Stable running with a two-segment compliant leg


This research presents a two-segment compliant leg model for understanding fast running locomotion of animals and extending to quadruped robot later. We introduce an approach toward a full understanding of the model by investigating the energy of the system and constructing a set of data, called Limit Cycle Set. The set is computed via optimization procedures and includes all the configurations of the model that contribute to its periodic, stable running locomotion. By introducing the creative design of the configurations, the two-segment compliant model is sufficiently general to be extended to other similar two-segment leg models. Along with the computation, we investigate the system stability and discover that it is possible to achieve stability of a compliant leg in real environments with a simple control strategy. The stable motion is successfully validated in real experiments.

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  1. 1.

    Blickhan R (1989) The spring-mass model for running and hopping. J Biomech 22:1217–1227

  2. 2.

    Seyfarth A, Geyer H, Gnther M, Blickhan R (2002) A movement criterion for running. J Biomech 35(5):649–655

  3. 3.

    Schwind WJ, Koditschekt DE (1997) Characterization of monoped equilibrium gaits. In: Proceedings IEEE international conference on robotics and automation, pp. 1986–1992

  4. 4.

    Cavagna GA, Saibene FP, Margaria R (1964) Mechanical work in running. J Appl Physiol 19(2):249–256

  5. 5.

    Alexander RM (1990) Optimum take-off techniques for high and long jumps. Philos Transact Biol Sci 329(1252):3–10

  6. 6.

    Geyer H, Seyfarth A, Blickhan R (2003) Positive force feedback in bouncing gaits. Proc Biol Sci B 270(1529):2173–2183

  7. 7.

    Shen ZH, Seipel JE (2012) A fundamental mechanism of legged locomotion with hip torque and leg damping. Bioinspir Biomim 7(4):046–061

  8. 8.

    Blum Y, Lipfert SW, Rummel J, Seyfarth a (2010) Swing leg control in human running. Bioinspir Biomim 5(2):026–037

  9. 9.

    Schmitt J (2006) A simple stabilizing control for sagittal plane locomotion. J Comput Nonlinear Dyn 1(4):348–375

  10. 10.

    Altendorfer R, Koditschek D, Holmes P (2004) Stability analysis of legged locomotion models by symmetry-factored return maps. Int J Robot Res 23(1011):979–999

  11. 11.

    Zhang ZG, Fukuokat Y, Kirnurat H (2004) Stable quadrupedal running based on a spring-loaded two-segment legged model. Proc IEEE Int Conf Robot Autom 3:2601–2606

  12. 12.

    Iida F, Minekawa Y, Rummel J, Seyfarth A (2007) Toward a human-like biped robot with compliant legs. Robot Auton Syst 57(2):139–144

  13. 13.

    Seyfarth A, Günther M, Blickhan R (2001) Stable operation of an elastic three-segment leg. Biol Cybern 84(5):365–382

  14. 14.

    Ingen JVAN (1989) From rotation to translation: constraints on multi-Joint movements and the unique action. Hum Mov Sci 8(4):301–337

  15. 15.

    Rummel J, Seyfarth A (2008) Stable running with segmented legs. Int J Robot Res 27(8):919–934

  16. 16.

    Lee YH, Tran DT, Hyun J, Phan LT, Koo IM, Yang SU, Choi HR (2015) A gait transition algorithm based on hybrid walking gait for a quadruped walking robot. Intel Serv Robotics 8:185–200

  17. 17.

    Baek S, Park J, Joo Y, Yim J, Choi Y (2016) Dynamic modeling and control of hopping robot in planar space. Intel Serv Robotics 9:153–161

  18. 18.

    Lee DV, Meek SG (2005) Directionally compliant legs influence the intrinsic pitch behaviour of a trotting quadruped. Proc R Soc B Biol Sci 272(1563):919–934

  19. 19.

    Rao SS (2009) Engineering optimization. Wiley, New York

  20. 20.

    Tucker W (2002) Computing accurate Poincaré maps. Phys D 171:127–137

  21. 21.

    Dare WN, Erefah AZ, Ogbe PD (2013) A comparative study on thigh length to leg length ratio in adult males of two southern states in Nigeria. Eur J Appl Sci 5(4):115–117

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This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005241).

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Correspondence to Hyouk Ryeol Choi.

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Phan, L.T., Lee, Y.H., Kim, D.Y. et al. Stable running with a two-segment compliant leg. Intel Serv Robotics 10, 173–184 (2017).

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  • Compliant leg
  • Segment leg
  • Running