Simultaneous control of the compass-gait biped to maintain symmetric gait across all mass ratios

It is known that the hybrid dynamical model of a compass-gait biped, which is used here to represent a patient using ankle-foot prostheses on both legs, exhibits a loss of stable period-one symmetric gait with increasing hip-to-leg mass ratio. For higher mass ratios, the period-one gait becomes unstable and bifurcates into a period-two asymmetric gait. In this work, the continuous-time single-support phase of the compass-gait biped is linearized about the upright position and simultaneously stabilized by a linear time-invariant controller that is simple, single-input single-output, and only second-order. This controller, when simulated with the underactuated nonlinear hybrid compass-gait biped model, is shown to maintain stable period-one symmetric gait across all physiologically meaningful mass distributions of the compass-gait biped.