Distributed combinatorial rigidity control in multi-agent networks

Williams, Ryan K.; Gasparri, Andrea; Priolo, Attilio; Sukhatme, Gaurav S.

doi:10.1109/cdc.2013.6760847

Cited by 18 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recent works introducing the rigidity theory into formation control has also provided provably correct methods to model and analyze the ad hoc network topologies within robotic teams [11][12][13][14][15]. For example, rigidity theory provides us tools for formation control using relative distance measurements instead of relative position measurements.…”

Section: Introductionmentioning

confidence: 99%

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

Eren

2016

Ad Hoc Networks

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Eren

2016

Ad Hoc Networks

View full text Add to dashboard Cite

show abstract

“…Definition 1 (Worst-case graph, [36]). Assume we have a topological constraint 2 , P, and a known space of reachable topologies G C (t) in which the network graph must lie, G(t) ∈ G C (t), for all t ≥ 0.…”

Section: Control Stability Analysismentioning

confidence: 99%

Global connectivity control for spatially interacting multi-robot systems with unicycle kinematics

Williams

Gasparri

Sukhatme

et al. 2015

2015 IEEE International Conference on Robotics and Automation (ICRA)

Self Cite

View full text Add to dashboard Cite

In this paper, we consider the problem of connectivity maintenance in multi-robot systems with unicycle kinematics. While previous work has approached this problem through local control techniques, we propose a solution which achieves global connectivity maintenance under nonholonomic constraints. In addition, our formulation only requires intermittent estimation of algebraic connectivity, and accommodates discontinuous spatial interactions among robots. Specifically, we extend a decision-based link maintenance framework to unicycle kinematics and discontinuous potential-based interaction, by exploiting techniques from nonsmooth analysis. Then, we couple this extension with an existing connectivity estimation technique which yields an estimate with tunable precision in finite time, achieving our result. To illustrate the correctness of our methods, we provide a brief simulation result that closes the paper

show abstract

“…Since rigidity is a desired property of networked systems, important efforts have been made towards control strategies for maintaining or recovering rigidity in networks with dynamic topology. The strategies adopted in earlier work can be classified as continuum [5]- [7] or combinatorial [8], [9]. Nevertheless, to develop fully decentralized algorithms is a common difficulty.…”

Section: Introductionmentioning

confidence: 99%

“…A combinatorial approach to rigidity maintenance was developed in [8]. Local rules for link addition and deletion are employed to dictate the robots' movements to preserve rigidity.…”

Section: Introductionmentioning

confidence: 99%

Subframework-Based Rigidity Control in Multirobot Networks

Presenza,

Alvarez-Hamelin,

Mas

et al. 2021

Preprint

View full text Add to dashboard Cite

This paper presents an alternative approach for analyzing distance-based rigidity in networks of mobile agents, based on a subframework scheme. The advantage of this point of view lies in expressing framework rigidity, which is inherently global, as a localized property. Also, we show that a framework's normalized rigidity eigenvalue degrades as its graph diameter increases. Thus, the rigidity eigenvalues associated to the subframeworks arise naturally as localized rigidity metrics. A decentralized subframework-based controller for maintaining rigidity using only range measurements is developed, which is also aimed to minimize the network's communication load. Finally, we show that the information exchange required by the controller is completed in a finite number of iterations, showing the convenience of the proposed scheme.

show abstract

Distributed combinatorial rigidity control in multi-agent networks

Cited by 18 publications

References 25 publications

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

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

Global connectivity control for spatially interacting multi-robot systems with unicycle kinematics

Subframework-Based Rigidity Control in Multirobot Networks

Contact Info

Product

Resources

About