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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Blickhan R (1989) The spring-mass model for running and hopping. J Biomech 22:1217–1227
Seyfarth A, Geyer H, Gnther M, Blickhan R (2002) A movement criterion for running. J Biomech 35(5):649–655
Schwind WJ, Koditschekt DE (1997) Characterization of monoped equilibrium gaits. In: Proceedings IEEE international conference on robotics and automation, pp. 1986–1992
Cavagna GA, Saibene FP, Margaria R (1964) Mechanical work in running. J Appl Physiol 19(2):249–256
Alexander RM (1990) Optimum take-off techniques for high and long jumps. Philos Transact Biol Sci 329(1252):3–10
Geyer H, Seyfarth A, Blickhan R (2003) Positive force feedback in bouncing gaits. Proc Biol Sci B 270(1529):2173–2183
Shen ZH, Seipel JE (2012) A fundamental mechanism of legged locomotion with hip torque and leg damping. Bioinspir Biomim 7(4):046–061
Blum Y, Lipfert SW, Rummel J, Seyfarth a (2010) Swing leg control in human running. Bioinspir Biomim 5(2):026–037
Schmitt J (2006) A simple stabilizing control for sagittal plane locomotion. J Comput Nonlinear Dyn 1(4):348–375
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
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
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
Seyfarth A, Günther M, Blickhan R (2001) Stable operation of an elastic three-segment leg. Biol Cybern 84(5):365–382
Ingen JVAN (1989) From rotation to translation: constraints on multi-Joint movements and the unique action. Hum Mov Sci 8(4):301–337
Rummel J, Seyfarth A (2008) Stable running with segmented legs. Int J Robot Res 27(8):919–934
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
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
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
Rao SS (2009) Engineering optimization. Wiley, New York
Tucker W (2002) Computing accurate Poincaré maps. Phys D 171:127–137
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
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005241).
Electronic supplementary material
Below is the link to the electronic supplementary material.
About this article
Cite this article
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). https://doi.org/10.1007/s11370-017-0218-9
- Compliant leg
- Segment leg