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117
Central pattern generators for locomotion control in animals and robots: a review
 NEURAL NETWORKS
, 2008
"... The problem of controlling locomotion is an area in which neuroscience and robotics can fruitfully interact. In this article, I will review research carried out on locomotor central pattern generators (CPGs), i.e. neural circuits capable of producing coordinated patterns of highdimensional rhythmic ..."
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Cited by 151 (20 self)
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The problem of controlling locomotion is an area in which neuroscience and robotics can fruitfully interact. In this article, I will review research carried out on locomotor central pattern generators (CPGs), i.e. neural circuits capable of producing coordinated patterns of highdimensional rhythmic output signals while receiving only simple, lowdimensional, input signals. The review will first cover neurobiological observations concerning locomotor CPGs and their numerical modelling, with a special focus on vertebrates. It will then cover how CPG models implemented as neural networks or systems of coupled oscillators can be used in robotics for controlling the locomotion of articulated robots. The review also presents how robots can be used as scientific tools to obtain a better understanding of the functioning of biological CPGs. Finally, various methods for designing CPGs to control specific modes of locomotion will be briefly reviewed. In this process, I will discuss different types of CPG models, the pros and cons of using CPGs with robots, and the pros and cons of using robots as scientific tools. Open research topics both in biology and in robotics will also be discussed. 1
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 49 (24 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
Decentralized, Adaptive Coverage Control for Networked Robots
, 2007
"... A decentralized, adaptive control law is presented to drive a network of mobile robots to an optimal sensing configuration. The control law is adaptive in that it uses sensor measurements to learn an approximation of the distribution of sensory information in the environment. It is decentralized in ..."
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Cited by 44 (7 self)
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A decentralized, adaptive control law is presented to drive a network of mobile robots to an optimal sensing configuration. The control law is adaptive in that it uses sensor measurements to learn an approximation of the distribution of sensory information in the environment. It is decentralized in that it requires only information local to each robot. The controller is then improved upon by implementing a consensus algorithm in parallel with the learning algorithm, greatly increasing parameter convergence rates. Convergence and consensus of parameters is proven. Finally, several variations on the learning algorithm are explored with a discussion of their stability in closed loop. The controller with and without parameter consensus is demonstrated in numerical simulations. These techniques are suggestive of broader applications of adaptive control methodologies to decentralized control problems in unknown dynamical environments. 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.
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 31 (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.
Decentralized, adaptive control for coverage with networked robots
 In Robotics and Automation, 2007 IEEE International Conference on
, 2007
"... AbstractA decentralized, adaptive control law is presented to drive a network of mobile robots to a nearoptimal sensing configuration. The control law is adaptive in that it integrates sensor measurements to provide a converging estimate of the distribution of sensory information in the environme ..."
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Cited by 31 (10 self)
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AbstractA decentralized, adaptive control law is presented to drive a network of mobile robots to a nearoptimal sensing configuration. The control law is adaptive in that it integrates sensor measurements to provide a converging estimate of the distribution of sensory information in the environment. It is decentralized in that it requires only information local to each robot. A Lyapunovtype proof is used to show that the control law causes the network to converge to a nearoptimal sensing configuration, and the controller is demonstrated in numerical simulations. This technique suggests a broader application of adaptive control methodologies to decentralized control problems in unknown dynamical environments.
Contraction Analysis of TimeDelayed Communications Using Simplified Wave Variables
 PS/0512070
, 2005
"... We study stability of interacting nonlinear systems with timedelayed communications, using contraction theory and a simplified wave variable design inspired by robotic teleoperation. We show that contraction is preserved through specific timedelayed feedback communications, and that this property ..."
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Cited by 29 (6 self)
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We study stability of interacting nonlinear systems with timedelayed communications, using contraction theory and a simplified wave variable design inspired by robotic teleoperation. We show that contraction is preserved through specific timedelayed feedback communications, and that this property is independent of the values of the delays. The approach is then applied to group cooperation with linear protocols, where it shown that synchronization can be made robust to arbitrary time delays. 1
Global entrainment of transcriptional systems to periodic inputs
, 2009
"... This paper addresses the problem of providing mathematical conditions that allow one to ensure that biological networks, such as transcriptional systems, can be globally entrained to external periodic inputs. Despite appearing obvious at first, this is by no means a generic property of nonlinear dyn ..."
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Cited by 26 (5 self)
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This paper addresses the problem of providing mathematical conditions that allow one to ensure that biological networks, such as transcriptional systems, can be globally entrained to external periodic inputs. Despite appearing obvious at first, this is by no means a generic property of nonlinear dynamical systems. Through the use of contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all their solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific cases of models of transcriptional systems as well as constructs of interest in synthetic biology. A selfcontained exposition of all needed results is given in the paper. Author Summary The activities of all living organisms are governed by complex sets of finely regulated biochemical reactions. Often, entrainment to certain external forcing signals helps control the timing and sequencing of reactions. For example, human activities are clearly regulated by the daynight cycle. That is, humans tend to adapt their function to some “external ” input. An important open problem is to understand the onset of entrainment and under what conditions it can be ensured in the presence of uncertainties, noise, and
A contraction theory approach to stochastic incremental stability
 IEEE Transactions on Automatic Control
, 2009
"... We investigate the incremental stability properties of Itô stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can ..."
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Cited by 19 (8 self)
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We investigate the incremental stability properties of Itô stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noisefree system. We illustrate these results in the contexts of stochastic nonlinear observers design and stochastic synchronization. 1
A theoretical study of different leader roles in networks
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2006
"... We study synchronization conditions for distributed dynamic networks with different types of leaders. The role of a “power ” leader specifying a desired global state trajectory through local interactions has long been recognized and modeled. This paper introduces the complementary notion of a “know ..."
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Cited by 18 (4 self)
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We study synchronization conditions for distributed dynamic networks with different types of leaders. The role of a “power ” leader specifying a desired global state trajectory through local interactions has long been recognized and modeled. This paper introduces the complementary notion of a “knowledge” leader holding information on the target dynamics, which is propagated to the entire network through local adaptation mechanisms. Different types of leaders can coexist in the same network. For instance, in a network of locally connected oscillators, the power leader may set the global phase while the knowledge leader may set the global frequency and the global amplitude. Knowledgebased leaderfollowers networks have many analogs in biology, e.g., in evolutionary processes and disease propagation.