Does a finite-time double support period increase walking stability for planar bipeds?

For many planar bipedal models, each step is divided into a finite time single support period and an instantaneous double support period. During single support, the biped is typically underactuated and thus has limited ability to reject disturbances. The instantaneous nature of the double support period prevents nonimpulsive control during this period. However, if the double support period is expanded to finite time, it becomes overactuated. While it has been hypothesized that this overactuation during a finite-time double support period may improve disturbance rejection capabilities, this has not yet been tested. This paper presents a refined biped model by developing a finite-time, adaptive double support controller capable of handling the overactuation and limiting slip. Using simulations, we quantify the disturbance rejection capabilities of this controller and directly compare them to a typical, instantaneous double support model for a range of gait speeds and perturbations. We find that the finite-time double support controller increased the walking stability of the biped in approximately half of the cases, indicating that a finite-time double support period does not automatically increase disturbance rejection capabilities. We also find that the timing and magnitude of the perturbation can affect if a finite-time double support period enhances stability. Finally, we demonstrate that the adaptive controller reduces slipping.