Equilibria and steering laws for planar formations

The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.

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“…For simplicity, we assume that all particles have unit speed. The particle kinematics are then given by (Justh and Krishnaprasad, 2004)…”

Section: Flocking Schooling and Vehicle Coordinationmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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“…For instance, a continuous model of particles moving at constant speed in the plane with steering control (heading rate) designed to couple the dynamics of the particles has been used for stabilization of circular and parallel collective motion [4,5]. The use of the same kinds of models in the engineered and natural settings is no accident.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Decision Making in Animal Group Motion

et al. 2009

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We present a continuous model of a multi-agent system motivated by simulation studies on dynamics of decision making in animal groups in motion. Each individual moves at constant speed in the plane and adjusts its heading in response to relative headings of others in the population. Two subgroups of the population are informed such that individuals in each subgroup have a preferred direction of motion. The model exhibits fast and slow time scales allowing for a reduction in the dimension of the problem. The stable solutions for the reduced model correspond to compromise by individuals with conflicting preferences. We study the global phase space for the proposed reduced model by computing equilibria and proving stability and bifurcations.

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“…Consensus on the circle is called synchronization, and it has been studied extensively in the context of coupled phase oscillators used to model a variety of interconnected periodic processes in biology and physics (e.g., firefly flashing and neuron firing) [80,81]. Justh and Krishnaprasad developed a geometric framework to design steering control laws to coordinate the motion of vehicles in [82]. This approach was generalized in the work of Sepulchre et al [83,84] using a model that extends coupled oscillator dynamics, in which the phase of each oscillator represents the direction of motion of a vehicle, to include the spatial dimensions, which represent the positions of the vehicles.…”

Section: Background and Historymentioning

confidence: 99%

Cooperative Vehicle Environmental Monitoring

Leonard

2016

Springer Handbook of Ocean Engineering

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Over the last decade, methodologies for automated cooperative control of robotic vehicles have been designed, deployed and proven to provide efficient, reliable, and sustained monitoring of the uncertain and inhospitable ocean environment. Unprecedented data sets have been collected from deployments of cooperative vehicles in the field, and both real-time and post-deployment analyses have led to new understanding of the environment. This first decade of success in cooperative vehicle environmental monitoring sets the stage for new opportunities and future gain, especially as the development of cooperative control methodologies can continue to leverage ongoing technological and scientific advances in underwater communication and sensing, energy and computational efficiency, vehicle size, speed, maneuverability and cost, and ocean modeling and prediction.Indeed, the demonstrated potential of cooperative vehicle control has led to increased demand for fleets of autonomous underwater vehicles (AUVs) for use in measuring ocean physics, biology, chemistry and geology to improve understanding of natural dynamics and human-influenced changes in the marine environment. Further, methodologies for cooperative control of robotic vehicles in the ocean are readily adaptable to applications on land, in the air and in space; likewise, there is much to be learned from developments in these other domains. The recent explosion in research on networks and complex systems, including investigation of mechanisms that explain a "collective intelligence" exhibited by animal aggregations on the move, are also being leveraged to advance design of cooperative vehicle dynamics.For environmental monitoring to be successful, physical, chemical, and biological variables must be measured across a range of spatial and temporal scales; in the ocean the monitoring strategy must also contend with a harsh, three-dimensional physical space that is highly uncertain and dynamic. Small spatial and temporal scales associated with the measured variables typically make a stationary sensor array impractical because a very large number of sensors would be needed to get sufficient resolution in space and/or time. An array of mobile sensors, however, may be very well suited to such a challenge since mobility can be exploited to dynamically distribute fewer sensors according to the spatial and temporal scales.The underlying principle of cooperative control of vehicles for environmental monitoring leverages mobility of sensors and uses an interacting dynamic among the individual sensors to yield a collective behavior that performs better than the sum of the parts. If the vehicles can communicate their state or measure the relative state of others in the team, then they can cooperate and the cooperative vehicle dynamics can provide coordinated motion of the team as a whole. The resulting vehicle network functions as a dynamically reconfigurable sensor array with a capability for high performance in environmental monitoring not available at the level of individual...

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Equilibria and steering laws for planar formations

Cited by 335 publications

References 16 publications

Synchronization in complex networks of phase oscillators: A survey

Synchronization in complex networks of phase oscillators: A survey

Dynamics of Decision Making in Animal Group Motion

Cooperative Vehicle Environmental Monitoring

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