Feedback control of an underactuated planar bipedal robot with impulsive foot action

Abstract

A planar underactuated bipedal robot with an impulsive foot model is considered. The analysis extends previous work on a model with unactuated point feet of Westervelt et al. to include the actuator model of Kuo. The impulsive actuator at each leg end is active only during the double support phase, which results in the model being identical to the model with unactuated point feet for the single support phase. However, the impulsive foot actuation results in a different model for the double support map. Conditions for the existence of a hybrid zero dynamics for the robot with foot actuation are studied. A feedback design method is proposed that integrates actuation in the single and double support phases. A stability analysis is performed using a Poincaré return map. As in Kuo's model, a more efficient gait is demonstrated with an impulsive foot action.