Hysteresis in the gait transition of a quadruped investigated using simple body mechanical and oscillator network models.

We investigated the dynamics of quadrupedal locomotion by constructing a simple quadruped model that consists of a body mechanical model and an oscillator network model. The quadruped model has front and rear bodies connected by a waist joint with a torsional spring and damper system and four limbs controlled by command signals from the oscillator network model. The simulation results reveal that the quadruped model produces various gait patterns through dynamic interactions among the body mechanical system, the oscillator network system, and the environment. They also show that it undergoes a gait transition induced by changes in the waist joint stiffness and the walking speed. In addition, the gait pattern transition exhibits a hysteresis similar to that observed in human and animal locomotion. We examined the hysteresis mechanism from a dynamic viewpoint.

[1]  J. Rogers Chaos , 1876, Molecular Vibrations.

[2]  S. Grillner,et al.  The locomotion of the acute spinal cat injected with clonidine i.v. , 1973, Brain research.

[3]  G. E. Goslow,et al.  The cat step cycle: Hind limb joint angles and muscle lengths during unrestrained locomotion , 1973, Journal of morphology.

[4]  David A. Rand,et al.  The bifurcations of duffing's equation: An application of catastrophe theory , 1976 .

[5]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[6]  J. Duysens Fluctuations in sensitivity to rhythm resetting effects during the cat's step cycle , 1977, Brain Research.

[7]  D. F. Hoyt,et al.  Gait and the energetics of locomotion in horses , 1981, Nature.

[8]  J. Desmedt Motor control mechanisms in health and disease , 1983 .

[9]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[10]  Ronald F. Zernicke,et al.  Modulation of limb dynamics in the swing phase of locomotion , 1985 .

[11]  S. Mori Integration of posture and locomotion in acute decerebrate cats and in awake, freely moving cats , 1987, Progress in Neurobiology.

[12]  N. Heglund,et al.  Speed, stride frequency and energy cost per stride: how do they change with body size and gait? , 1988, The Journal of experimental biology.

[13]  M Solomonow,et al.  The effect of joint velocity on the contribution of the antagonist musculature to knee stiffness and laxity , 1990, The American journal of sports medicine.

[14]  G Schöner,et al.  A synergetic theory of quadrupedal gaits and gait transitions. , 1990, Journal of theoretical biology.

[15]  C T Farley,et al.  A mechanical trigger for the trot-gallop transition in horses. , 1991, Science.

[16]  R. Alexander,et al.  A model of bipedal locomotion on compliant legs. , 1992, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[17]  W. Ditto,et al.  Controlling chaos in the brain , 1994, Nature.

[18]  Gentaro Taga,et al.  Emergence of bipedal locomotion through entrainment among the neuro-musculo-skeletal system and the , 1994 .

[19]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[20]  Collins,et al.  Controlling nonchaotic neuronal noise using chaos control techniques. , 1995, Physical review letters.

[21]  Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS 1996, November 4-8, 1996, Osaka, Japan , 1996, IROS.

[22]  John W. Clark,et al.  Phase response characteristics of model neurons determine which patterns are expressed in a ring circuit model of gait generation , 1997, Biological Cybernetics.

[23]  Ian Stewart,et al.  A modular network for legged locomotion , 1998 .

[24]  Zhiwei Luo,et al.  A mathematical model of adaptive behavior in quadruped locomotion , 1998, Biological Cybernetics.

[25]  M T Turvey,et al.  Can the transitions to and from running and the metabolic cost of running be determined from the kinetic energy of running? , 1999, Journal of motor behavior.

[26]  Toshio Aoyagi,et al.  OSCILLATOR NEURAL NETWORK RETRIEVING SPARSELY CODED PHASE PATTERNS , 1999 .

[27]  M. Golubitsky,et al.  Symmetry in locomotor central pattern generators and animal gaits , 1999, Nature.

[28]  S. Grillner,et al.  Neuronal Control of Locomotion 'From Mollusc to Man ' , 1999 .

[29]  S. Grillner,et al.  Neuronal Control of LocomotionFrom Mollusc to Man , 1999 .

[30]  J. Duysens,et al.  Load-regulating mechanisms in gait and posture: comparative aspects. , 2000, Physiological reviews.

[31]  R. Poppele,et al.  Proprioception from a spinocerebellar perspective. , 2001, Physiological reviews.

[32]  A. M. Degtyarenko,et al.  Patterns of locomotor drive to motoneurons and last-order interneurons: clues to the structure of the CPG. , 2001, Journal of neurophysiology.

[33]  P. Holmes,et al.  Mechanical models for insect locomotion: stabilty and parameter studies , 2001 .

