Stability analysis of limit cycle walking in traversing steps based on semianalytical solution of transition function of state error

Abstract

This paper analyzes the gait properties of a limit-cycle walker that achieves constraint on impact posture in traversing steps. First, we develop the mathematical model of a simple walker and describe the problem formulation. Second, we analytically derive the transition function of state error for the stance phase according to our method. The function derived is a semianalytical solution because it includes an unknown parameter. We then conduct numerical simulations to examine the accuracy of the semianalytical solution of the transition function obtained through comparison with the numerical solution. We also discuss the changes in the state error when the walker traverses small steps.