Abstract
One of the authors have developed the method independent of numerical integration for analyzing the stability of limit cycle walking with constraint on impact posture. In this paper, we extend the method to a kneed biped model and analyze the stability and gait properties. First, a planar three-linked biped model is introduced and its mathematical model is developed. The underactuated bipedal gait is generated by applying an output following control to the desired-time trajectories of the hip and knee joint angles. Second, the transition function of the state error is analytically derived based on linearization of motion and quadratic approximation of mechanical energy. Finally, we discuss how the gait properties change according to the system parameters. The symbolic calculation task in the three-linked model is heavy, so we partially apply numerical calculation.
