Three-dimensional walking of a simulated muscle-driven quadruped robot with neuromorphic two-level central pattern generators

We aim to design a neuromorphic controller for the locomotion of a quadruped robot with muscle-driven leg mechanisms. To this end, we use a simulated cat model; each leg of the model is equipped with three joints driven by six muscle models incorporating two-joint muscles. For each leg, we use a two-level central pattern generator consisting of a rhythm generation part to produce basic rhythms and a pattern formation part to synergistically activate a different set of muscles in each of the four sequential phases (swing, touchdown, stance, and liftoff). Conventionally, it was difficult for a quadruped model with such realistic neural systems and muscle-driven leg mechanisms to walk even on flat terrain, but because of our improved neural and mechanical components, our quadruped model succeeds in reproducing motoneuron activations and leg trajectories similar to those in cats and achieves stable three-dimensional locomotion at a variety of speeds. Moreover, the quadruped is capable of walking upslope and over irregular terrains and adapting to perturbations, even without adjusting the parameters.

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

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

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

[4]  S. Grillner Control of Locomotion in Bipeds, Tetrapods, and Fish , 1981 .

[5]  N. Ogihara,et al.  Contributions of phase resetting and interlimb coordination to the adaptive control of hindlimb obstacle avoidance during locomotion in rats: a simulation study , 2013, Biological Cybernetics.

[6]  G E Goslow,et al.  The cat step cycle: Electromyographic patterns for hindlimb muscles during posture and unrestrained locomotion , 1978, Journal of morphology.

[7]  Akio Ishiguro,et al.  A Quadruped Robot Exhibiting Spontaneous Gait Transitions from Walking to Trotting to Galloping , 2017, Scientific Reports.

[8]  Vítor Matos,et al.  Gait transition and modulation in a quadruped robot: A brainstem-like modulation approach , 2011, Robotics Auton. Syst..

[9]  R. Full,et al.  The role of the mechanical system in control: a hypothesis of self-stabilization in hexapedal runners , 1999 .

[10]  J. J. Collins,et al.  Hard-wired central pattern generators for quadrupedal locomotion , 1994, Biological Cybernetics.

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

[12]  J. Cabelguen,et al.  CENTRAL PATTERN GENERATION OF FORELIMB AND HINDLIMB LOCOMOTOR ACTIVITIES IN THE CAT , 1981 .

[13]  Sangdeok Park,et al.  Central pattern generator based reflexive control of quadruped walking robots using a recurrent neural network , 2014, Robotics Auton. Syst..

[14]  Ilya A Rybak,et al.  Computational modeling of spinal circuits controlling limb coordination and gaits in quadrupeds , 2017, eLife.

[15]  Örjan Ekeberg,et al.  A neuro-mechanical model of legged locomotion: single leg control , 1998, Biological Cybernetics.

[16]  Kenichi Narioka,et al.  Producing alternating gait on uncoupled feline hindlimbs: muscular unloading rule on a biomimetic robot , 2014, Adv. Robotics.

[17]  Roger D. Quinn,et al.  Development and Training of a Neural Controller for Hind Leg Walking in a Dog Robot , 2017, Front. Neurorobot..

[18]  Yasuhiro Fukuoka,et al.  Autonomous gait transition and galloping over unperceived obstacles of a quadruped robot with CPG modulated by vestibular feedback , 2019, Robotics Auton. Syst..

[19]  R. Alexander,et al.  A dynamic similarity hypothesis for the gaits of quadrupedal mammals , 2009 .

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

[21]  F. V. D. Meché Locomotion in the cat : a behavioural and neurophysiological study of interlimb coordination , 1976 .

[22]  Sergey N Markin,et al.  Annals of the New York Academy of Sciences Afferent Control of Locomotor Cpg: Insights from a Simple Neuromechanical Model , 2022 .

[23]  Simon M. Danner,et al.  Central control of interlimb coordination and speed‐dependent gait expression in quadrupeds , 2016, The Journal of physiology.

[24]  Shinya Aoi,et al.  A stability-based mechanism for hysteresis in the walk–trot transition in quadruped locomotion , 2013, Journal of The Royal Society Interface.

[25]  Jacob Reighard,et al.  The Anatomy of the Cat , 1901, Nature.

