Effect of Finite-time DS Controllers on Disturbance Rejection 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 control during this period. However, if the double support period is expanded to finite time, this introduces an overactuated period into the model which may improve disturbance rejection capabilities. This paper derives and compares the performance of two finite-time double support controllers. The first controller uses time to drive the progression of the double support period and controls the joint angles. The second controller uses a time-invariant phase variable to drive the progression of the double support period and controls the joint velocities since it is not possible to control the joint positions. The disturbance rejection capabilities of both controllers are then quantified using simulations. The instantaneous double support model is also simulated for comparison. The instantaneous double support model can recover from the largest disturbances but it requires the greatest number of steps to do. The time-based double support controller can recover from the smallest range of disturbances but requires the fewest number of steps for a given perturbation size.