Nonlinear stability of flock solutions in second-order swarming models

Carrillo, José A.; Huang, Yanghong; Martin, Stephan

doi:10.1016/j.nonrwa.2013.12.008

Cited by 48 publications

(56 citation statements)

References 32 publications

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“…[64] illustrate the effect of nonlinearities on the stability of networked systems through bifurcations. Alternate methods for stability analysis include tools from renormalization groups [22] and the theory of normally hyperbolic invariant manifolds [65]. The Laplacian matrix defined above can be replaced by its variant, the edge Laplacian matrix, to solve for stability as well as robustness and optimality [66].…”

Section: F Synchronization and Hierarchical Stability For Swarmsmentioning

confidence: 99%

A Survey on Aerial Swarm Robotics

et al. 2018

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Abstract-The use of aerial swarms to solve real-world problems has been increasing steadily, accompanied by falling prices and improving performance of communication, sensing, and processing hardware. The commoditization of hardware has reduced unit costs, thereby lowering the barriers to entry to the field of aerial swarm robotics. A key enabling technology for swarms is the family of algorithms that allow the individual members of the swarm to communicate and allocate tasks amongst themselves, plan their trajectories, and coordinate their flight in such a way that the overall objectives of the swarm are achieved efficiently. These algorithms, often organized in a hierarchical fashion, endow the swarm with autonomy at every level, and the role of a human operator can be reduced, in principle, to interactions at a higher level without direct intervention. This technology depends on the clever and innovative application of theoretical tools from control and estimation. This paper reviews the state of the art of these theoretical tools, specifically focusing on how they have been developed for, and applied to, aerial swarms. Aerial swarms differ from swarms of ground-based vehicles in two respects: they operate in a three-dimensional (3-D) space, and the dynamics of individual vehicles adds an extra layer of complexity. We review dynamic modeling and conditions for stability and controllability that are essential in order to achieve cooperative flight and distributed sensing. The main sections of the paper focus on major results covering trajectory generation, task allocation, adversarial control, distributed sensing, monitoring, and mapping. Wherever possible, we indicate how the physics and subsystem technologies of aerial robots are brought to bear on these individual areas.

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Section: F Synchronization and Hierarchical Stability For Swarmsmentioning

confidence: 99%

A Survey on Aerial Swarm Robotics

et al. 2018

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“…Flocking dynamics described by Reynolds' rule are known to be asymptotically stable under fairly weak conditions on the topology of the underlying graph [17], [18], [24], [25]. Stronger results, such as exponential stability, have been found for linear time-varying consensus protocol for single integrator systems [26], in the context of synchronization for second-order Euler-Lagrange systems [20]- [22], and using tools from dynamical systems theory for time-invariant, undirected graph topologies in second-order, two-dimensional (2-D) flocking dynamics [27]. Preliminary results on exponential stability of flocks under tree and star topology constraints are presented in [8].…”

Section: A Overview Of the Literaturementioning

confidence: 99%

“…Assumption 1 is satisfied by connected undirected graphs [27] and by strongly connected and balanced digraphs [16].…”

Section: Basis For So(3)mentioning

confidence: 99%

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Robotic Herding of a Flock of Birds Using an Unmanned Aerial Vehicle

et al. 2018

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Abstract-In this paper, we derive an algorithm for enabling a single robotic unmanned aerial vehicle to herd a flock of birds away from a designated volume of space, such as the air space around an airport. The herding algorithm, referred to as the mwaypoint algorithm, is designed using a dynamic model of bird flocking based on Reynolds' rules. We derive bounds on its performance using a combination of reduced-order modeling of the flock's motion, heuristics, and rigorous analysis. A unique contribution of the paper is the experimental demonstration of several facets of the herding algorithm on flocks of live birds reacting to a robotic pursuer. The experiments allow us to estimate several parameters of the flocking model, and especially the interaction between the pursuer and the flock. The herding algorithm is also demonstrated using numerical simulations.

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“…Furthermore, these systems are ubiquitous in mathematical modelling appearing in granular media models [10, 61], swarming models for animal collective behavior [30, 46, 59], equilibrium states for self-assembly and molecules [47, 54, 70, 76], and mean-field games in socioeconomics [17, 43] among others.…”

Section: Introductionmentioning

confidence: 99%

Convergence of a linearly transformed particle method for aggregation equations

et al. 2018

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We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in and norms depending on the regularity of the initial data. Moreover, we give convergence estimates in bounded Lipschitz distance for measure valued solutions. For singular interaction forces, we establish the convergence of the error between the approximated and exact flows up to the existence time of the solutions in norm.

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Nonlinear stability of flock solutions in second-order swarming models

Abstract: 09.10.14 Kb. Ok to add published version to spiral, OA paper under CC b

Cited by 48 publications

References 32 publications

A Survey on Aerial Swarm Robotics

A Survey on Aerial Swarm Robotics

Robotic Herding of a Flock of Birds Using an Unmanned Aerial Vehicle

Convergence of a linearly transformed particle method for aggregation equations

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