Spine morphology and energetics: how principles from nature apply to robotics

Inspired by the locomotive advantages that an articulated spine enables in quadrupedal animals, we explore and quantify the energetic effect that an articulated spine has in legged robots. We compare two model instances of a conceptual planar quadruped: one with a traditional rigid main body and one with an articulated main body with an actuated spinal joint. Both models feature four distinct legs, series elastic actuation, distributed mass in all body segments, and limits on actuator torque and speed. Using optimal control to find the energetically optimal joint trajectories, actuator inputs, and footfall timing, we examine and compare the positive mechanical work cost of transport of both models across multiple gaits and speeds. Our results show that an articulated spine increases the maximum possible speed and improves the locomotor economy at higher velocities, especially for asymmetrical gaits. The driving factors for these improvements are the same mechanistic effects that facilitate asymmetrical gaits in nature: improved leg recirculation, elastic energy storage in the spine, and enlarged stride lengths.

[1]  R. McN. Alexander,et al.  The Gaits of Bipedal and Quadrupedal Animals , 1984 .

[2]  Roland Siegwart,et al.  ScarlETH: Design and control of a planar running robot , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[3]  R. F. Ker,et al.  Elastic structures in the back and their rôle in galloping in some mammals , 2009 .

[4]  Majid Nili Ahmadabadi,et al.  Comparing effects of rigid, flexible, and actuated series-elastic spines on bounding gait of quadruped robots , 2013, 2013 First RSI/ISM International Conference on Robotics and Mechatronics (ICRoM).

[5]  Andy Ruina,et al.  DESIGN AND CONTROL OF RANGER: AN ENERGY-EFFICIENT, DYNAMIC WALKING ROBOT , 2012 .

[6]  Hartmut Witte,et al.  Comparing the effect of different spine and leg designs for a small bounding quadruped robot , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

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

[8]  Yevgeniy Yesilevskiy,et al.  Selecting gaits for economical locomotion of legged robots , 2016, Int. J. Robotics Res..

[9]  R. M. Alexander,et al.  Optimization and gaits in the locomotion of vertebrates. , 1989, Physiological reviews.

[10]  Aaron D. Ames,et al.  Realizing dynamic and efficient bipedal locomotion on the humanoid robot DURUS , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[11]  Jesse C Dean,et al.  Energetic costs of producing muscle work and force in a cyclical human bouncing task. , 2011, Journal of applied physiology.

[12]  R. Blickhan The spring-mass model for running and hopping. , 1989, Journal of biomechanics.

[13]  Auke Jan Ijspeert,et al.  Spinal joint compliance and actuation in a simulated bounding quadruped robot , 2017, Auton. Robots.

[14]  M. Hildebrand The Adaptive Significance of Tetrapod Gait Selection , 1980 .

[15]  Qian Zhao,et al.  The effect of spine actuation and stiffness on a pneumatically-driven quadruped robot for cheetah-like locomotion , 2013, 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO).

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

[17]  J. Bertram,et al.  Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop , 2009, Journal of The Royal Society Interface.

[18]  M. Hildebrand Motions of the Running Cheetah and Horse , 1959 .

[19]  Andrew A Biewener,et al.  Outrun or Outmaneuver: Predator-Prey Interactions as a Model System for Integrating Biomechanical Studies in a Broader Ecological and Evolutionary Context. , 2015, Integrative and comparative biology.

[20]  R. M. Alexander Why Mammals Gallop , 1988 .

[21]  M. Hildebrand Further Studies on Locomotion of the Cheetah , 1961 .

[22]  Koushil Sreenath,et al.  MABEL, a new robotic bipedal walker and runner , 2009, 2009 American Control Conference.

[23]  Zhenyu Gan,et al.  Passive Dynamics Explain Quadrupedal Walking, Trotting, and Tölting. , 2016, Journal of computational and nonlinear dynamics.

[24]  Brooke M. Haueisen Investigation of an Articulated Spine in a Quadruped Robotic System , 2011 .

[25]  Horton E. Newsom,et al.  V, Cr, and Mn in the earth, moon, EPB, and SPB and the origin of the moon - Experimental studies , 1989 .

[26]  Alexander Spröwitz,et al.  ATRIAS: Design and validation of a tether-free 3D-capable spring-mass bipedal robot , 2016, Int. J. Robotics Res..

[27]  Matthew M. Williamson,et al.  Series elastic actuators , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[28]  Karl Frederick Leeser Locomotion experiments on a planar quadruped robot with articulated spine , 1996 .

[29]  C. David Remy,et al.  Optimal exploitation of natural dynamics in legged locomotion , 2011 .

[30]  G. Cavagna,et al.  Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. , 1977, The American journal of physiology.

[31]  G. Lichtwark,et al.  In vivo mechanical properties of the human Achilles tendon during one-legged hopping , 2005, Journal of Experimental Biology.

[32]  H. Ralston Energy-speed relation and optimal speed during level walking , 1958, Internationale Zeitschrift für angewandte Physiologie einschließlich Arbeitsphysiologie.

[33]  Stefano Stramigioli,et al.  Parallel stiffness in a bounding quadruped with flexible spine , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[34]  C. David Remy,et al.  Optimal gaits and motions for legged robots , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[35]  Monica A. Daley,et al.  Don't break a leg: running birds from quail to ostrich prioritise leg safety and economy on uneven terrain , 2014, Journal of Experimental Biology.

[36]  Qu Cao,et al.  On the energetics of quadrupedal bounding with and without torso compliance , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[37]  V. Tucker The energetic cost of moving about. , 1975, American Scientist.

[38]  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.

[39]  P. E. di Prampero,et al.  The energy cost of human locomotion on land and in water. , 1986 .

[40]  Yannick Aoustin,et al.  Optimal reference trajectories for walking and running of a biped robot , 2001, Robotica.

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

[42]  Roland Siegwart,et al.  Design of an articulated robotic leg with nonlinear series elastic actuation , 2009 .

[43]  Roland Siegwart,et al.  Quadrupedal Robots with Stiff and Compliant Actuation , 2012, Autom..

[44]  Roland Siegwart,et al.  Starleth: A compliant quadrupedal robot for fast, efficient, and versatile locomotion , 2012 .

[45]  Majid Nili Ahmadabadi,et al.  Benefits of an active spine supported bounding locomotion with a small compliant quadruped robot , 2013, 2013 IEEE International Conference on Robotics and Automation.