Analytical solution of target steady walking speed in 1-DOF limit cycle walking

This paper investigates the analytical solution of target steady walking speed in 1-DOF limit cycle walking. We introduce an active combined rimless wheel (CRW) model to analyze the target steady walking state when the CRW walks on level ground. The walking speed is determined by the step period because the step length is constant. First we propose a two-period stepwise control system and the target walking period can be generated by solving the equations of boundary conditions. Second we extend this method to (n + 1)-period stepwise control system and generate a general formula for the boundary equation. At last we generate the target steady step period in the continuous control systems by calculating the approximate solution based on discretization of control input. We verify all the results through numerical simulations. If the generated walking gait is single-step-cycle, we can generate the target steady step period by our general formula in most of control systems.