On the Adaptation of Dynamic Walking to Persistent External Forcing using Hybrid Zero Dynamics Control

Abstract — This paper investigates the ability of dynamically walking bipeds to adapt their motion to persistent exogenous forcing. Applications that involve physical interactions between a bipedal robot and other robots (or humans), require that the robot adjust its stepping pattern in response to externally applied force signals. In our setting, an underactuated bipedal robot model walks under the influence of an external force. First, the hybrid zero dynamics method is used to design con-trollers that stabilize periodic walking motions in the absence of the external force. Then, conditions are derived analytically under which these (unforced) periodic gaits are modified to new (possibly aperiodic) stepping patterns that are consistent with the external force. It is deduced that underactuation holds the key to the ability of our model to adapt to external forces. I