The aim of this paper is to explore strategies for maintaining formations with more limited communi- cation/sensing requirements. An inductive construction method for provably rigid formations is proposed, and a method for optimum angle measures between vehicles is developed. The method scales with the number of vehicles and is ∞exible to support many rigid formation shapes. Copyright c ∞2002 IFAC

Closing ranks in vehicle formations based on rigidity

In this paper, a systematic way of maintaining rigidity in case of vehicle removals in formations for coordinating mobile autonomous vehicles with limited communication/sensing links is presented. The main concern is the minimal rearrangement of links in such a way that the links that have not been removed are preserved as they are, and the minimum number of new links are created in the formation to maintain rigidity. The problem is solved by the tools used in the Henneberg method. This method gives us provably rigid formations with the minimum number of links. The proposed framework meets this challenge for removed vehicles with any number of links in both 2 and 3-space. The same problem is also considered for the minimal Delaunay edge formations, which is a special class of the formations created by the Henneberg method with some geometrical properties.

Graphical properties of easily localizable sensor networks

The sensor network localization problem is one of determining the Euclidean positions of all sensors in a network given knowledge of the Euclidean positions of some, and knowledge of a number of inter-sensor distances. This paper identifies graphical properties which can ensure unique localizability, and further sets of properties which can ensure not only unique localizability but also provide guarantees on the associated computational complexity, which can even be linear in the number of sensors on occasions. Sensor networks with minimal connectedness properties in which sensor transmit powers can be increased to increase the sensing radius lend themselves to the acquiring of the needed graphical properties. Results are presented for networks in both two and three dimensions.

Sensor and network topologies of formations with direction, bearing, and angle information between agents

Sensor and network topologies of formations of autonomous agents are considered. The aim of the paper is to suggest an approach for such topologies for formations with direction, bearing and angle information between agents in the plane and in 3-space. A number of results are translated from prior work in this field and in the study of constraints in CAD programming, in rigidity theory, in structural engineering and in discrete mathematics. Some new results are presented both for the plane and for 3-space. A number of unsolved problems are also mentioned.

Information structures to secure control of rigid formations with leader-follower architecture

This paper is concerned with rigid formations of mobile autonomous agents that have leader-follower architecture. In a previous paper, Baillieul and Suri gave a proposition as a necessary condition for stable rigidity. They also gave a separate theorem as a sufficient condition for stable rigidity. This paper suggests an approach to analyze rigid formations that have leader-follower architecture. It proves that the third condition in the proposition given by Baillieul and Suri is redundant, and it proves that this proposition is a necessary and sufficient condition for stable rigidity. Simulation results are also presented to illustrate rigidity.

Further results on sensor network localization using rigidity

Two further results, which extend the previous work on the use of rigidity in sensor network localization, are given. The previous work provided the conditions for the localization of an entire network in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. First, the paper gives the conditions for partial localization of a subnetwork when an entire network is not localizable. Second, the paper gives the conditions for localization in which some nodes know their locations and other nodes determine their locations by measuring the bearings (angle of arrivals) to their neighbors rather than the distances.

Merging Globally Rigid Formations of Mobile Autonomous Agents

This paper focuses on developing techniques and strategies for the analysis and design of sensor and network topologies required to merge globally rigid formations for cooperative tasks. Central to the development of these techniques and strategies is the use of tools from rigidity theory, and graph theory.

A Theoretical Analysis of the Conditions for Unambiguous Node Localization in Sensor Networks

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 distances or bearings to their neighbors. Distance information is the separation between two nodes connected by a sensing/communication link. Bearing is the angle between a sensing/communication link and the x-axis of a node’s local coordinate system. We construct grounded graphs to model network localization and apply graph rigidity theory and parallel drawings to test the conditions for unique localizability and to construct uniquely localizable networks. We further investigate partially localizable networks.