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A Prototype 2N-Legged (insect-like) Robot. A Non-Linear Dynamical System Approach

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Spatial Temporal Patterns for Action-Oriented Perception in Roving Robots II

Part of the book series: Cognitive Systems Monographs ((COSMOS,volume 21))

Abstract

A nonlinear closed lattice or ring is proposed as a central pattern generator (CPG) for controlling hexapodal robots. We show that the ring composed of six anharmonically interacting units coupled to the limb actuators permits to reproduce typical hexapod gaits. We provide an electronic circuit implementation of the CPG providing the corresponding gaits. Then we propose a method to incorporate the actuator (motor) and leg dynamics in the units of the CPG. With this electro-mechanical device we close the loop CPG—environment—CPG, thus obtaining a decentralized approach for the leg control that does not require higher level CPG intervention during locomotion in a non-smooth hence non flat landscape. The gaits generated by our CPG are not rigid, but adapt to obstacles faced by the robot.

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References

  1. E.R. Kandel, J.H. Schwartz, T.M. Jessell, Principles of Neural Science (McGraw-Hill, New York, 2000)

    Google Scholar 

  2. C.A. Wiersma, Invertebrate Nervous Systems (University Chicago Press, 1968)

    Google Scholar 

  3. H. Cruse, What mechanisms coordinate leg movement in working arthropods? Trends. Neurosci. 13, 15–21 (1990)

    Article  Google Scholar 

  4. J. Dean, T. Kindermann, J. Schmitz, M. Schumm, H. Cruse, Control of walking in the stick insect: from behavior and physiology to modeling. Newblock Auton. Robots 7, 271–288 (1999)

    Google Scholar 

  5. P. Arena, L. Fortuna, M. Branciforte, Reaction-diffusion CNN algorithms to generate and control artificial locomotion. IEEE Trans. Circuits Systems I, 46, 253–260 (1999)

    Google Scholar 

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

    Google Scholar 

  7. G. Yiang, W.Y. Schooner, J.A.S. Kelso, A synergetic theory of quadrupedal gaits and gait transition. J. Theor. Biol. 142, 359–391 (1990)

    Google Scholar 

  8. J.J Collins, I. Stewart, Coupled nonlinear oscillators and the symmetries of animal gaits. Nonlinear Sci. 3, 349–392 (1993)

    Google Scholar 

  9. J.J. Collins, I. Stewart, Hexapodal gaits and coupled nonlinear oscillator models. Biol. Cyb. 68, 287–298 (1993)

    Article  MATH  Google Scholar 

  10. J.J. Collins, I. Stewart, A group-theoretic approach to rings of coupled biological oscillators. Biol. Cyb. 71, 95–103 (1994)

    Article  MATH  Google Scholar 

  11. M. Golubitsky, P.L. Buono, I. Stewart, J.J. Collins, A modular network for legged locomotion. Physica D 115, 56–72 (1998)

    Google Scholar 

  12. M. Golubitsky, P.L. Buono, I. Stewart, J.J. Collins, The role of symmetry in animal locomotion. Nature 401, 693–695 (1999)

    Google Scholar 

  13. J. Gray, Animal Locomotion (Weidenfeld and Nicolson, London, 1968)

    Google Scholar 

  14. L.O. Chua, CNN: A Paradigm for Complexity (World Scientific, New Jersey, 1998)

    Google Scholar 

  15. G. Manganaro, P. Arena, L. Fortuna, Cellular Neural Networks. Chaos, Complexity and VLSI Processing (Springer, Berlin, 1999)

    Google Scholar 

  16. V.I. Nekorkin, M.G Velarde, Synergetic Phenomena in Active Lattices. Patterns, Waves, Solitons, Chaos (Springer, Berlin, 2002)

    Google Scholar 

  17. E. Del Rio, V.A. Makarov, M.G. Velarde, W. Ebeling, Mode transitions and wave propagation in a driven-dissipative toda-rayleigh ring. Phys. Rev. E 67, 056208–056217 (2003)

