A novel gait generation method independent of target settling-time adjustment for underactuated limit cycle walking

This paper proposes a novel gait generation method for surely achieving constraint on impact posture in limit cycle walking. First, we introduce an underactuated rimless wheel model without ankle-joint actuation and formulate a state-space realization of the control output using the stance-leg angle as a time parameter through an input–output linearization. Second, we determine a control input that moves the control output to a terminal value at a target stance-leg angle during the single-support phase. Third, we conduct numerical simulations to observe the fundamental gait properties and discuss the relationship between the gait symmetry and mechanical energy restoration. Furthermore, we mathematically prove the asymptotic stability of the generated walking gait by analytically deriving the restored mechanical energy.