Time-dependent orbital stabilization of underactuated bipedal walking

In this paper, we propose to study the orbitally exponential stabilization of underactuated bipedal robotic walking with an impulse effect through time-dependent output feedback control. In gait characterization, symmetric periodic gaits are considered and defined. Input-output linearization is then utilized to synthesize an output feedback controller, which drives the directly controlled joints to track some desired time functions that are defined based on the desired periodic symmetric gait. Due to the underactuation, nonautonomous internal dynamics exists and determines the closed-loop stability of the control system. By introducing a new state, the nonautonomous closed-loop system can be transformed into an equivalent autonomous system with an augmented set of states. Stability conditions of the original nonautonomous closed-loop system are then established based on the stability analysis of the equivalent autonomous system. Finally, simulation results showed that the proposed time-dependent output feedback control can indeed realize orbitally exponential stabilization of underactuated bipedal robotic walking if the proposed stability conditions are satisfied.

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