Stability analysis of underactuated bipedal gait using linearized model

This paper investigates the self-stabilization principle underlying an underactuated bipedal gait generated by trajectory tracking control of the hip-joint angle. First, we introduce a planar underactuated compass-like biped robot with semicircular feet, and develop its dynamics and linearized system equation. We then design an output following control for the linearized robot´s hip-joint angle. Second, we analytically derive the transition equation of state error for the stance and collision phases from the state space representation. We then solve the stability limit and optimal condition of the stance phase and show the stability of the collision phase. Finally, the validity of the theoretical results is verified through numerical simulations.