The optimal swing-leg retraction rate for running

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.