    Google Scholar 

  18. W. Ebeling, Makarov, V.A and M.G. Velarde, Soliton-like waves on dissipative toda lattices. Int. J. Bifurcation Chaos 10, 1075–1089 (2000)

    Google Scholar 

  19. V.A. Makarov, E. del Rio, W. Ebeling, M.G. Velarde, Dissipative toda-rayleigh lattice and its oscillatory modes. Phys. Rev. E 64, 036601 (2001)

    Google Scholar 

  20. M. Toda. Theory of Nonlinear Lattices (Springer, New York, 1981)

    Google Scholar 

  21. M. Toda. Nonlinear Waves and Solitons (Kluwer, Dordrecht, 1983)

    Google Scholar 

  22. J.W. Rayleigh, The Theory of Sound (Dover reprint, New York, 1945)

    Google Scholar 

  23. G. M. Nelson, R.J. Bachmann, D.A Kingsley, J.T. Offi,T.J Allen, R.D. Quinn, R.E. Ritzmann, Parallel complementary strategies for implementing biological principles into mobile robots. Int. J. Robotics Res. 22, 164–186 (2003)

    Google Scholar 

  24. M. Schumm, H. Cruse, Control of swing movement: influences of differenly shaped substrate. J. Comparative Physiol. A 192, 1147–1164 (2006)

    Article  Google Scholar 

  25. H. Cruse, C. Bartling, T. Kindermann, High-pass filtered positive feedback for decentralized control of cooperation, (Springer, Berlin, 1995), pp. 668–678

    Google Scholar 

  26. T. Kindermann, Behavior and adaptability of a six-legged walking system with highly distributed control. Adapt. Behav. 9, 16–41 (2002)

    Article  Google Scholar 

  27. A. Schneider, H. Cruse, J. Schmitz, A biologically inspired active compliant joint using local positive velocity feedback (lpvf). IEEE Trans. Syst. Man Cyb. Part B: Cyb. 35, 1120–1130 (2005)

    Google Scholar 

  28. J. Schmitz, J. Dean, T. Kindermann, M. Schumm, H. Cruse, A biologically inspired controller for hexapod walking: simple solutions by exploiting physical properties. Biol. Bull. 200, 195–200 (2001)

    Google Scholar 

  29. V. Durr, J. Schmitz, H. Cruse, Behaviour-based modelling of hexapod locomotion: linking biology and technical application. Arthropod Struct. Devel. 33, 237–250 (2004)

    Google Scholar 

  30. A.C. Singer, A.V. Oppenheim, Circuit implementations of soliton systems. Int. J. Bifurcation Chaos 9, 571–590 (1999)

    Article  MATH  Google Scholar 

  31. B. Van der Pol, On relaxation-oscillations. Phil. Mag. 2, 978–983 (1926)

    Google Scholar 

  32. B. Van der Pol, Forced oscillations in a circuit with non-linear resistance. Phil. Mag. 3, 65–70 (1927)

    Google Scholar 

  33. Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory. (Springer, New York, 1995)

    Google Scholar 

  34. V.A. Makarov, M.G. Velarde, A. Chetverikov and W. Ebeling, Anharmonicity and its significance to non-ohmic electric conduction. Phys. Rev. E 73, 066626–066612 (2006)

    Google Scholar 

  35. P. Horowitz, W. Hill, The Art of Electronics ( Cambridge University Press, Cambridge, 1987)

    Google Scholar 

  36. N. Islam, J.P. Singh, K. Steiglitz, Soliton phase shifts in a dissipative lattice. J. Appl. Phys. 62, 689–693 (1987)

    Google Scholar 

  37. S. Still, K. Hepp, R.J. Douglas, Neuromorphic walking gait control. IEEE Trans. Neural Netw. 37, 496–508 (2006)

    Google Scholar 

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del Rio, E., Velarde, M. (2014). A Prototype 2N-Legged (insect-like) Robot. A Non-Linear Dynamical System Approach. In: Arena, P., Patanè, L. (eds) Spatial Temporal Patterns for Action-Oriented Perception in Roving Robots II. Cognitive Systems Monographs, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-319-02362-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-02362-5_5

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