Generation of bipedal walking through interactions among the robot dynamics, the oscillator dynamics, and the environment: Stability characteristics of a five-link planar biped robot

We previously developed a locomotion control system for a biped robot using nonlinear oscillators and verified the performance of this system in order to establish adaptive walking through the interactions among the robot dynamics, the oscillator dynamics, and the environment. In order to clarify these mechanisms, we investigate the stability characteristics of walking using a five-link planar biped robot with a torso and knee joints that has an internal oscillator with a stable limit cycle to generate the joint motions. Herein we conduct numerical simulations and a stability analysis, where we analytically obtain approximate periodic solutions and examine local stability using a Poincaré map. These analyses reveal (1) stability characteristics due to locomotion speed, torso, and knee motion, (2) stability improvement due to the modulation of oscillator states based on phase resetting using foot-contact information, and (3) the optimal parameter in the oscillator dynamics for adequately exploiting the interactions among the robot dynamics, the oscillator dynamics, and the environment in order to increase walking stability. The results of the present study demonstrate the advantage and usefulness of locomotion control using oscillators through mutual interactions.

[1]  M. Coleman,et al.  Motions of a Rimless Spoked Wheel: a Simple 3D System with Impacts , 1997 .

[2]  H. Benjamin Brown,et al.  c ○ 2001 Kluwer Academic Publishers. Manufactured in The Netherlands. RHex: A Biologically Inspired Hexapod Runner ∗ , 2022 .

[3]  K. Tsuchiya,et al.  Self-stability of a simple walking model driven by a rhythmic signal , 2007 .

[4]  Max Suell Dutra,et al.  Modeling of a bipedal robot using mutually coupled Rayleigh oscillators , 2004, Biological Cybernetics.

[5]  Masahiro Fujita,et al.  A small biped entertainment robot exploring attractive applications , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[6]  Daniel A. Kingsley,et al.  Parallel Complementary Strategies for Implementing Biological Principles into Mobile Robots , 2003, Int. J. Robotics Res..

[7]  Kenji KANEKO,et al.  Humanoid robot HRP-3 , 2004, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[8]  Daniel E. Koditschek,et al.  Hybrid zero dynamics of planar biped walkers , 2003, IEEE Trans. Autom. Control..

[9]  Hiroshi Shimizu,et al.  Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment , 1991, Biological Cybernetics.

[10]  M. Coleman,et al.  The simplest walking model: stability, complexity, and scaling. , 1998, Journal of biomechanical engineering.

[11]  Gentaro Taga,et al.  A model of the neuro-musculo-skeletal system for human locomotion , 1995, Biological Cybernetics.

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

[13]  Tad McGeer,et al.  Passive Dynamic Walking , 1990, Int. J. Robotics Res..

[14]  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..

[15]  George A. Bekey,et al.  Gait Adaptation in a Quadruped Robot , 2002, Auton. Robots.

[16]  Frans C. T. van der Helm,et al.  How to keep from falling forward: elementary swing leg action for passive dynamic walkers , 2005, IEEE Transactions on Robotics.

[17]  Jonathan E. Clark,et al.  Stride Period Adaptation for a Biomimetic Running Hexapod , 2001, ISRR.

[18]  David A. Winter,et al.  Biomechanics and Motor Control of Human Movement , 1990 .

[19]  Koh Hosoda,et al.  Biped robot design powered by antagonistic pneumatic actuators for multi-modal locomotion , 2008, Robotics Auton. Syst..

[20]  G. B. Kauffman,et al.  Efficient Bipedal Robots Based on Passive-Dynamic Walkers , 2005 .

[21]  I. Stewart,et al.  Coupled nonlinear oscillators and the symmetries of animal gaits , 1993 .

[22]  Miomir Vukobratović,et al.  Biped Locomotion: Dynamics, Stability, Control and Application , 1990 .

[23]  Shinya Aoi,et al.  Stability analysis of a simple walking model driven by an oscillator with a phase reset using sensory feedback , 2006, IEEE Transactions on Robotics.

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

[25]  Shugen Ma,et al.  Neural oscillator network-based controller for meandering locomotion of snake-like robots , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[26]  Max Suell Dutra,et al.  Modeling of a bipedal locomotor using coupled nonlinear oscillators of Van der Pol , 2003, Biological Cybernetics.