[34]  R. Poppele,et al.  Independent representations of limb axis length and orientation in spinocerebellar response components. , 2002, Journal of neurophysiology.

[35]  John L Hudson,et al.  Emerging Coherence in a Population of Chemical Oscillators , 2002, Science.

[36]  B. Abernethy,et al.  Are transitions in human gait determined by mechanical, kinetic or energetic factors? , 2002, Human movement science.

[37]  Gianfranco Bosco,et al.  Sophisticated spinal contributions to motor control , 2003, Trends in Neurosciences.

[38]  S. Grillner The motor infrastructure: from ion channels to neuronal networks , 2003, Nature Reviews Neuroscience.

[39]  Bruce J. West,et al.  Nonlinear dynamical model of human gait. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  D. F. Hoyt,et al.  Biomechanical and energetic determinants of the walk–trot transition in horses , 2004, Journal of Experimental Biology.

[41]  V. B. Kokshenev Dynamics of human walking at steady speeds. , 2004, Physical review letters.

[42]  T. Ichinomiya Frequency synchronization in a random oscillator network. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  B. Conway,et al.  Proprioceptive input resets central locomotor rhythm in the spinal cat , 2004, Experimental Brain Research.

[44]  D. McCrea,et al.  Deletions of rhythmic motoneuron activity during fictive locomotion and scratch provide clues to the organization of the mammalian central pattern generator. , 2005, Journal of neurophysiology.

[45]  Edward Ott,et al.  Theoretical mechanics: crowd synchrony on the Millennium Bridge. , 2005 .

[46]  P. Aerts,et al.  Spatiotemporal characteristics of the walk-to-run and run-to-walk transition when gradually changing speed. , 2006, Gait & posture.

[47]  D. McCrea,et al.  Modelling spinal circuitry involved in locomotor pattern generation: insights from deletions during fictive locomotion , 2006, The Journal of physiology.

[48]  John Guckenheimer,et al.  The Dynamics of Legged Locomotion: Models, Analyses, and Challenges , 2006, SIAM Rev..

[49]  Manoj Srinivasan,et al.  Computer optimization of a minimal biped model discovers walking and running , 2006, Nature.

[50]  D. McCrea,et al.  Modelling spinal circuitry involved in locomotor pattern generation: insights from the effects of afferent stimulation , 2006, The Journal of physiology.

[51]  Monika Sharma,et al.  Chemical oscillations , 2006 .

[52]  Reinhard Blickhan,et al.  Compliant leg behaviour explains basic dynamics of walking and running , 2006, Proceedings of the Royal Society B: Biological Sciences.

[53]  A. Ijspeert,et al.  From Swimming to Walking with a Salamander Robot Driven by a Spinal Cord Model , 2007, Science.

[54]  W Brent Edwards,et al.  Effects of changing protocol, grade, and direction on the preferred gait transition speed during human locomotion. , 2007, Gait & posture.

[55]  Yasuhiro Fukuoka,et al.  Adaptive Dynamic Walking of a Quadruped Robot on Natural Ground Based on Biological Concepts , 2007, Int. J. Robotics Res..

[56]  Shinya Aoi,et al.  A Multilegged Modular Robot That Meanders: Investigation of Turning Maneuvers Using Its Inherent Dynamic Characteristics , 2007, SIAM J. Appl. Dyn. Syst..

[57]  Auke Jan Ijspeert,et al.  Central pattern generators for locomotion control in animals and robots: A review , 2008, Neural Networks.

[58]  Kei-Ichi Ueda,et al.  Instability-induced hierarchy in bipedal locomotion. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  D. McCrea,et al.  Organization of mammalian locomotor rhythm and pattern generation , 2008, Brain Research Reviews.

[60]  Toshio Aoyagi,et al.  Co-evolution of phases and connection strengths in a network of phase oscillators. , 2009, Physical review letters.

[61]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[62]  Ikkyu Aihara,et al.  Modeling synchronized calling behavior of Japanese tree frogs. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[63]  Yoji Kawamura,et al.  Collective-phase description of coupled oscillators with general network structure. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[64]  P. Guertin The mammalian central pattern generator for locomotion , 2009, Brain Research Reviews.

[65]  P J Beek,et al.  Steady and transient coordination structures of walking and running. , 2009, Human movement science.

[66]  Taishin Nomura,et al.  Dynamic stability and phase resetting during biped gait. , 2009, Chaos.

[68]  F. Wörgötter,et al.  Self-organized adaptation of a simple neural circuit enables complex robot behaviour , 2010, ArXiv.

[69]  Shinya Aoi,et al.  Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator , 2010, Biological Cybernetics.