Skip to main content

The effects of swing-leg retraction on running performance: analysis, simulation, and experiment

  • J. G. Daniël Karssen (a1), Matt Haberland (a2), Martijn Wisse (a1) and Sangbae Kim (a2)

Using simple running models, researchers have argued that swing-leg retraction can improve running robot performance. In this paper, we investigate whether this holds for a more realistic simulation model validated against a physical running robot. We find that swing-leg retraction can improve stability and disturbance rejection. Alternatively, swing-leg retraction can simultaneously reduce touchdown forces, slipping likelihood, and impact energy losses. Surprisingly, swing-leg retraction barely affected net energetic efficiency. The retraction rates at which these effects are the greatest are strongly model-dependent, suggesting that robot designers cannot always rely on simplified models to accurately predict such complex behaviors.

Corresponding author
*Corresponding author. E-mail:
Hide All
1.Raibert, M., Blankespoor, K., Nelson, G., Playter, R. and the BigDog Team, “Bigdog, the Rough-Terrain Quadruped Robot,” Proceedings of the 17th World Congress, (2008) pp. 10823–10825.
2.Saranli, U., Buehler, M. and Koditschek, D. E., “Rhex: A simple and highly mobile hexapod robot,” Int. J. Robot. Res. 20 (7), 616631 (2001).
3.Kim, S., Clark, J. E. and Cutkosky, M. R., “iSprawl: Design and tuning for high-speed autonomous open-loop running,” Int. J. Robot. Res. 25 (9), 903912 (2006).
4.Müller, R. and Blickhan, R., “Running on uneven ground: Leg adjustments to altered ground level,” Hum. Mov. Sci. 29 (4), 578589 (2010).
5.Blum, Y., Lipfert, S. W., Rummel, J. and Seyfarth, A., “Swing leg control in human running,” Bioinspiration Biomimetics 5, 026006 (2010).
6.Seyfarth, A. and Geyer, H., “Natural Control of Spring-Like Running: Optimized Self-Stabilization,” Proceedings of the Fifth International Conference on Climbing and Walking Robots (2002) pp. 81–85.
7.Raibert, M. H., Brown, H. B. Jr., Chepponis, M., Koechling, J. and Hodgins, J. K., “Dynamically stable legged locomotion,” Technical Report, DTIC Document (1989). URL: Accessed February 13, 2014.
8.Hobbelen, D. G. E. and Wisse, M., “Limit Cycle Walking,” In: Humanoid Robots, Human-like Machines Hackel, M, ed.) (I-Tech, Vienna, Austria, 2007a) pp. 277294.
9.Asano, F., “Effects of Swing-Leg Retraction and Mass Distribution on Energy-Loss Coefficient in Limit Cycle Walking,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2009 (IROS 2009) (IEEE, New York, 2009) pp. 32143219.
10.Wisse, M., Atkeson, C. G. and Kloimwieder, D. K., “Dynamic Stability of a Simple Biped Walking System with Swing Leg Retraction,” In: Fast Motions in Biomechanics and Robotics, Diehl, Moritz and Mombaur, Katja, eds.), Lecture Notes in Control and Information Sciences, vol. 340 (Springer, Berlin, Germany, 2006) pp. 427443. ISBN 978-3-540-36118-3. URL:
11.Hobbelen, D. G. E. and Wisse, M., “Swing-leg retraction for limit cycle walkers improves disturbance rejection,” IEEE Trans. Robot. 24 (2), 377389 (2008).
12.Seyfarth, A., Geyer, H. and Herr, H., “Swing-leg retraction: A simple control model for stable running,” J. Exp. Biol. 206 (15), 25472555 (2003).
13.Ernst, M., Geyer, H. and Blickhan, R., “Spring-Legged Locomotion on Uneven Ground: A Control Approach to Keep the Running Speed Constant,” International Conference on Climbing and Walking Robots (2009) pp. 639–644.
