Swing-leg retraction was introduced as a way to improve the stability and disturbance rejection of running robots. It was also suggested that the reduced foot speed due to swing-leg retraction can help reduce impact energy losses, decrease peak forces, and minimize foot slipping. However, the extent to which swing-leg retraction rate influences all these benefits was unknown. In this paper, we present a study on the effect of swing-leg retraction rate on these benefits. The results of this study show that swing-leg retraction can indeed improve the performance of running robots in all of the suggested areas. However, the results also show that, for moderate and high running speeds, the optimal retraction rate for maximal disturbance rejection and stability is different from the optimal retraction rate for minimal impact losses, peak forces, and foot slipping. This discrepancy indicates an inherent tradeoff to consider when selecting the retraction rate for a robot control system: in general, retraction rate can be optimized for better stability and disturbance rejection or for more favorable efficiency, impact forces, and footing stability, but not all simultaneously. Furthermore, this tradeoff becomes more severe as running speed increases.

Swing leg retraction reduces touchdown energy losses of running by decreasing foot speed at the moment of ground contact, but does the additional acceleration of the swing leg cost more energy than is saved? To determine whether swing leg retraction can increase the overall energy efficiency of running robots, we find the optimally efficient gaits of a McGeer-like runner over a range of retraction rates. Results show that overall energy usage, including that used to swing the legs, scales with energy loss at touchdown, which is minimized at the retraction rate that zeros foot tangential speed at ground contact. Other benefits of swing leg retraction, such as reduced foot slippage and damaging touchdown forces, are realized simultaneously with optimal energy efficiency.