SO(2)-Networks as Neural Oscillators

Pasemann, Frank; Hild, Manfred; Zahedi, Keyan

doi:10.1007/3-540-44868-3_19

Cited by 77 publications

(59 citation statements)

References 10 publications

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“…6 (left) shows an implementation of a neural rhythm generator. It is based on a two neuron loop, called SO(2)-network [17]. These networks with a special weight matrix generate quasi-periodic oscillations with a sine-shaped wave form.…”

Section: Neural Processing Of Auditory Signalsmentioning

confidence: 99%

Dynamical Systems in the Sensorimotor Loop: On the Interrelation Between Internal and External Mechanisms of Evolved Robot Behavior

Hülse

Wischmann

Manoonpong

et al. 2007

50 Years of Artificial Intelligence

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Abstract. This case study demonstrates how the synthesis and the analysis of minimal recurrent neural robot control provide insights into the exploration of embodiment. By using structural evolution, minimal recurrent neural networks of general type were evolved for behavior control. The small size of the neural structures facilitates thorough investigations of behavior relevant neural dynamics and how they relate to interactions of robots within the sensorimotor loop. We argue that a clarification of dynamical neural control mechanisms in a reasonable depth allows quantitative statements about the effects of the sensorimotor loop and suggests general qualitative implications about the embodiment of autonomous robots and biological systems as well.

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Section: Neural Processing Of Auditory Signalsmentioning

confidence: 99%

Dynamical Systems in the Sensorimotor Loop: On the Interrelation Between Internal and External Mechanisms of Evolved Robot Behavior

Hülse

Wischmann

Manoonpong

et al. 2007

50 Years of Artificial Intelligence

Self Cite

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“…That controller has been applied to control a four-legged walking machine. Here a so-called "2-neuron network" [118] is employed. It is used as a central pattern generator (CPG) which follows the basic principle of locomotion control of walking animals (cf.…”

Section: The Neural Oscillator Networkmentioning

confidence: 99%

“…The network parameters are experimentally adjusted via the ISEE to acquire the optimal oscillating output signals for generating locomotion of the walking machines. The parameter set is selected with respect to the dynamics of the 2-neuron system staying near the Neimark-Sacker bifurcation where the quasi-periodic attractors occur [118]. Examples of different oscillating output signals generated by different weights and bias terms are presented in Figure 5.25.…”

Section: The Neural Oscillator Networkmentioning

confidence: 99%

Neural Preprocessing and Control of Reactive Walking Machines

Manoonpong¹

2007

Cognitive Technologies

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Research in the domain of biologically inspired walking machines has focused for the most part on the mechanical designs and locomotion control. Although some of this research has been concentrated on the generation of a reactive behavior of walking machines, it has been restricted only to a few of such reactive behaviors. However, from this research, there are only few examples where different behaviors have been implemented in one machine at the same time. In general, these walking machines were solely designed for pure locomotion, i.e. without sensing environmental stimuli.Therefore, in this thesis, biologically inspired walking machines with different reactive behaviors are presented. Inspired by obstacle avoidance and escape behavior of scorpions and cockroaches, such behavior is implemented in the walking machines as a negative tropism. On the other hand, a sound induced behavior called "sound tropism", in analogy to the prey capture behavior of spiders, is employed as a model of a positive tropism. The biological sensing systems which those animals use to trigger the described behaviors are investigated so that they can be reproduced in the abstract form with respect to their principle functionalities. In addition, the morphologies of a salamander and a cockroach which are designed for efficient locomotion are also taken into account for the leg and trunk designs of the four-and six-legged walking machines, respectively. Different behavior controls for generating the biologically inspired reactive behaviors are developed on the basis of a modular neural structure. Each behavior control consists of a neural preprocessing module and a neural control module. Preprocessing is for sensory signals while the neural control generates basic locomotion and changes the appropriate motions, e.g. turning left, right or walking backward, with respect to sensory signals. Neural preprocessing and control are formed by realizing discrete-time dynamical properties of recurrent neural networks. Parts of the networks are generated iii iv Abstract and optimized by using an evolutionary algorithm. Utilizing the modular neural structure, the coupling of the neural control module with different neural preprocessing modules leads to the desired behavior controllers, e.g. obstacle avoidance and sound tropism. Furthermore, these behavior controllers are then fused by using a sensor fusion technique consisting of lookup table and time scheduling methods to obtain an effective behavior fusion controller, whereby different neural preprocessing modules have to cooperate.Eventually, all of these reactive behavior controllers together with the physical sensor systems are implemented on the physical walking machines to be tested in a real world environment. The fully equipped walking machines can be seen as artificial perception-action systems. As a result, the walking machine(s) is able to respond to environmental stimuli, e.g. wandering around, sound tropism (positive tropism), avoiding obstacles and even escaping from corners a...

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“…Since continuous-time Hopfield neural networks have been first considered in [2,3], they have received much attention because of their applicability in problems of optimizations, signal processing, image processing, solving nonlinear algebraic equations, pattern recognitions, associative memories, and so on. The stability and the existence of periodic or quasiperiodic solutions of discrete-time Hopfield neural networks with or without delays have been considered in [4][5][6][7][8]. In [9], a bifurcation analysis has been studied for a two-dimensional discrete neural model with multidelays by applying the Euler method to continuous-time Hopfield neural networks with no selfconnections.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays

Ren

2007

International Journal of Mathematics and Mathematical Sciences

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A bifurcation analysis is undertaken for a discrete-time Hopfield neural network with four delays. Conditions ensuring the asymptotic stability of the null solution are obtained with respect to two parameters of the system. Using techniques developed by Kuznetsov to a discrete-time system, we study the Neimark-Sacker bifurcation (also called Hopf bifurcation for maps) of the system. The direction and the stability of the Neimark-Sacker bifurcation are investigated by applying the normal form theory and the center manifold theorem.

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SO(2)-Networks as Neural Oscillators

Cited by 77 publications

References 10 publications

Dynamical Systems in the Sensorimotor Loop: On the Interrelation Between Internal and External Mechanisms of Evolved Robot Behavior

Dynamical Systems in the Sensorimotor Loop: On the Interrelation Between Internal and External Mechanisms of Evolved Robot Behavior

Neural Preprocessing and Control of Reactive Walking Machines

Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays

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