14.Karssen, J. G. D., Haberland, M., Wisse, M. and Kim, S., “The Optimal Swing-Leg Retraction Rate for Running,” Proceedings of IEEE International Conference on Robotics and Automation (IEEE, New York, 2011) pp. 40004006.
15.Peuker, F., Seyfarth, A. and Grimmer, S., “Inheritance of SLIP Running Stability to a Single-Legged and Bipedal Model with Leg Mass and Damping,” 4th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, 2012 (BioRob) (IEEE, New York, 2012) pp. 395400.
16.Daley, M. A. and Usherwood, J. R., “Two explanations for the compliant running paradox: Reduced work of bouncing viscera and increased stability in uneven terrain,” Biol. Lett. 6 (3), 418421 (2010).
17.Raibert, M. H., Legged Robots that Balance (MIT Press, Cambridge, MA, 1986).
18.Haberland, M., Karssen, J. G. D., Kim, S. and Wisse, M.The Effect of Swing Leg Retraction on Running Energy Efficiency,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, New York, 2011) pp. 39573962.
19.Blickhan, R., “The spring-mass model for running and hopping,” J. Biomech. 22 (11), 12171227 (1989).
20.Schwind, W. J. and Koditschek, D. E., “Characterization of Monoped Equilibrium Gaits,” In: Proceedings of IEEE International Conference on Robotics and Automation, vol. 3 (IEEE, New York, 1997) pp. 19861992.
21.Ghigliazza, R. M., Altendorfer, R., Holmes, P. and D. Koditschek, “A simply stabilized running model,” SIAM Revi. 47 (3), 519549 (2005). ISSN . URL:
22.Poulakakis, I. and Grizzle, J. W., “Modeling and Control of the Monopedal Robot Thumper,” Proceedings of IEEE International Conference on Robotics and Automation (IEEE, New York, 2009) pp. 33273334.
23.Blickhan, R. and Full, R. J., “Similarity in multilegged locomotion: Bouncing like a monopode,” J. Comp. Physiol. Neuroethol. Sens. Neural. Behav. Physiol. 173 (5), 509517 (1993).
24.Full, R. J. and Koditschek, D. E., “Templates and anchors: Neuromechanical hypotheses of legged locomotion on land,” J. Exp. Biol. 202 (23), 33253332 (1999).
25.van der Linde, R. Q. and Schwab, A. L., “Multibody Dynamics B” (2011). URL: (accessed May 8, 2014).
26.Haberland, M., “Extracting Principles from Biology for Application to Running Robots” Ph.D. Thesis (Massachusetts Institute of Technology, 2014).
27.McGeer, T., “Passive bipedal running,” Proc. R. Soc. 240 (1297), 107134 (1990).
28.Hobbelen, D. G. E. and Wisse, M., “A disturbance rejection measure for limit cycle walkers: The gait sensitivity norm,” IEEE Trans. Robot. 23 (6), 12131224 (2007).
29.Bruijn, S. M., Meijer, O. G., Beek, P. J. and Van Dieën, J. H., “Assessing the stability of human locomotion: A review of current measures,” J. R. Soc. Interface 10 (83) (2013).
30.Jindrich, D. al., “Dynamic stabilization of rapid hexapedal locomotion,” J. Exp. Biol. 205 (18), 28032823 (2002).
31.Karssen, J. G. D. and Wisse, M., “Running with improved disturbance rejection by using non-linear leg springs,” Int. J. Robot. Res. 30 (13), 15851595 (2011).
32.McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9 (2), 6282 (1990).
33.Pratt, J., Chew, C. M., Torres, A., Dilworth, P. and Pratt, G., “Virtual model control: An intuitive approach for bipedal locomotion,” Int. J. Robot. Res. 20 (2), 129 (2001).
34.Wisse, M., Schwab, A. L., van der Linde, R. Q. and van der Helm, F. C. T., “How to keep from falling forward: Elementary swing leg action for passive dynamic walkers,” IEEE Trans. Robot. 21 (3), 393401 (2005).
35.Blanchard, B. S., Verma, D. and Peterson, E. L., Maintainability: A Key to Effective Serviceability and Maintenance Management, vol. 13 (Wiley-Interscience, Hoboken, NJ, 1995).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed