Stability analysis of underactuated compass gait based on linearization of motion

This paper investigates the stability principle underlying an underactuated compass gait generated by strict output following control of the hip-joint angle. First, we introduce a planar underactuated compass-like biped robot with semicircular feet and develop its mathematical model. We then linearize the equation of motion and design an output following control for the relative hip-joint angle of the linearized model. Second, we analytically derive the transition function of the state error for the stance phase based on the state space representation and discuss its physical meaning. We also mathematically show that the collision phase is always stable. Finally, the validity of the theoretical results is verified through numerical simulations.