Fully analytical solution to discrete behavior of hybrid zero dynamics in limit cycle walking with constraint on impact posture

摘要

This paper proposes a fully analytical solution to the discrete behavior of hybrid zero dynamics (HZD) in limit cycle walking with constraint on impact posture. First, we introduce a passive rimless wheel and explain the stability principle through derivations of the analytical transition functions of the state error for the stance and collision phases. Second, we consider an active rimless wheel driven by a steady control input for investigating the stability of semi-passive dynamic walking, and propose a method for analytically deriving the transition function for the stance phase without including unknown parameters. We then numerically investigate the solution accuracy and discuss how the discrete behavior of the HZD changes according to the control parameters. Furthermore, we extend the analysis to level walking of an underactuated rimless wheel with a torso and show that the discrete behavior of the HZD can be determined in the same manner.