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296
The hydrodynamics of swimming microorganisms
 Reports on Progress in Physics
, 2009
"... Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below. A ..."
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Cited by 72 (13 self)
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Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below. At this scale, inertia is unimportant and the Reynolds number is small. Our emphasis is on the simple physical picture and fundamental flow physics phenomena in this regime. We first give a brief overview of the mechanisms for swimming motility, and of the basic properties of flows at low Reynolds number, paying special attention to aspects most relevant for swimming such as resistance matrices for solid bodies, flow singularities and kinematic requirements for net translation. Then we review classical theoretical work on cell motility, in particular early calculations of swimming kinematics with prescribed stroke and the application of resistive force theory and slenderbody theory to flagellar locomotion. After examining the physical means by which flagella are actuated, we outline areas of active research, including hydrodynamic interactions, biological locomotion in complex fluids, the design of smallscale artificial swimmers and the optimization of locomotion strategies.
Stable concurrent synchronization in dynamic system networks
 Neural Networks
, 2007
"... In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple “rhythms ” interacting and functional assemblies combining neural oscillators of ..."
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Cited by 47 (23 self)
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In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple “rhythms ” interacting and functional assemblies combining neural oscillators of many different types. Mathematically, stable concurrent synchronization corresponds to convergence to a flowinvariant linear subspace of the global state space. We derive a general condition for such convergence to occur globally and exponentially. We also show that, under mild conditions, global convergence to a concurrently synchronized regime is preserved under basic system combinations such as negative feedback or hierarchies, so that stable concurrently synchronized aggregates of arbitrary size can be constructed. Simple applications of these results to classical questions in systems neuroscience and robotics are discussed. 1
Graph theory and networks in biology
 IET Systems Biology, 1:89 – 119
, 2007
"... In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarch ..."
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Cited by 44 (0 self)
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In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation. 1
State agreement for continuoustime coupled nonlinear systems
 SIAM Journal on Control and Optimization
, 2007
"... Abstract. Two related problems are treated in continuous time. First, the state agreement problem is studied for coupled nonlinear differential equations. The vector fields can switch within a finite family. Associated to each vector field is a directed graph based in a natural way on the interactio ..."
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Cited by 42 (2 self)
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Abstract. Two related problems are treated in continuous time. First, the state agreement problem is studied for coupled nonlinear differential equations. The vector fields can switch within a finite family. Associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems. Generalizing the work of Moreau, under the assumption that the vector fields satisfy a certain subtangentiality condition, it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time. The proof uses nonsmooth analysis. Secondly, the rendezvous problem for kinematic pointmass mobile robots is studied when the robots ’ fields of view have a fixed radius. The circumcenter control law of Ando et al. [1] is shown to solve the problem. The rendezvous problem is a kind of state agreement problem, but the interaction structure is state dependent.
Distributed control of robotic networks: a mathematical approach to motion coordination algorithms
, 2009
"... (i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 ..."
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Cited by 38 (1 self)
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(i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 “Distributed Control of Robotic Networks ” by F. Bullo, J. Cortés and S. Martínez
Collective motion and oscillator synchronization
 Proc. Block Island Workshop on Cooperative Control
, 2003
"... Summary. This paper studies connections between phase models of coupled oscillators and kinematic models of groups of selfpropelled particles. These connections are exploited in the analysis and design of feedback control laws for the individuals that stabilize collective motions for the group. 1 ..."
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Cited by 36 (9 self)
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Summary. This paper studies connections between phase models of coupled oscillators and kinematic models of groups of selfpropelled particles. These connections are exploited in the analysis and design of feedback control laws for the individuals that stabilize collective motions for the group. 1
Distributed geodesic control laws for flocking of nonholonomic agents
 IEEE Transaction on Automatic Control
, 2005
"... Abstract—We study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions. By analyzing the velocity vectors of agents on a circle (for planar motion) or sphere (for 3D motion), we develop a geodesic control law that minimizes a misalignment ..."
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Cited by 35 (6 self)
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Abstract—We study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions. By analyzing the velocity vectors of agents on a circle (for planar motion) or sphere (for 3D motion), we develop a geodesic control law that minimizes a misalignment potential and results in velocity alignment and flocking. The proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected. We further show that flocking is possible even when the topology of the proximity graph changes over time, so long as a weaker notion of joint connectivity is preserved. Index Terms—Cooperative control, distributed coordination, flocking, multiagent systems. I.
Passivitybased control of multiagent systems
 ADVANCES IN ROBOT CONTROL: FROM EVERYDAY PHYSICS TO HUMANLIKE MOVEMENTS
"... In this paper we study passivitybased control for the problem of coordination and synchronization of multiagent systems. We treat agents described by affine nonlinear systems that are inputoutput passive and that exchange information over a network described by an interconnection graph. We tre ..."
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Cited by 33 (2 self)
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In this paper we study passivitybased control for the problem of coordination and synchronization of multiagent systems. We treat agents described by affine nonlinear systems that are inputoutput passive and that exchange information over a network described by an interconnection graph. We treat both linear interconnections on balanced, directed graphs and nonlinear interconnections on undirected graphs. We present synchronization results for both fixed and switching graphs. Finally, we treat the realistic case of time delay in the communication of information among agents. Our results unify several existing results from the literature on multiagent systems. As applications of our results we present a constructive methodology to solve the local exponential convergence problem for Kuramoto oscillators. We then apply our results to the general problem of synchronization of multiple Lagrangian systems. Using a network of simple pendula, the phenomena of oscillator death, synchronization, and antisynchronization are all shown to be special cases of our results, depending on whether or not the natural frequencies of the pendula are identical or distinct. We also show that the general problem of multirobot coordination can be handled using the results in this paper.
VisionBased, Distributed Control Laws for Motion Coordination of Nonholonomic Robots
 ACCEPTED FOR PUBLICATION IN IEEE TRANSACTIONS ON ROBOTICS
"... We study the problem of distributed motion coordination among a group of planar nonholonomic agents. Inspired by social aggregation phenomena such as flocking and schooling in birds and fish, we develop visionbased control laws for parallel and circular formations using a consensus approach. The pr ..."
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Cited by 29 (3 self)
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We study the problem of distributed motion coordination among a group of planar nonholonomic agents. Inspired by social aggregation phenomena such as flocking and schooling in birds and fish, we develop visionbased control laws for parallel and circular formations using a consensus approach. The proposed control laws are distributed, in the sense that only information from neighboring agents are included. Furthermore, the control laws are coordinatefree and do not rely on measurement or communication of heading information among neighbors, but instead require measurements of bearing, optical flow and timetocollision, all of which can be measured using vision. Collision avoidance capabilities are added to the team members and the effectiveness of the control laws are demonstrated on a group of mobile robots.