Analytical solution of steady step period in 1-DOF limit cycle walking driven by stepwise control inputs

This paper investigates the analytical solution of steady step period in 1-DOF limit cycle walking driven by stepwise control inputs. We introduce an active combined rimless wheel (CRW) model with a motor to analyse the steady walking state when the CRW is walking on level ground. The initial and terminal boundary conditions of three kinds of basic control systems are analysed. The steady step period can be calculated by solving the equations of boundary conditions and we verify the results through numerical simulations. At last we extend the method to N-period stepwise control system and calculate the general solutions of the steady step period. If the generated walking gait is single-step-cycle, we can calculate the steady step period by our general formula solutions in any N-period stepwise control systems.