Skip to main content

Advertisement

SpringerLink
Log in

Evolution of a 3D Gallop in a Quadrupedal Model with Biological Characteristics

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

The gallop is the preferred high-speed gait for dynamic locomotion in most cursorial mammals. Due to the lack of good analytical models and proven control strategies, however, the gallop remains an elusive goal in the field of legged robotics. While there have been several attempts at creating a gallop, none have captured all of the important dynamic characteristics of the gait. In this work, we present a practical approach for producing a stable 3D gallop in a quadrupedal model which includes these characteristics. The dynamic model utilizes biologically-based assumptions including articulated legs with nonzero mass, compliance at the knee joints, and a body with an asymmetric mass distribution. Furthermore, the resulting 3D gallop contains the prominent features found in the biological gait: early leg retraction, phase-locked leg motion creating an asymmetric footfall pattern, a significant gathered flight phase, unconstrained spatial dynamics, and a smooth gait. To obtain these results, we employ a multiobjective genetic algorithm with a carefully designed vector fitness function to search for various control parameters. Furthermore, we partition the search space in roughly orthogonal subspaces to find parameters for each sub-controller. A critical component of the controller is an energy control law that ensures a fixed amount of energy in the knee springs during each stride. A characterization of the resulting gait is presented, which highlights biological properties and the visual realism of the solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Raibert, M.H.: Trotting, pacing, and bounding by a quadruped robot. J. Biomech. 23, 79–98 (1990)

    Article  Google Scholar 

  2. Furushu, J., Akihito, S., Masamichi, S., Eichi, K.: Realization of a bounce gait in a quadruped robot with articular-joint-type legs. In: Proceedings of the 1995 IEEE International Conference on Robotics and Automation (ICRA), (Nagoya, Japan), pp. 697–702 (1995)

  3. Kimura, H., Akiyama, S., Sakurama, K.: Realization of dynamic walking and running of the quadruped using neural oscillator. Auton. Robots 7, 247–258 (1999)

    Article  Google Scholar 

  4. Hoyt, D.F., Taylor, C.R.: Gait and the energetics of locomotion in horses. Nature 292, 239–240 (1981)

    Article  Google Scholar 

  5. Gambaryan, P.P.: How Mammals Run: Anatomical Adaptations. Wiley, New York (1974)

    Google Scholar 

  6. Alexander, R.M., Jayes, A.S., Ker, R.F.: Estimates of energy cost for quadrupedal running gaits. J. Zool. 190, 155–192 (1980)

    Article  Google Scholar 

  7. Nanua, P., Waldron, K.J.: Energy comparison between trot, bound, and gallop using a simple model. ASME J. Biomech. Eng. 117, 466–473 (1995)

    Article  Google Scholar 

  8. Rubin, C.T., Lanyon, L.E.: Limb mechanics as a function of speed and gait: A study of functional strains in the radius and tibia of horse and dog. J. Exp. Biol. 101, 187–211 (1982)

    Google Scholar 

  9. Biewener, A.A., Taylor, C.R.: Bone strain: A determinant of gait and speed? J. Exp. Biol. 123, 383–400 (1986)

    Google Scholar 

  10. Farley, C.T., Taylor, C.R.: A mechanical trigger for the trot-gallop transition in horses. Science 253, 306–308 (1991)

    Article  Google Scholar 

  11. Schmiedeler, J.P.: The Mechanics of and Robotic Design for Quadrupedal Galloping. Ph.D. thesis, The Ohio State University, Columbus, Ohio (2001)

  12. Smith, J.A., Poulakakis, I.: Rotary gallop in the untethered Quad-ru-pe-dal quadrupedal robot Scout II. In: Proceedings of the International Conference on Intelligent Robots and Systems (IROS) 2004, (Sendai, Japan), pp. 2556–2561 (2004)

  13. Nanua, P., Waldron, K.J.: Instability and chaos in quadruped gallop. J. Mech. Des. 116, 1096–1101 (1994)

    Article  Google Scholar 

  14. Ringrose, R.: Self-stabilizing running. In: Proceedings of the 1997 IEEE International Conference on Robotics and Automation (ICRA), pp. 487–493 (1997)

  15. Marhefka, D.W., Orin, D.E., Schmiedeler, J.P., Waldron, K.J.: Intelligent control of quadruped gallops. IEEE/ASME Trans. Mechatron. 8, 446–456 (2003)

