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Characterization of Dynamic Behaviors in a Hexapod Robot

  • Haldun KomsuogluEmail author
  • Anirudha Majumdar
  • Yasemin Ozkan Aydin
  • Daniel E. Koditschek
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 79)

Abstract

This paper investigates the relationship between energetic efficiency and the dynamical structure of a legged robot’s gait. We present an experimental data set collected from an untethered dynamic hexapod, EduBot [1] (a RHex-class [2] machine), operating in four distinct manually selected gaits. We study the robot’s single tripod stance dynamics of the robot which are identified by a purely jointspace-driven estimation method introduced in this paper. Our results establish a strong relationship between energetic efficiency (simultaneous reduction in power consumption and increase in speed) and the dynamical structure of an alternating tripod gait as measured by its fidelity to the SLIP mechanics—a dynamical pattern exhibiting characteristic exchanges of kinetic and spring-like potential energy [3]. We conclude that gaits that are dynamic in this manner give rise to better utilization of energy for the purposes of locomotion.

Keywords

Slip Model Slip Parameter World Coordinate System Legged Robot Hexapod Robot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Burden, S., Clark, J.E., Weingarten, J.D., Komsuoglu, H., Koditschek, D.E.: Heterogeneous leg stiffness and roll in dynamic running. In: Proceedings of IEEE Conference of Robotics and Automation (2007)Google Scholar
  2. 2.
    Saranli, U., Buehler, M., Koditschek, D.E.: Rhex - a simple and highly mobile hexapod robot. International Journal of Robotics Research 20(7), 616–631 (2001)CrossRefGoogle Scholar
  3. 3.
    Blickhan, R.: The spring-mass model for running and hopping. Journal of Biomechanics 22(11/12), 1217–1227 (1989)CrossRefGoogle Scholar
  4. 4.
    Gabrielli, G., von Karman, T.: What price speed? Mechanical Engineering, 775–781 (1950)Google Scholar
  5. 5.
    Greenewalt, C.H.: The energetics of locomotion-is small size really disadvantageous? Proceedings of the American Philosophical Society 121, 100–106 (1976)Google Scholar
  6. 6.
    Cavagna, G.A., Heglund, N.C., Taylor, C.R.: Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. American Journal of Physiology 5(233), R243–R261 (1977)Google Scholar
  7. 7.
    Taylor, C.R., Heglund, N.C., Maloiy, G.M.O.: Energetics and mechanics of terrestrial locomotion. Journal of Experimental Biology 97, 1–21 (1982)Google Scholar
  8. 8.
    Roberts, T.J., Kram, R., Weyand, P.G., Taylor, C.R.: Energetics of bipedal running. The Journal of Experimental Biology 201, 2745–2751 (1998)Google Scholar
  9. 9.
    Kerdok, A.E., Biewener, A.A., McMahon, T.A., Weyand, P.G., Herr, H.M.: Energetics and mechanics of human running on surfaces of different stiffnesses. Journal of Applied Physiology 92, 469–478 (2002)Google Scholar
  10. 10.
    Herr, H.M., Huang, G.T., McMahon, T.A.: A model of scale effects in mammalian quadrupedal running. Journal of Experimental Biology 205, 959–967 (2002)Google Scholar
  11. 11.
    Gregorio, P., Ahmadi, M., Buehler, M.: Design, control, and energetics of an electrically actuated legged robot. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 27(4), 626–634 (1997)CrossRefGoogle Scholar
  12. 12.
    Brown Jr., H.B., Zeglin, G.: The bow leg hopping robot. In: Proceedings of International Conference on Robotics and Automation (1998)Google Scholar
  13. 13.
    Ahmadi, M., Buehler, M.: The arl monopod ii running robot: Control and energetics. In: International Conference on Robotics and Automation (1999)Google Scholar
  14. 14.
    Garcia, M., Chatterjee, A., Ruina, A.: Efficiency, speed, and scaling of two-dimensional passive-dynamic walking. Dynamics and Stability of Systems 15(2), 75–99 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Weingarten, J.D., Lopes, G.A.D., Buehler, M., Groff, R.E., Koditschek, D.E.: Automated gait adaptation for legged robots. In: Int. Conf. Robotics and Automation. IEEE, New Orleans (2004)Google Scholar
  16. 16.
