Self-organization in a Simple Task of Motor Control Based on Spatial Encoding

Abstract

This paper elaborates on the possibilities for self-adjustment of a biological neural network used as feedback controller in the motor control system of a six-legged walker. As biological systems, in contrast to technical systems, show an impressive capability of self-adaptation, this is meant as a proof of principle. Complementing an intensity encoded system (Linder, 2002), where scalar values are represented as the activity of a given neuron, this mechanism is based on spatial encoding, where a scalar value is represented as the location of the most active neuron in a chain of neurons. This encoding scheme can often be observed in biological systems. While the intensity encoded system requires linear input characteristics and symmetrical distribution of the input values over the whole range for both target angles and actual angles, the spatially encoded system presented here is completely self-organizing for evenly distributed target angles and actual angles. By employing an internal teaching signal, it can even adjust for arbitrary (i.e., biologically relevant) distributions of the input. This internal signal is provided through body geometry. Instead of error back-propagation, the system exploits local neuronal mechanisms implicated by a biologically plausible realization of self-organizing maps.

Keywords

self-organization spatial encoding DSOM self-organizing map motor control neural mechanism

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References

Baldi, P. , & Heiligenberg, W. (1988). How sensory maps could enhance resolution through ordered arrangements of broadly tuned receivers . Biological Cybernetics, 59, 313-318 .

Bässler, U. (1983). Neural basis of elementary behavior in stick insects. Berlin: Springer .

Batschelet, E. (1981). Circular statistics in biology. London: Academic Press .

Coombs, S. , Görner, P. , & Münz, H. (1900). The mechanosensory lateral line: Neurobiology and evolution. Berlin: Springer .

Cruse, H. (1979). The control of the anterior extreme position of the hindleg of a walking insect . Physiological Entomology, 4, 121-124 .

Cruse, H. (1996). Neural networks as cybernetic systems. Stuttgart: Thieme .

Cruse, H. (2002). The functional sense of central oscillations in walking . Biological Cybernetics, 86, 271-280 .

Cruse, H. , Bartling, C. , & Kindermann, T. (1995). High-pass filtered positive feedback for decentralized control of cooperation. In F. Moran , A. Moreno , J. J. Merelo , & P. Chacon (Eds.), Advances in artificial life (pp. 668-678). Berlin: Springer .

Cruse, H. , Kindermann, T. , Schumm, M. , Dean, J. , & Schmitz, J. (1998a). Walknet—A biologically inspired network to control six-legged walking . Neural Networks, 11, 1435-1447 .

10.

Cruse, H. , Steinkühler, U. , & Burkamp, C. (1998b). MMC—A recurrent neural network which can be used as manipulable body model . In R. Pfeifer , B. Blumberg , J. A. Meyer , & S. W. Wilson (Eds.), Proceedings of the Fifth International Conference on Simulation of Adaptive Behavior 1998: From animals to animats Vol. 5, (pp. 381-389 ). Cambridge, MA: MIT Press.

11.

Dean, J. , & Wendler, G. (1983). Stick insect locomotion on a walking wheel: Interleg coordination of leg position . Journal of Experimental Biology, 103, 75-94 .

12.

Fritzke, B. (1997). A self-organizing network that can follow non-stationary distributions . In W. Gerstner , A. Germond , M. Hasler & J.-D. Nicoud (Eds.), Proceedings of ICANN-97 (pp. 613-618 ), Berlin: Springer.

13.

Guenther, F. H. , & Barreca, D. M. (1997). Neural models for flexible control of redundant systems. In P. G. Morasso , & V. Sanguineti (Eds.), Self-organization, Computational Maps and Motor Control (pp. 383-421). Amsterdam: Elsevier-North Holland .

14.

Hartmann, G. , & Wehner, R. (1995). The ant’s path integration system: A neural architecture . Biological Cybernetics, 73, 483-497 .

15.

Jordan, M. I. , & Rumelhart, D. E. (1992). Forward models: Supervised learning with a distal teacher . Cognitive Science, 16, 307-354 .

16.

Kasai, H. , Matsuzaki, M. , Noguchi, J. , Yasumatsu, N. , & Nakahara, H. (2003). Structure-stability-function relationships of dendritic spines . TINS, 26, 360-368 .

17.

Kohonen, T. (1993). Physiological interpretation of the selforganizing map algorithm . Neural Networks, 6, 895-905 .

18.

Kohonen, T. (2001). Self-organizing maps, (3rd ed.). Berlin: Springer .

19.

Kuperstein, M. (1988). Neural model of adaptive hand-eye coordination for single postures . Science, 239, 1308-1311 .

20.

Linder, C. R. (2002). Self organisation in a simple task of motor control . In B. Hallam , J.-A. Meyer , G. Hayes , J. Hallam , & D. Floreano (Eds.), Proceedings of the Seventh International Conference on Simulation of Adaptive Behavior: From animals to animats 7 (pp. 185-194 ). Cambridge, MA: MIT Press.

21.

Merzenich, M. M. , & Brugge, J. F. (1973). Representation of the cochlear partition of the superior temporal plane of the macaque monkey . Brain Research, 50, 275-296 .

22.

Nolfi, S. , & Floreano, D. (1999). Learning and evolution . Autonomous Robots, 7, 89-113 .

23.

O’Reilly, R. C. (1996). Biologically plausible error-driven learning using local activation differences: The generalized recirculation algorithm . Neural Computation, 8(5), 895-938 .

24.

Pfeifer, R. , & Scheier, C. (1999). Understanding intelligence. Cambridge, MA: MIT Press .

25.

Rumelhart, D. E. , Hinton, G. E. , & Williams, R. J. (1986). Learning representations by back-propagating errors . Nature, 323, 533-536 .

26.

Schmitz, J. , & Hassfeld, G. (1989). The treading-on-tarsus reflex in stick insects: Phase-dependence and modifications of the motor output during walking . Journal of Experimental Biology, 143, 373-388 .

27.

Schumm, M. (in preparation). Ph.D. thesis. University of Bielefeld, Germany.

28.

Stemmler, M. , & Koch, C. (1999). How voltage-dependent conductances can adapt to maximize the information encoded by neuronal firing rate . Nature Neuroscience, 2, 521-527 .

29.

Turrigiano, G. G. , Leslie, K. R. , Desai, N. S. , Rutherford, L. C. , & Nelson, S. B. (1998). Activity-dependent scaling of quantal amplitude in neocortical neurons . Nature, 391, 892-896 .

30.

Usherwood, P. N. R. , Runion, H. , & Campbell, J. (1968). Structure and physiology of a chordotonal organ in the locust leg . Journal of Experimental Biology, 48, 305-323 .

31.

Walter, J. , Nölker, C. , & Ritter, H. (2000). The PSOM algorithm and applications . In Proceedings of International Symposium on Neural Computation (pp. 758-764 ). Berlin.

32.

Watson, A. H. D. , & Burrows, M. (1988). The distribution and morphology of synapses on nonspiking local interneurons in the thoracic nervous system of the locust . Journal of Comparative Neurology, 272, 605-616 .