[26]  K. Pearson Role of sensory feedback in the control of stance duration in walking cats , 2008, Brain Research Reviews.

[27]  Auke Jan Ijspeert,et al.  Towards dynamic trot gait locomotion: Design, control, and experiments with Cheetah-cub, a compliant quadruped robot , 2013, Int. J. Robotics Res..

[28]  G M Barnwell,et al.  Mathematical models of central pattern generators in locomotion: I. Current problems. , 1985, Journal of motor behavior.

[29]  G. E. Loeb,et al.  A hierarchical foundation for models of sensorimotor control , 1999, Experimental Brain Research.

[30]  B. Prilutsky,et al.  A Neuromechanical Model of Spinal Control of Locomotion , 2016 .

[31]  P. Holmes,et al.  The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model , 1982, Journal of mathematical biology.

[32]  Ronald M Harris-Warrick,et al.  Neuronal activity in the isolated mouse spinal cord during spontaneous deletions in fictive locomotion: insights into locomotor central pattern generator organization , 2012, The Journal of physiology.

[33]  J. Willis On the interaction between spinal locomotor generators in quadrupeds , 1980, Brain Research Reviews.

[34]  Sergiy Yakovenko,et al.  Contribution of stretch reflexes to locomotor control: a modeling study , 2004, Biological Cybernetics.

[35]  Olivier Michel,et al.  Cyberbotics Ltd. Webots™: Professional Mobile Robot Simulation , 2004 .

[36]  Yasuhiro Fukuoka,et al.  A simple rule for quadrupedal gait generation determined by leg loading feedback: a modeling study , 2015, Scientific Reports.

[37]  Roger D. Quinn,et al.  Using Animal Data and Neural Dynamics to Reverse Engineer a Neuromechanical Rat Model , 2015, Living Machines.

[38]  D. Carrier,et al.  External work and potential for elastic storage at the limb joints of running dogs. , 1998, The Journal of experimental biology.

[39]  Weihai Chen,et al.  CPGs with Continuous Adjustment of Phase Difference for Locomotion Control , 2013 .

[40]  Kazuo Tsuchiya,et al.  Adaptive gait pattern control of a quadruped locomotion robot , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[41]  R. Blickhan,et al.  Stabilizing function of skeletal muscles: an analytical investigation. , 1999, Journal of theoretical biology.

[42]  Ian E. Brown,et al.  Mechanics of feline soleus: II design and validation of a mathematical model , 1996, Journal of Muscle Research & Cell Motility.

[43]  Hiroshi Kimura,et al.  Towards a general neural controller for quadrupedal locomotion , 2007 .

[44]  Simon Yang,et al.  A Bio-Inspired Control Strategy for Locomotion of a Quadruped Robot , 2018 .

[45]  Nalin Harischandra,et al.  System identification of muscle–joint interactions of the cat hind limb during locomotion , 2008, Biological Cybernetics.

[46]  J. Kalaska,et al.  Sequential activation of muscle synergies during locomotion in the intact cat as revealed by cluster analysis and direct decomposition. , 2006, Journal of neurophysiology.

[47]  Olivier Michel,et al.  Cyberbotics Ltd. Webots™: Professional Mobile Robot Simulation , 2004, ArXiv.

[48]  Kunikatsu Takase,et al.  Towards a general neural controller for 3D quadrupedal locomotion , 2008, 2008 SICE Annual Conference.

[49]  A.J. Ijspeert,et al.  Passive compliant quadruped robot using Central Pattern Generators for locomotion control , 2008, 2008 2nd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics.

[50]  Kiyotoshi Matsuoka,et al.  Mechanisms of frequency and pattern control in the neural rhythm generators , 1987, Biological Cybernetics.

[51]  Yasuhiro Fukuoka,et al.  Adaptive Dynamic Walking of a Quadruped Robot on Irregular Terrain Based on Biological Concepts , 2003, Int. J. Robotics Res..

[52]  Junmin Li,et al.  Gait Planning and Stability Control of a Quadruped Robot , 2016, Comput. Intell. Neurosci..

[53]  K. Pearson,et al.  Computer simulation of stepping in the hind legs of the cat: an examination of mechanisms regulating the stance-to-swing transition. , 2005, Journal of neurophysiology.