    Full, R.J.: Concepts of efficiency and economy in land locomotion. In: Blake, R.W. (ed.) Efficiency and Economy in Animal Physiology, pp. 97–131. Cambridge University Press (1991)Google Scholar
  17. 17.
    Binnard, M.B.: Design of a small pneumatic walking robot. MS, Massachusetts Institute of Technology (1995)Google Scholar
  18. 18.
    Zeglin, G.: The bow leg hopping robot. Doctoral Thesis in Robotics, Carnegie Mellon University (1999)Google Scholar
  19. 19.
    McMordie, D., Buehler, M.: Towards pronking with a hexapod robot. In: Proceedings of 4th International Conference on Climbing and Walking Robots, Germany (September 2001)Google Scholar
  20. 20.
    Campbell, D., Buehler, M.: Preliminary bounding experiments in a dynamic hexa-pod. In: Siciliano, B., Dario, P. (eds.) Experimental Robotics, ch. VIII, pp. 612–621. Springer (2003)Google Scholar
  21. 21.
    Autumn, K., Buehler, M., Cutkosky, M., Fearing, R.S., Full, R.J., Goldman, D.I., Groff, R., Provancher, W., Rizzi, A.A., Saranli, U., Saunders, A., Koditschek, D.E.: Robotics in scansorial environments. In: Proceedings of SPIE 2005, pp. 291–302 (2005)Google Scholar
  22. 22.
    Koditschek, D.E., Full, R.J., Buehler, M.: Mechanical aspects of legged locomotion control. Antropod Structure and Development 33, 251–272 (2004)CrossRefGoogle Scholar
  23. 23.
    Ker, R.F., Bennett, M.B., Bibby, S.R., Kester, R.C., Alexander, R.M.: The spring in the arch of the human foot. Nature 325, 147–149 (1987)CrossRefGoogle Scholar
  24. 24.
    Alexander, R.M., Bennet-Clark, H.C.: Storage of elastic strain energy in muscle and other tissues. Nature 265, 114–117 (1977)CrossRefGoogle Scholar
  25. 25.
    Alexander, R.M.: Three uses for springs in legged locomotion. The International Journal of Robotics Research 9(2), 53–61 (1990)CrossRefGoogle Scholar
  26. 26.
    Alexander, R.M.: Elastic mechanisms in animal movement. Cambridge University Press (1988)Google Scholar
  27. 27.
    Dickinson, M.H., Farley, C.T., Full, R.J., Koehl, M.A.R., Kram, R., Lehman, S.: How animals move: An integrative view. Science 288, 100–106 (2000)CrossRefGoogle Scholar
  28. 28.
    Blickhan, R., Full, R.J.: Similarity in multilegged locomotion: Bouncing like a monopode. Journal of Comparative Physiology 173, 509–517 (1993)Google Scholar
  29. 29.
    Komsuoglu, H.: Dynamic legged mobility—an overview. In: Proceedings of International Joint Robotics Conference and Workshop (2009)Google Scholar
  30. 30.
    Raibert, M.H.: Legged robots that balance. MIT Press series in artifficial intelligence. MIT Press, Boston (1986)Google Scholar
  31. 31.
    Berkemeier, M.D., Desai, K.V.: Design of a robot leg with elastic energy storage, comparison to biology, and preliminary experimental results. In: Proceedings of IEEE Conference on Robotics and Automation, Minneapolis, vol. 1, pp. 213–218 (April 1996)Google Scholar
  32. 32.
    Buehler, M., Battaglia, R., Cocosco, A., Hawker, G., Sarkis, J., Yamazaki, K.: Scout: A simple quadruped that walks, climbs, and runs. In: International Conference on Robotics and Automation (1998)Google Scholar
  33. 33.
    McBride, B., Longoria, R., Krotkov, E.: Off-road mobility of small robotic ground vehicles. In: Messina, E., Meystel, A. (eds.) Measuring the Performance and Intelligence of Systems: Proceedings of the 2003 PerMIS Workshop, vol. NIST Special Publication 1014, September 16-18, pp. 405–412 (2003)Google Scholar
  34. 34.
    Georgiades, C., Hogue, A., Liu, H., Ripsman, A., Sim, R., Torres, L.A., Zhang, P., Prahacs, C., Buehler, M., Dudek, G., Jenkin, M., Milios, E.: Aqua: an aquatic walking robot. Dalhousie University, Technical Report CS-2003-08 (November 2003)Google Scholar
  35. 35.
    Saranli, U., Rizzi, A., Koditschek, D.E.: Model-based dynamic self-righting ma- neuvers for a hexapedal robot. International Journal of Robotics Research 23(9), 903–918 (2004)CrossRefGoogle Scholar
  36. 36.
    Spagna, J.C., Goldman, D.I., Lin, P.-C., Koditschek, D.E., Full, R.J.: Distributed feet enhance mobility in many-legged animals and robots. Journal of Bioinspiration and Biomimetics 2(1), 9–18 (2007)CrossRefGoogle Scholar
