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

Eren, Tolga; Whiteley, Walter; Morse, A. Stephen; Belhumeur, Peter N.; Anderson, Brian D. O.

doi:10.1109/cdc.2003.1273093

Cited by 90 publications

(120 citation statements)

References 6 publications

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“…It is well known that first-order rigidity implies all of the other standard forms of rigidity for a formation, but the converse can fail [18], [43], [53]. For readers thinking of other concepts of rigidity, we point out that if one of these alternative forms of rigidity holds for a non-empty open set, then all of the properties in Theorem 3 hold [43], [53].…”

Section: A Rigiditymentioning

confidence: 84%

“…In this paper, we have drawn on techniques and results from the first two fields, also combined in some previous joint work [18], as well as specific results on global rigidity [12], [30]. With these concepts, we were able to lay a coherent solid foundation for the underlying problem of when a network is uniquely localizable, for almost all configurations of the points.…”

Section: Discussionmentioning

confidence: 99%

“…give new insights where certain patterns of angles or headings are used [18], as well as insights into the complexity of general patterns of angle constraints. This will be explored further in a future paper.…”

Section: Discussionmentioning

confidence: 99%

“…It is possible to derive useful sufficient conditions and inductive constructions for generically globally rigid graphs in spaces of all dimensions [12], [18].…”

Section: Inductive Construction Of Generically Globally Rigid Graphsmentioning

confidence: 99%

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A Theory of Network Localization

Aspnes

Eren

Goldenberg

et al. 2006

IEEE Trans. on Mobile Comput.

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563

396

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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.

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Section: A Rigiditymentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…It is possible to derive useful sufficient conditions and inductive constructions for generically globally rigid graphs in spaces of all dimensions [12], [18].…”

Section: Inductive Construction Of Generically Globally Rigid Graphsmentioning

confidence: 99%

See 2 more Smart Citations

A Theory of Network Localization

Aspnes

Eren

Goldenberg

et al. 2006

IEEE Trans. on Mobile Comput.

Self Cite

563

396

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show abstract

“…As far as bearing rigidity in R 2 (or parallel rigidity) is concerned, it is determined by the definition of normal constraints over the directions of neighboring agents, namely the edges of the sensing/communication graph associated to the framework, as explained in [8]- [13]. These constraints entail the preservation of the angles formed between pairs of agents and the lines joining them, i.e., the inter-agent bearings.…”

Section: Introductionmentioning

confidence: 99%

Bearing rigidity theory in SE(3)

Michieletto

Cenedese

Franchi

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-Rigidity theory has recently emerged as an efficient tool in the control field of coordinated multi-agent systems, such as multi-robot formations and UAVs swarms, that are characterized by sensing, communication and movement capabilities. This work aims at describing the rigidity properties for frameworks embedded in the three-dimensional Special Euclidean space SE(3) wherein each agent has 6DoF. In such scenario, it is assumed that the devices are able to gather bearing measurements w.r.t. their neighbors, expressing them into their own body frame. The goal is then to identify the framework transformations that allow to preserve such measurements maintaining it rigid. Rigidity properties are mathematically formalized in this work which differs from the previous ones as it faces the extension in three-dimensional space dealing with the 3D rotations manifold. In particular, the attention is focused on the infinitesimal SE(3)-rigidity for which a necessary and sufficient condition is provided.

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Bearing‐based autonomous communication relay positioning under field‐of‐view constraints

Fabris

Zelazo

2022

Adv Control Appl

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This article investigates the problem of communication relay establishment for multiple agent‐based mobile units using a relay vehicle. The objective is to drive autonomously the relay vehicle to attain a position for communication relay establishment while maintaining the other vehicles inside of its field‐of‐view. A bearing‐based control law is proposed for the relay drone and designed for both single and multiple agents. We also provide a collision avoidance scheme that ensures no collisions between the relay and other agents. Numerical simulations and experimental results are reported as well to show the efficacy of the proposed approach.

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

Cited by 90 publications

References 6 publications

A Theory of Network Localization

A Theory of Network Localization

Bearing rigidity theory in SE(3)

Bearing‐based autonomous communication relay positioning under field‐of‐view constraints

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