Realization of Dynamic Walking and Running of the Quadruped Using Neural Oscillator

In the present study we attempt to induce a quadruped robot to walk dynamically on irregular terrain and run on flat terrain by using a nervous system model. For dynamic walking on irregular terrain, we employ a control system involving a neural oscillator network, a stretch reflex and a flexor reflex. Stable dynamic walking when obstructions to swinging legs are present is made possible by the flexor reflex and the crossed extension reflex. A modification of the single driving input to the neural oscillator network makes it possible for the robot to walk up a step. For running on flat terrain, we combine a spring mechanism and the neural oscillator network. It became clear in this study that the matching of two oscillations by the spring-mass system and the neural oscillator network is important in order to keep jumping in a pronk gait. The present study also shows that entrainment between neural oscillators causes the running gait to change from pronk to bound. This finding renders running fairly easy to attain in a bound gait. It must be noticed that the flexible and robust dynamic walking on irregular terrain and the transition of the running gait are realized by the modification of a few parameters in the neural oscillator network.     

Synchronization and desynchronization in a network of locallycoupled Wilson-Cowan oscillators

A network of Wilson-Cowan (WC) oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a 2D matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piecewise linear approximation to the WC oscillator) synchronizes, and we present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation.     

Separation of speech from interfering sounds based on oscillatorycorrelation

A multistage neural model is proposed for an auditory scene analysis task-segregating speech from interfering sound sources. The core of the model is a two-layer oscillator network that performs stream segregation on the basis of oscillatory correlation. In the oscillatory correlation framework, a stream is represented by a population of synchronized relaxation oscillators, each of which corresponds to an auditory feature, and different streams are represented by desynchronized oscillator populations. Lateral connections between oscillators encode harmonicity, and proximity in frequency and time. Prior to the oscillator network are a model of the auditory periphery and a stage in which mid-level auditory representations are formed. The model has been systematically evaluated using a corpus of voiced speech mixed with interfering sounds, and produces improvements in terms of signal-to-noise ratio for every mixture. A number of issues including biological plausibility and real-time implementation are also discussed.     

A discrete dynamics model for synchronization of pulse-coupledoscillators

Biological information processing systems employ a variety of feature types. It has been postulated that oscillator synchronization is the mechanism for binding these features together to realize coherent perception. A discrete dynamic model of a coupled system of oscillators is presented. The network of oscillators converges to a state where subpopulations of cells become phase synchronized. It has potential applications to describing biological perception as well as for the construction of multifeature pattern recognition systems. It is shown that this model can be used to detect the presence of short line segments in the boundary contour of an object. The Hough transform, which is the standard method for detecting curve segments of a specified shape in an image was found not to be effective for this application. Implementation of the discrete dynamics model of oscillator synchronization is much easier than the differential equation models that have appeared in the literature. A systematic numerical investigation of the convergence properties of the model has been performed and it is shown that the discrete dynamics model can scale up to large number of oscillators.     

On connectedness: a solution based on oscillatory correlation

A long-standing problem in Neural Comp has been the problem of connectedness, first identified by Minsky and Papert (1969). This problem served as the cornerstone for them to establish analytically that perceptrons are fundamentally limited in computing geometrical (topological) properties. A solution to this problem is offered by a different class of neural networks: oscillator networks. To solve the problem, the representation of oscillatory correlation is employed, whereby one pattern is represented as a synchronized block of oscillators and different patterns are represented by distinct blocks that desynchronize from each other. Oscillatory correlation emerges from LEGION (locally excitatory globally inhibitory oscillator network), whose architecture consists of local excitation and global inhibition among neural oscillators. It is further shown that these oscillator networks exhibit sensitivity to topological structure, which may lay a neurocomputational foundation for explaining the psychophysical phenomenon of topological perception.     

Synchronization of nonlinear electronic oscillators for neural computation.

This paper deals with coupled oscillators as the building blocks of a bioinspired computing paradigm and their implementation. In order to accomplish the low-power and fast-processing requirements of autonomous applications, we study the microelectronic analog implementation of physical oscillators, instead of the software computer-simulated implementation. With this aim, the original oscillator has been adapted to a suitable microelectronic form. So as to study the hardware nonlinear oscillators, we propose two macro models, demonstrating that they preserve the synchronization properties. Secondary effects such as mismatch and output delay and their relation to network synchronization are analyzed and discussed. We show the correct operation of the proposed electronic oscillators with simulations and experimental results from a manufactured integrated test circuit. The proposed architecture is intended to perform the scene segmentation stage of an autonomous focal-plane self-contained visual processing system for artificial vision applications.     

Class-E self-oscillation for the transmission of wireless power to implants

This paper develops the concept of Class-E self oscillation for wireless power delivery to implantable sensors with the comparison of several topologies. Power amplifiers and oscillators are considered as two separate blocks in wireless power transmission. By combining these topologies into a self-oscillating power transmitter, greater efficiency can be achieved. Various topologies are compared with measured hardware results, determining that a crystal feedback network provides both accuracy and high power output. A new crystal feedback Class-E self oscillator has been implemented by transmitting power through 2 cm-thick biological tissue. The paper includes a second order modelling and design process that can be used to design a Class-E self oscillator as an inductive power transmitter as well as measured results.     

