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
E.R. Kandel, J.H. Schwartz, T.M. Jessell, Principles of Neural Science (McGraw-Hill, New York, 2000)
C.A. Wiersma, Invertebrate Nervous Systems (University Chicago Press, 1968)
H. Cruse, What mechanisms coordinate leg movement in working arthropods? Trends. Neurosci. 13, 15–21 (1990)
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)
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)
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)
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)
J.J Collins, I. Stewart, Coupled nonlinear oscillators and the symmetries of animal gaits. Nonlinear Sci. 3, 349–392 (1993)
J.J. Collins, I. Stewart, Hexapodal gaits and coupled nonlinear oscillator models. Biol. Cyb. 68, 287–298 (1993)
J.J. Collins, I. Stewart, A group-theoretic approach to rings of coupled biological oscillators. Biol. Cyb. 71, 95–103 (1994)
M. Golubitsky, P.L. Buono, I. Stewart, J.J. Collins, A modular network for legged locomotion. Physica D 115, 56–72 (1998)
M. Golubitsky, P.L. Buono, I. Stewart, J.J. Collins, The role of symmetry in animal locomotion. Nature 401, 693–695 (1999)
J. Gray, Animal Locomotion (Weidenfeld and Nicolson, London, 1968)
L.O. Chua, CNN: A Paradigm for Complexity (World Scientific, New Jersey, 1998)
G. Manganaro, P. Arena, L. Fortuna, Cellular Neural Networks. Chaos, Complexity and VLSI Processing (Springer, Berlin, 1999)
V.I. Nekorkin, M.G Velarde, Synergetic Phenomena in Active Lattices. Patterns, Waves, Solitons, Chaos (Springer, Berlin, 2002)
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)
W. Ebeling, Makarov, V.A and M.G. Velarde, Soliton-like waves on dissipative toda lattices. Int. J. Bifurcation Chaos 10, 1075–1089 (2000)
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)
M. Toda. Theory of Nonlinear Lattices (Springer, New York, 1981)
M. Toda. Nonlinear Waves and Solitons (Kluwer, Dordrecht, 1983)
J.W. Rayleigh, The Theory of Sound (Dover reprint, New York, 1945)
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)
M. Schumm, H. Cruse, Control of swing movement: influences of differenly shaped substrate. J. Comparative Physiol. A 192, 1147–1164 (2006)
H. Cruse, C. Bartling, T. Kindermann, High-pass filtered positive feedback for decentralized control of cooperation, (Springer, Berlin, 1995), pp. 668–678
T. Kindermann, Behavior and adaptability of a six-legged walking system with highly distributed control. Adapt. Behav. 9, 16–41 (2002)
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)
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)
V. Durr, J. Schmitz, H. Cruse, Behaviour-based modelling of hexapod locomotion: linking biology and technical application. Arthropod Struct. Devel. 33, 237–250 (2004)
A.C. Singer, A.V. Oppenheim, Circuit implementations of soliton systems. Int. J. Bifurcation Chaos 9, 571–590 (1999)
B. Van der Pol, On relaxation-oscillations. Phil. Mag. 2, 978–983 (1926)
B. Van der Pol, Forced oscillations in a circuit with non-linear resistance. Phil. Mag. 3, 65–70 (1927)
Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory. (Springer, New York, 1995)
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)
P. Horowitz, W. Hill, The Art of Electronics ( Cambridge University Press, Cambridge, 1987)
N. Islam, J.P. Singh, K. Steiglitz, Soliton phase shifts in a dissipative lattice. J. Appl. Phys. 62, 689–693 (1987)
S. Still, K. Hepp, R.J. Douglas, Neuromorphic walking gait control. IEEE Trans. Neural Netw. 37, 496–508 (2006)
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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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