Abstract
It was clarified that underactuated dynamic bipedal walkers with free ankles can generate fast-convergent level gaits by achieving constraint on impact posture. This paper then identifies the condition for achieving deadbeat gait generation through mathematical investigations of simple rimless spoked walkers and proposes a method for generating fast-convergent gaits based on the obtained results. First, we simplify the transition functions for the state error of the stance phase of a passive rimless wheel by eliminating the steady step period. Second, we consider an active rimless wheel that generates ballistic gaits on level ground and show that the transition function of the stance phase can be specified in the same manner as the passive case. Based on the theoretical results, we design a control law for achieving deadbeat gait generation and investigate the validity through numerical simulations. The physical meaning of the derived transition function is also discussed. Furthermore, we extend the method to an underactuated rimless wheel with a torso by applying a discrete-time output deadbeat control. Through mathematical and numerical investigations, it is clarified that the driving effect that changes from acceleration to deceleration tends to achieve deadbeat generate generation.