Range image segmentation using a relaxation oscillator network

A locally excitatory globally inhibitory oscillator network (LEGION) is constructed and applied to range image segmentation, where each oscillator has excitatory lateral connections to the oscillators in its local neighborhood as well as a connection with a global inhibitor. A feature vector, consisting of depth, surface normal, and mean and Gaussian curvatures, is associated with each oscillator and is estimated from local windows at its corresponding pixel location. A context-sensitive method is applied in order to obtain more reliable and accurate estimations. The lateral connection between two oscillators is established based on a similarity measure of their feature vectors. The emergent behavior of the LEGION network gives rise to segmentation. Due to the flexible representation through phases, our method needs no assumption about the underlying structures in image data and no prior knowledge regarding the number of regions. More importantly, the network is guaranteed to converge rapidly under general conditions. These unique properties may lead to a real-time approach for range image segmentation in machine perception.     

Synchronization in Time-delayed Binary Oscillatory Network

We introduce a network of binary oscillators coupled with time delays. Based on the investigation of the dynamics of single time-delayed binary oscillator, the behaviour of a pair of oscillators with excitatory coupling is analyzed in detail. It is shown that perfect synchronous solutions exist for a wide range of initial conditions in the presented oscillatory network.     

Synchrony and desynchrony in integrate-and-fire oscillators.

Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrate-and-fire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrate-and-fire oscillators. We illustrate that a LEGION architecture with integrate-and-fire oscillators can be similarly used to address image analysis.     

Synchronization in complex networks of phase oscillators: A survey

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.     

Criteria for global pinning-controllability of complex networks

In this paper, we study pinning-controllability of networks of coupled dynamical systems. In particular, we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network. The reference trajectory is generated by an exogenous independent oscillator, and pinned nodes are coupled to it through a linear state feedback. We describe the time evolution of the complex dynamical system in terms of the error dynamics. Thereby, we reformulate the pinning-controllability problem as a global asymptotic stability problem. By using Lyapunov-stability theory and algebraic graph theory, we establish tractable sufficient conditions for global pinning-controllability in terms of the network topology, the oscillator dynamics, and the linear state feedback.     

Beyond synchronization: String instability in coupled harmonic oscillator systems

In this paper, we consider the problem of disturbance response and error amplification for a simple system of coupled harmonic oscillators. We first suppose that identical oscillators are connected in a string in which each oscillator attempts to track its predecessor by using the same control law that depends on the relative position information from its immediate predecessor. Such an oscillator string is called a homogeneous oscillator string with predecessor‐following architecture. Motivated by terminology from the problem of vehicle platooning, we say that the synchronized oscillator system is string unstable if the effect of a disturbance to the lead oscillator is amplified as it propagates along the string. With the use of a new Bode‐like integral relation that must be satisfied by the complementary sensitivity function, we provide sufficient conditions for string instability. The sufficient conditions show that any string of oscillators that satisfies certain time domain performance specifications and bandwidth limitations must necessarily be string unstable. We further introduce a concept of time headway for the oscillator system and extend our analysis of string instability to consider the heterogeneous oscillator string and a more general communication range. Copyright © 2014 John Wiley & Sons, Ltd.     

Synchronisation of heterogeneous Kuramoto oscillators with sampled information and a constant leader

The Kuramoto oscillator has been widely studied because it can model a wide variety of engineering problems. Conditions for frequency synchronisation of a network of undirected coupled Kuramoto oscillators have been well established. However, the topology that describes the interaction between oscillators may not be connected due to environmental limitations or link failures. In this work we propose a consensus-based control strategy that forces the network to follow a virtual agent with a constant frequency, and where only few agents have access to the leader state. The controller is based on the exchange of information between the oscillators through a communication network. We introduce conditions for synchronisation and phase cohesiveness with the proposed control strategy that depends on the interaction between the physical topology and the communication topology. Finally, we study two applications to illustrate concepts presented in this work: (1) frequency synchronisation in smart grids; and (2) vehicle coordination.     

Texture segmentation using Gaussian-Markov random fields and neuraloscillator networks

We propose an image segmentation method based on texture analysis. Our method is composed of two parts. The first part determines a novel set of texture features derived from a Gaussian-Markov random fields (GMRF) model. Unlike a GMRF-based approach, our method does not employ model parameters as features or require the extraction of features for a fixed set of texture types a priori. The second part is a 2D array of locally excitatory globally inhibitory oscillator networks (LEGION). After being filtered for noise suppression, features are used to determine the local couplings in the network. When LEGION runs, the oscillators corresponding to the same texture tend to synchronize, whereas different texture regions tend to correspond to distinct phases. In simulations, a large system of differential equations is solved for the first time using a recently proposed method for integrating relaxation oscillator networks. We provide results on real texture images to demonstrate the performance of our method.     

On Exponential Synchronization of Kuramoto Oscillators

In this technical note we study the problem of exponential synchronization for one of the most popular models of coupled phase oscillators, the Kuramoto model. We consider the special case of finite oscillators with distinct, bounded natural frequencies. Our first result derives a lower bound on the coupling gain which is necessary for the onset of synchronization. This bound improves the one derived by Jadbabaie . We then calculate a lower bound on the coupling gain that is sufficient to guarantee oscillator synchronization and derive further sufficient conditions to ensure exponential synchronization of the angular frequencies of all oscillators to the mean natural frequency of the group. We also characterize the coupling gain that is sufficient for the oscillator phase differences to approach any desired compact set in finite time.      

Synchronization of coupled harmonic oscillators with local instantaneous interaction

In this brief we propose a distributed algorithm for synchronization of coupled harmonic oscillators with local instantaneous interaction. We provide convergence analysis for such algorithm without and with a leader over fixed and switching undirected network topologies, respectively. We also establish the conditions by which the coupled harmonic oscillators achieve synchronized oscillatory motions under instantaneous network connectivity. It is shown that the coupled harmonic oscillators can be synchronized even each oscillator instantaneously exchanges the velocity information with its neighbors only at discrete moments. Subsequently, numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results.     

Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.