Swing Leg Retraction

Swing leg retraction (SLR) is a behavior exhibited by humans and animals in which the airborne front leg rotates rearward prior to touchdown. It is hypothesized that SLR enhances running performance of biological systems, and that we might use SLR to improve the performance of legged robots. To test these hypotheses, the Biomimetic Robotics Lab investigates the effects of swing leg retraction on several metrics of running performance,

  • Small disturbance stability and large disturbance rejection
  • Touchdown energy losses and overall energetic efficiency
  • Potential for injury, as measured by leg forces
  • Footing stability, as measured by foot slip distance and horizontal forces

using several models of varying complexity,

and with two methods,

  • Simulate the effects of a given control law for which swing leg retraction rate can be independently varied to measure running performance
  • Optimize periodic trajectories (limit cycles) that maximize a measure of running performance for each of a range of swing leg retraction rates

We use the results of these studies to develop intuition for robot controller design.

optimal retraction rate vs horizontal velocity

According to a modified SLIP model, the optimal retraction rate for minimal impact losses (and presumably higher overall energetic efficiency) is generally higher than the optimal retraction rate for maximum stability and disturbance rejection. Moreover, this tradeoff between energetic efficiency and stability becomes increasingly severe as running speed increases.

mechanical cost of transport vs foot tangential speed

For simple telescopic-legged robots, increasing swing leg retraction rate (increasing foot tangential speed) results in improved energetic efficiency (lower mechanical cost of transport) up to a point. More specifically, for a range of running speeds, the swing leg retraction rate which minimizes mechanical cost of transport is that required to zero the foot tangential speed (that is, the component of the absolute velocity of the foot at touchdown in the direction perpendicular to the axis of the leg).


Karssen, J. G. D., M. Haberland, M. Wisse, and S. Kim, "The effects of swing-leg retraction on running performance: analysis, simulation, and experiment", Robotica, vol. 33, issue 10, pp. 2137-2155, December 2015.

Karssen, J. G. D., M. Haberland, M. Wisse, and S. Kim, "The optimal swing-leg retraction rate for running", Robotics and Automation (ICRA), 2011 IEEE International Conference on, Shanghai, China, IEEE, 05/2011.

Haberland, M., J. G. D. Karssen, S. Kim, and M. Wisse, "The effect of swing leg retraction on running energy efficiency", Intelligent Robots and Systems (IROS), 2011 IEEE/RSJ International Conference on, San Francisco, CA, IEEE, 09/2011.