The neurological mechanism used for generating rhythmic patterns for functions such as swallowing, walking, and chewing has been modeled computationally by the neural oscillator. It has been widely studied by biologists to model various aspects of organisms and by computer scientists and robotics engineers as a method for controlling and coordinating the gaits of walking robots. Although there has been significant study in this area, it is difficult to find basic guidelines for programming neural oscillators. In this paper, the authors approach neural oscillators from a programmer’s point of view, providing background and examples for developing neural oscillators to generate rhythmic patterns that can be used in biological modeling and robotics applications. 1. Introduction Scientists have long employed neural oscillators as a method to study neuron/ganglia-based processes that serve as central pattern generators for various organisms and as a method to generate control and coordination signals for various robotic mechanisms. For example, significant work has been done in trying to understand the functions of various neurons and components of such biological neural networks [1, 2], developing properties general to all networks of neural oscillators [3], and the modeling of processes such as locomotion in simple animals [4–8]. Associative neural network models with behavior similar to central path generators have also been developed [9]. Computer scientists have researched and developed several varieties of artificial neural networks that model natural neural networks to some extent. Artificial neural network is a well-developed field, and the literature in this general area is quite vast; however, literature related to neural oscillators and central pattern generators using these computerized neural network models, such as in [10], is not so prevalent. Even so, the use of such models in controlling the motion of robots has been well established [11–13]. For researchers wanting to apply the techniques of neural oscillators and/or central path generators for the programming robotic controls, modeling rhythmic patterns, and so forth, without the necessity of understanding complex theoretical mathematical models or learning how simple invertebrates swim, there appears to be no single source of basic information available. Many articles provide basic diagrams of oscillators and occasionally some tuning parameters, but most do not provide discussions concerning the general nature of the mechanism, conceptual overviews, or implementation information. To help
References
[1]
A. I. Selverston, “Are central pattern generators understandable,” Behavioral and Brain Sciences, vol. 3, no. 4, pp. 535–571, 1980.
[2]
D. M. Wilson, “The central nervous control of flight in a locust,” The Journal of Experimental Biology, vol. 38, no. 2, pp. 471–490, 1961.
[3]
F. C. Hoppensteadt and E. M. Izhikevich, “Synaptic organizations and dynamical properties of weakly connected neural oscillators. I. Analysis of a canonical model,” Biological Cybernetics, vol. 75, no. 2, pp. 117–127, 1996.
[4]
P. Getting, “Reconstruction of small neural networks,” in Methods in Neural Modeling, C. Koch, Ed., pp. 171–196, MIT Press, Cambridge, Mass, USA, 1989.
[5]
A. J. Ijspeert, “A connectionist central pattern generator for the aquatic and terrestrial gaits of a simulated salamander,” Biological Cybernetics, vol. 84, no. 5, pp. 331–348, 2001.
[6]
A. J. Ijspeert and J. Kodjabachian, “Evolution and development of a central pattern generator for the swimming of a lamprey,” Artificial Life, vol. 5, no. 3, pp. 247–269, 1999.
[7]
S. R. Lockery and T. J. Sejnowski, “The computational leech,” Trends in Neurosciences, vol. 16, no. 7, pp. 283–290, 1993.
[8]
A. Roberts and M. J. Tunstall, “Mutual re-excitation with post-inhibitory rebound: a simulation study on the mechanisms for locomotor rhythm generation in the spinal cord of Xenopus embryos,” European Journal of Neuroscience, vol. 2, no. 1, pp. 11–23, 1990.
[9]
D. Kleinfeld and H. Sompolinsky, “Associative neural network model for the generation of temporal patterns. Theory and application to central pattern generators,” Biophysical Journal, vol. 54, no. 6, pp. 1039–1051, 1988.
[10]
D. Meunier and H. Paugam-Moisy, “Neural networks for computational neuroscience,” in Proceedings of the European Symposium on Artificial Neural Networks—Advances in Computational Intelligence and Learning, pp. 367–378, Bruges, Belgium, April 2008.
[11]
H. J. Chiel, R. D. Beer, and J. C. Gallagher, “Evolution and analysis of model CPGs for walking—I. Dynamical modules,” Journal of Computational Neuroscience, vol. 7, no. 2, pp. 99–118, 1999.
[12]
H. Inada and K. Ishii, “Behavior generation of bipedal robot using central pattern generator(CPG),” in Proceedings of the IEEE International Conference on Intelligent Robots and Systems, vol. 3, pp. 2179–2184, Las Vegas, Nev, USA, October 2003.
[13]
Y. Nakamura, T. Mori, M. A. Sato, and S. Ishii, “Reinforcement learning for a biped robot based on a CPG-actor-critic method,” Neural Networks, vol. 20, no. 6, pp. 723–735, 2007.
[14]
B. You, R. Peslin, C. Duvivier, V. D. Vu, and J. P. Grilliat, “Expiratory capnography in asthma: evaluation of various shape indices,” European Respiratory Journal, vol. 7, no. 2, pp. 318–323, 1994.