  37. 37.
    Komsuoglu, H., Sohn, K., Full, R.J., Koditschek, D.E.: A physical model for dynamical arthropod running on level ground. In: Proceedings of 11th International Symposium on Experimental Robotics (2008)Google Scholar
  38. 38.
    Li, C., Umbanhowar, P.B., Komsuoglu, H., Koditschek, D.E., Goldman, D.I.: Sensitive dependence of the motion of a legged robot on granular media. Proceedings of National Academy of Science (PNAS) 106(9), 3029–3034 (2009), http://www.pnas.org/content/106/9/3029.full.pdf+html CrossRefGoogle Scholar
  39. 39.
    Full, R.J., Koditschek, D.E.: Templates and anchors: Neuromechanical hypotheses of legged locomotion. The Journal of Experimental Biology 202(23), 3325–3332 (1999)Google Scholar
  40. 40.
    Altendorfer, R., Saranli, U., Komsuoglu, H., Koditschek, D.E., Brown Jr., H.B., Buehler, M., Moore, N., McMordie, D., Full, R.J.: Evidence for spring loaded inverted pendulum running in a hexapod robot. In: Proceedings on International Symposium on Experimental Robotics (2000)Google Scholar
  41. 41.
    Saranli, U., Koditschek, D.E.: Template based control of hexapedal running. In: Proceedings of International Conference on Robotics and Automation, vol. 1, pp. 1374–1379 (September 2003)Google Scholar
  42. 42.
    Alexander, R.M., Jayes, A.S.: Vertical movements in walking and running. Journal of Zoology 185, 27–40 (1978)CrossRefGoogle Scholar
  43. 43.
    Alexander, R.M., Jayes, A.S.: Fourier analysis of forces exerted in walking and running. Journal of Biomechanics 13, 383–390 (1980)CrossRefGoogle Scholar
  44. 44.
    Galloway, K.C., Clark, J.E., Koditschek, D.E.: Design of a tunable stiffness composite leg for dynamic locomotion. In: Proceedings of the ASME Int. Design Engineering Tech. Conferences (2009)Google Scholar
  45. 45.
    Komsuoglu, H., Mellinger, D.: Surface classiffication with a dynamic hexapod robot. In: Proceedings of International Symposium on Experimental Robotics (2010) (in preparation)Google Scholar
  46. 46.
    Weingarten, J.D., Koditschek, D.E., Komsuoglu, H., Massey, C.: Robotics as the delivery vehicle: A contexualized, social, self paced, engineering education for life-long learners. In: Proceedings of Robotics and System Science Conference (2007)Google Scholar
  47. 47.
    Komsuoglu, H., McMordie, D., Saranli, U., Moore, N., Buehler, M., Koditschek, D.E.: Proprioception based behavioral advances in a hexapod robot. In: Proceedings of International Conference on Robotics and Automation, Seoul, Korea (2001)Google Scholar
  48. 48.
    Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7(4), 308–313 (1965), http://comjnl.oxfordjournals.org/cgi/content/abstract/7/4/308 zbMATHCrossRefGoogle Scholar
  49. 49.
    Altendorfer, R., Koditschek, D.E., Holmes, P.J.: Stability analysis of a clock- driven rigid-body slip model of rhex. International Journal of Robotics Research 23(10-11), 1001–1012 (2004)CrossRefGoogle Scholar
  50. 50.
    Holmes, P.J., Koditschek, D.E., Full, R.J., Guckenheimer, J.: Dynamics of legged locomotion: Models, analysis and challenges. Society of Industrial and Applied Mathematics 48(2), 207–304 (2006), http://repository.upenn.edu/esepapers/200/ MathSciNetzbMATHGoogle Scholar
  51. 51.
    Seipel, J.E., Holmes, P.J.: A simple model for clock-actuated legged locomotion. Journal of Regular and Chaotic Dynamics 12(5), 502–520 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52.
    Saranli, U.: Dynamic locomotion in a hexapod robot. PhD, Univerisity of Michigan (2002)Google Scholar
  53. 53.
    Johnson, A., Haynes, G.C., Koditschek, D.E.: Disturbance detection, identication, and ecovery by gait transition in legged robots. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (2010) (submitted)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2014

Authors and Affiliations

  • Haldun Komsuoglu
    • 1
    Email author
  • Anirudha Majumdar
    • 1
  • Yasemin Ozkan Aydin
    • 2
  • Daniel E. Koditschek
    • 1
  1. 1.University of PennsylvaniaPhiladelphiaUSA
  2. 2.Middle East Technical UniversityAnkaraTurkey

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