    Article  Google Scholar 

  16. Herr, H.M., McMahon, T.A.: A galloping horse model. Int. J. Robot. Res. 20(1), 26–37 (2001)

    Article  Google Scholar 

  17. Krasny, D.P., Orin, D.E.: Generating high-speed dynamic running gaits in a quadruped robot using an evolutionary search. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 34, 1685–1696 (2004)

    Article  Google Scholar 

  18. Berkemeier, M.: Modeling the dynamics of quadrupedal running. Int. J. Robot. Res. 17, 971–985 (1998)

    Article  Google Scholar 

  19. Buchner, H.H.F., Savelberg, H.H.C.M., Schamhardt, H.C., Barneveld, A.: Inertial properties of Dutch Warmblood horses. J. Biomech. 30(6), 653–658 (1997). Technical Note.

    Article  Google Scholar 

  20. McMillan, S., Orin, D.E., McGhee, R.B.: DynaMechs: An object oriented software package for efficient dynamic simulation of underwater robotic vehicles. In: Yuh, J. (ed.) Underwater Robotic Vehicles: Design and Control pp. 73–98. TSI, Albuquerque (1995)

    Google Scholar 

  21. Craig, J.J.: Introduction to Robotics: Mechanics and Control pp. 48–49. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  22. Heglund, N.C., Taylor, C.R.: Speed, stride frequency and energy cost per stride: how do they change with body size and gait? J. Exp. Biol. 138, 301–318 (1988)

    Google Scholar 

  23. Hildebrand, M.: Walking and running. In: Hildebrand, M., Bramble, D.M., Liem, K.F., Wake, D.B. (eds.) Functional Vertebrate Morphology, pp. 25–65. Belknap, Cambridge (1985)

    Google Scholar 

  24. Hildebrand, M.: The adaptive significance of tetrapod gait selection. Am. Zool. 20, 97–103 (1977)

    Google Scholar 

  25. Krasny, D.P.: Evolving Dynamic Maneuvers in a Quadruped Robot. Ph.D. thesis, The Ohio State University, Columbus, Ohio (2005). www.ohiolink.edu/etd

  26. Corne, D.W., Deb, K., Fleming, P.J., Knowles, J.D.: The good of the many outweighs the good of the one: Evolutionary multi-objective optimization. IEEE Connections Newsletter 1, 9–13 (2003)

    Google Scholar 

  27. Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: Formulation, discussion, and generalization. In: Genetic Algorithms: Proceedings of the Fifth International Conference, pp. 416–423. Morgan-Kaufmann, San Mateo (1993)

    Google Scholar 

  28. Deb, K., and Goel, T.: Controlled elitist non-dominated sorting genetic algorithm for better convergence. In: Proceedings of the First International Conference on Evolutionary Multi-criterion Optimization, pp. 67–81 (2001)

  29. Herr, H.M., Huang, G.T., McMahon, T.A.: A model of scale effects in mammalian quadrupedal running. J. Exp. Biol. 205, 959–967 (2002)

    Google Scholar 

  30. Marhefka, D.W.: Fuzzy Control and Dynamic Simulation of a Quadruped Galloping Machine. Ph.D. thesis, The Ohio State University, Columbus, Ohio (2000)

  31. Minetti, A.E., Ardigò, L.P., Reinach, E., Saibene, F.: The relationship between mechanical work and energy expenditure of locomotion in horses. J. Exp. Biol. 202, 2329–2338 (1999)

    Google Scholar 

  32. McMahon, T.A.: The role of compliance in mammalian running gaits. J. Exp. Biol. 115, 263–282 (1985)

    Google Scholar 

  33. Vakakis, A.F., Burdick, J.W., Caughey, T.K.: An ‘interesting’ strange attractor in the dynamics of a hopping robot. Int. J. Rob. Res. 10(6), 606–618 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, 43210, USA

    Darren P. Krasny & David E. Orin

Authors
  1. Darren P. Krasny
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David E. Orin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Darren P. Krasny.

Additional information

This work was supported in part by the National Defense Science and Engineering Graduate Fellowship, The Ohio State University Dean’s Distinguished University Fellowship, and the National Science Foundation under Grant IIS-0535098.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krasny, D.P., Orin, D.E. Evolution of a 3D Gallop in a Quadrupedal Model with Biological Characteristics. J Intell Robot Syst 60, 59–82 (2010). https://doi.org/10.1007/s10846-010-9409-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-010-9409-8

Keywords

Search

Navigation