Abstract
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 stance phase from the state space representation, and solve the stability and optimal conditions. Finally, the validity of the theoretical results is verified through numerical simulations.
