Approximate solution of steady step period in one-period limit cycle walking based on discretization of control input

This paper investigates the analytical solution of the steady step period in one-period limit cycle walking. First, we introduce the active combined rimless wheel (CRW) model with motor to analyze the steady walking state when the CRW is walking on the level ground. Second, the initial and terminal boundary conditions of n-period control systems are analyzed to calculate steady walking periods by solving the equations of boundary conditions. Then we analyze the linear control system by converting the linear control system into the discrete function and calculate the steady step period by the equations of n-period-discrete control system. Finally we extend the method to some more complex continuous piecewise control system successfully. In general, that for most of the piecewise control systems, we can calculate the steady step period by our general formula solutions is a great progress in generating a target walking speed.