Instability-based mechanism for body undulations in centipede locomotion.

Centipedes have many body segments and legs and they generate body undulations during terrestrial locomotion. Centipede locomotion has the characteristic that body undulations are absent at low speeds but appear at faster speeds; furthermore, their amplitude and wavelength increase with increasing speed. There are conflicting reports regarding whether the muscles along the body axis resist or support these body undulations and the underlying mechanisms responsible for the body undulations remain largely unclear. In the present study, we investigated centipede locomotion dynamics using computer simulation with a body-mechanical model and experiment with a centipede-like robot and then conducted dynamic analysis with a simple model to clarify the mechanism. The results reveal that body undulations in these models occur due to an instability caused by a supercritical Hopf bifurcation. We subsequently compared these results with data obtained using actual centipedes. The model and actual centipedes exhibit similar dynamic properties, despite centipedes being complex, nonlinear dynamic systems. Based on our findings, we propose a possible passive mechanism for body undulations in centipedes, similar to a follower force or jackknife instability. We also discuss the roles of the muscles along the body axis in generating body undulations in terms of our physical model.

[1]  A. Garrod.  Animal Locomotion , 1874, Nature.

[2]  Çîîëîãèÿ áåñïîçâîíî÷íûõ,et al.  Invertebrate Zoology , 1927, Nature.

[3]  T. Beal.  Dynamic stability of a flexible missile under constant and pulsating thrusts , 1965 .

[4]  S. Manton,et al.  The evolution of arthropodan locomotory mechanisms , 1972 .

[5]  J. J. Wu.  On the stability of a free-free beam under axial thrust subjected to directional control , 1975 .

[6]  M. L. Shik,et al.  Neurophysiology of locomotor automatism. , 1976, Physiological reviews.

[7]  Stephen A. Wainwright,et al.  Mechanical Design in Organisms , 2020 .

[8]  R. McNeill Alexander,et al.  Mechanics and energetics of animal locomotion , 1977 .

[9]  J. Winn,et al.  Brain , 1878, The Lancet.

[10]  D. A. Crolla,et al.  The lateral stability of tractor and trailer combinations , 1979 .

[11]  Joel W. Hedgpeth,et al.  The Arthropoda: Habits, Functional Morphology and Evolution , 1979 .

[12]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[13]  H. Troger,et al.  A Nonlinear Analysis of the Generic Types of Loss of Stability of the Steady State Motion of a Tractor-Semitrailer∗ , 1984 .

[14]  C. D. Mote,et al.  The maximum controlled follower force on a free-free beam carrying a concentrated mass , 1985 .

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

[16]  R. A. Davidoff.  Neural Control of Rhythmic Movements in Vertebrates , 1988, Neurology.

[17]  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.

[18]  A H Cohen,et al.  The role of heterarchical control in the evolution of central pattern generators. , 1992, Brain, behavior and evolution.

[19]  W. Soedel,et al.  CLOSED-LOOP DIRECTIONAL STABILITY OF CAR-TRAILER COMBINATIONS IN STRAIGHT-LINE MOTION , 1992 .

[20]  J. Schmitz.  LOAD-COMPENSATING REACTIONS IN THE PROXIMAL LEG JOINTS OF STICK INSECTS DURING STANDING AND WALKING , 1993 .

[21]  Jayne,et al.  Axial kinematics and muscle activity during terrestrial locomotion of the centipede Scolopendra heros , 1995, The Journal of experimental biology.

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

[23]  Thomas Kindermann,et al.  Walknet--a biologically inspired network to control six-legged walking , 1998, Neural Networks.

[24]  著者なし.  16 , 1871, Animals at the End of the World.

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

[26]  Thomas Kindermann,et al.  Control of Walking in the Stick Insect: From Behavior and Physiology to Modeling , 1999, Auton. Robots.

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

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

[29]  M. Dickinson,et al.  Wing rotation and the aerodynamic basis of insect flight. , 1999, Science.

[30]  Alessandro Minelli,et al.  The evolution of segmentation of centipede trunk and appendages , 2000 .

[31]  Yoshihiko Sugiyama,et al.  Dynamic stability of columns subjected to follower loads : A survey , 2000 .

[32]  Barbara Webb,et al.  Robots in invertebrate neuroscience , 2002, Nature.

[33]  T. Greenhalgh.  42 , 2002, BMJ : British Medical Journal.

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

[35]  R. Quinn,et al.  Convergent evolution and locomotion through complex terrain by insects, vertebrates and robots. , 2004, Arthropod structure & development.

[36]  Russ Tedrake,et al.  Efficient Bipedal Robots Based on Passive-Dynamic Walkers , 2005, Science.

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

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

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

[40]  R. Pfeifer,et al.  Self-Organization, Embodiment, and Biologically Inspired Robotics , 2007, Science.

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

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

[43]  A. Büschges,et al.  The extensor tibiae muscle of the stick insect: biomechanical properties of an insect walking leg muscle , 2007, Journal of Experimental Biology.

[44]  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..

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

[46]  R. Full,et al.  Active tails enhance arboreal acrobatics in geckos , 2008, Proceedings of the National Academy of Sciences.

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

[49]  A. Cohen,et al.  Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming , 2010, Proceedings of the National Academy of Sciences.

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

[51]  K. Tsuchiya,et al.  Hysteresis in the gait transition of a quadruped investigated using simple body mechanical and oscillator network models. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  W. Marsden.  I and J , 2012 .

[53]  48 , 2015, Slow Burn.