Swing-leg retraction efficiency in bipedal walking

In biped walking, swing-leg retraction can reduce the energy loss at heel-strike by reducing the foot speed relative to the ground at touch-down. However, it also takes extra effort to brake and then accelerate the swing leg in the rearward direction. This energetic trade-off of retraction is influenced by the mechanical coupling with the stance leg preemptive push-off, and changes with different step lengths and speeds. Previously it has not been clear under which circumstances a retracting hip torque has a net energetic benefit (if ever). Here, using a simple biped model probed with numerical and analytic methods, we show how the effectiveness of leg retraction is influenced by actuator efficiencies for positive and negative work. As the efficiency of negative work decreases, the energetic advantage of retracting hip torque is found (mainly) for longer steps, whereas at shorter steps the hip joint extends (not retracts) prior to heel-strike. For fast walking, however, a braking hip torque is still required at the end of swing phase to ensure heel-strike.