Analysis of steady and target walking speeds in limit cycle walking

Abstract

This paper presents the mathematical analysis of steady walking speed and target walking speed generation in 1-DOF limit cycle walking driven by time-settling control inputs. An actuated combined rimless wheel (CRW) model is introduced to analyse the steady walking state when the CRW is walking on level ground. First the initial and terminal boundary conditions driven by discrete stepwise control systems are analysed. The steady step period can be calculated and the target walking period can be generated by the formulas. Second we extend the mathematical analysis to \((n+1)\)-period stepwise control system and derive the general formula of the steady step period. Finally, the continuous piecewise control systems are analysed mathematically by discretizing the control input, and thus the boundary conditions can be analysed by the formula of \((n+1)\)-period stepwise control system. As a result, if the generated walking gait is single-step-cycle, the steady step period can be calculated and target walking steady speeds can be generated by our general formulas in the time-settling control systems.