[27]  T. Takenaka,et al.  The development of Honda humanoid robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

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

[29]  Martin Buehler,et al.  Modeling and Experiments of Untethered Quadrupedal Running with a Bounding Gait: The Scout II Robot , 2005, Int. J. Robotics Res..

[30]  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.

[31]  Masafumi Yano,et al.  Real-time Control of Walking of Insect; Self-organization of the Constraints and Walking Patterns , 2002, DARS.

[32]  Tamio Arai,et al.  CPG model for autonomous decentralized multi-legged robot system - generation and transition of oscillation patterns and dynamics of oscillators , 2003, Robotics Auton. Syst..

[33]  Koh Hosoda,et al.  Controlling the Walking Period of a Pneumatic Muscle Walker , 2006, Int. J. Robotics Res..

[34]  Shinya Aoi,et al.  Adaptive behavior in turning of an oscillator-driven biped robot , 2007, Auton. Robots.

[35]  Shinya Aoi,et al.  Locomotion Control of a Biped Robot Using Nonlinear Oscillators , 2005, Auton. Robots.

[36]  Shinya Aoi,et al.  Simulating Adaptive Human Bipedal Locomotion Based on Phase Resetting Using Foot-Contact Information , 2008, Adv. Robotics.

[37]  Gentaro Taga,et al.  A model of the neuro-musculo-skeletal system for human locomotion , 1995, Biological Cybernetics.

[38]  Jun Morimoto,et al.  Learning from demonstration and adaptation of biped locomotion , 2004, Robotics Auton. Syst..

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

[40]  H. Yuasa,et al.  Coordination of many oscillators and generation of locomotory patterns , 1990, Biological Cybernetics.

[41]  Bernard Espiau,et al.  Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws , 1997, Auton. Robots.

[42]  Arthur D Kuo,et al.  Energetics of actively powered locomotion using the simplest walking model. , 2002, Journal of biomechanical engineering.

[43]  Daniel E. Koditschek,et al.  RHex: A Simple and Highly Mobile Hexapod Robot , 2001, Int. J. Robotics Res..

[44]  Franck Plestan,et al.  Asymptotically stable walking for biped robots: analysis via systems with impulse effects , 2001, IEEE Trans. Autom. Control..

[45]  Atsuo Takanishi,et al.  Development of a bipedal humanoid robot-control method of whole body cooperative dynamic biped walking , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[46]  Ludovic Righetti,et al.  Programmable central pattern generators: an application to biped locomotion control , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

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

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

[49]  Taiga Yamasaki,et al.  Possible functional roles of phase resetting during walking , 2003, Biological Cybernetics.

[50]  M. Mori,et al.  Control method of biped locomotion giving asymptotic stability of trajectory , 1984, at - Automatisierungstechnik.

[51]  Fumihiko Asano,et al.  Virtual gravity and coupling control for robotic gait synthesis , 2001, IEEE Trans. Syst. Man Cybern. Part A.

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

[53]  G. Courtine,et al.  Human walking along a curved path. II. Gait features and EMG patterns , 2003, The European journal of neuroscience.

[54]  S. Grillner.  Neurobiological bases of rhythmic motor acts in vertebrates. , 1985, Science.

[55]  Masayuki Inaba,et al.  Design and development of research platform for perception-action integration in humanoid robot: H6 , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[56]  M. Vukobratovic,et al.  Biped Locomotion , 1990 .

[57]  Friedrich Pfeiffer,et al.  Sensors and Control Concept of Walking “Johnnie” , 2003, Int. J. Robotics Res..

[58]  Taishin Nomura,et al.  Stumbling with optimal phase reset during gait can prevent a humanoid from falling , 2006, Biological Cybernetics.

[59]  Ralph Etienne-Cummings,et al.  An in silico central pattern generator: silicon oscillator, coupling, entrainment, and physical computation , 2003, Biological Cybernetics.

[60]  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.

[61]  T. Calvert,et al.  Model of a pattern generator for locomotion in mammals. , 1985, The American journal of physiology.

[62]  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).

[63]  Teresa Zielińska.  Coupled oscillators utilised as gait rhythm generators of a two-legged walking machine , 2004, Biological Cybernetics.

[64]  Shinya Aoi,et al.  Bifurcation and chaos of a simple walking model driven by a rhythmic signal , 2006 .

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

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