Rotary galloping with a lock–unlock elastic spinal joint

Abstract

The effect of the spinal joint on dynamic performance of quadrupedal model in galloping gait is presented in this paper. A 12-DOF sagittal planner galloping model with one spinal joint and four actuated legs including hip and knee joints is introduced. The spinal joint is controlled by a lock–unlock mechanism, in which the spinal joint is locked when maximum extension or flexion is obtained and unlocked when proper conditions are met (at the instance of the back trailing leg touches the ground or at a certain body angle). The differences between the dynamic models with and without a spine and the effect of different initial angles of the spinal joint, different postures (landing angle differences, swing angles and initial heights of center of mass), and different horizontal velocities on the dynamic performance are analyzed. It is illustrated that a quadrupedal model using a slightly controlled spinal joint with proper body postures when galloping exhibits considerable improvement of dynamic performance, and legged systems should not employ rotary galloping pattern until running speeds are sufficient.

Keywords

Quadrupedal model rotary galloping planar model spinal joint elastic joint

Get full access to this article

View all access options for this article.

References

Alexander

. Optimization and gaits in the locomotion of vertebrates. Physiol Rev 1989; 69: 1199–1229.

Muybridge

. Animals in motion, New York, NY: Dover Publications, 1957.

Hoyt

Taylor

. Gait and the energetics of locomotion in horses. Nature 1981; 292: 239–240.

Griffin

Kram

Wickler

. Biomechanical and energetic determinants of the walk–trot transition in horses. J Exp Biol 2004; 207: 4215–4223.

Wickler

Hoyt

Cogger

. The energetics of the trot–gallop transition. J Exp Biol 2003; 206: 1557–1564.

Hildebrand

. Motions of the running cheetah and horse. J Mammal 1959; 40: 481–495.

Biancardi

Minetti

. Biomechanical determinants of transverse and rotary gallop in cursorial mammals. J Exp Biol 2012; 215: 4144–4156.

Farley

Taylor

. A mechanical trigger for the trot-gallop transition in horses. Science 1991; 253: 306–308.

Bertram

JEA

Gutmann

. Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop. J R Soc Interface 2008; 6: 549–559.

10.

National Geographic. Running cheetah on high speed HD camera, 2012. Available at: www.youtube.com/watch?v=NuyeVN7PuTM?.

11.

Hildebrand

. Further studies on locomotion of the cheetah. J Mammal 1961; 42: 84–91.

12.

Gray

. How animals move, London: Cambridge University Press, 1960.

13.

Alexander

Dimery

Ker

. Elastic structures in the back and their role in galloping in some mammals. J Zool 1985; 207: 467–482.

14.

Alexander

Dimery

Ker

. Elastic structures in the back and their role in galloping in some mammals. J Zool A 1985; 207: 467–482.

15.

Hackert

. Dynamics of Pikas' half-bound: spinal flexion contributes to dynamic stability. PhD Thesis, Friedrich-Schiller-University Jena, Germany, 2003.

16.

English

. The functions of the lumbar spine during stepping in the cat. J Morphol 1980; 165: 55–66.

17.

Leeser

. Locomotion experiments on a planar quadruped robot with articulated spine, Massachusetts Institute of Technology, 1996.

18.

Boston Dynamics. CHEETAH - fastest legged robot, 2013. Available at: http://www.bostondynamics.com/robot_cheetah.html.

19.

Kim

. Cheetah-inspired quadruped: high-speed locomotion platform, 2013.. Available at: http://biomimetics.mit.edu:8100/wordpress/.

20.

Sinnet

Jiang

Ames

. A human-inspired framework for bipedal robotic walking design. Int J Biomechatron Biomed Robot 2013, to appear.

21.

Raibert

. Legged robots that balance, Cambridge, MA: MIT Press, 1986.

22.

Park H-W and Kim S. Variable speed galloping control using vertical impulse modulation for quadruped robots: application to MIT cheetah robot, 2013. Available at: http://www-personal.umich.edu/∼parkhw/MITCheetah.pdf.

23.

Nanua

Waldron

. Dynamics of a galloping quadruped. PhD Thesis, The Ohio State University, United States, 1992.

24.

Cao Q and Poulakakis I. Passive Quadrupedal Bounding with a Segmented Flexible Torso. 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Algarve, Portugal, 7--12 October 2012, pp.2484--2489. IEEE.

25.

Cao Q and Poulakakis I. Self-stable bounding with a flexible torso. Available at: http://research.me.udel.edu/∼poulakas/Publications/papers/cao_poulakakis_AMAM13.pdf.

26.

Cao

Poulakakis

. Quadrupedal bounding with a segmented flexible torso: passive stability and feedback control. Bioinspiration Biomimetics 2013; 8: 046007–046007.

27.

Culha U and Saranli U. Quadrupedal bounding with an actuated spinal joint. In: Robotics and Automation (ICRA), 2011 IEEE International Conference, Shanghai, Peoples Republic of China, 9--13 May 2011, pp.1392–1397.

28.

Culha

. An actuated flexible spinal mechanism for a bounding quadrupedal robot, Bilkent University, 2012.

29.

Deng

Wang

. Quasi passive bounding of a quadruped model with articulated spine. Mech Machine Theor 2012; 52: 232–242.

30.

Haueisen

. Investigation of an articulated spine in a quadruped robotic system, The University of Michigan, 2011.

31.

Folkertsma GA, Kim S and Stramigioli S. Parallel stiffness in a bounding quadruped with flexible spine. In: Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ international conference, IEEE, Algarve, Portugal, 7–12 October 2012, pp.2210–2215.

32.

Sreenath

Park

H-W

Poulakakis

. A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on MABEL. Int J Robot Res 2011; 30: 1170–1193.

33.

Walter

Carrier

. Ground forces applied by galloping dogs. J Exp Biol 2007; 210: 208–216.

34.

Hudson

Corr

Wilson

. High speed galloping in the cheetah (Acinonyx jubatus) and the racing greyhound (Canis familiaris): spatio-temporal and kinetic characteristics. J Exp Biol 2012; 215: 2425–2434.

35.

Pandy

Kumar

Berme

. The dynamics of quadrupedal locomotion. J Biomech Eng 1988; 110: 230–237.

36.

Maes

Herbin

Hackert

. Steady locomotion in dogs: temporal and associated spatial coordination patterns and the effect of speed. J Exp Biol 2008; 211: 138–149.

37.

Haberland M, Karssen JD, Kim S, et al. The effect of swing leg retraction on running energy efficiency. In: Intelligent Robots and Systems (IROS), 2011 IEEE/RSJ international conference, IEEE, San Francisco, 25--30 September 2011, pp.3957–3962.

38.

Karssen JD, Haberland M, Wisse M, et al. The optimal swing-leg retraction rate for running. In: Robotics and Automation (ICRA), 2011 IEEE international conference, IEEE, Shanghai, Peoples Republic of China, 9--13 May 2011, pp.4000–4006.

39.

Khalil

Dombre

. Modeling, identification and control of robots, Bristol, PA, USA: Taylor & Francis, Inc., 2002.