Dynamics-based virtual holonomic constraint for PDAC running

Our research goal is to unify walking and running by using Passive Dynamic Autonomous Control (PDAC), which has been proposed in our previous research. The PDAC is classified into a limit-cycle-based gait, and its dynamics is freely designed by a virtual holonomic constraint (VHC) for a contact angle with the ground. Hence, we expect to unify walking and running by a design theory of this VHC such that characteristics of walking and running are reflected. In this paper, we control running by the PDAC because it has not been achieved to date. The VHC design is based on a damping and spring loaded inverted pendulum model (D-SLIP model). Time-varying dynamics of D-SLIP model is converted to a differential equation for the contact angle. We solve this equation and obtain a dynamics-based VHC. As a result, we controlled running by the PDAC with the dynamics-based VHC. The PDAC running made the limit cycle converge on a certain cycle; i.e., the PDAC running achieved asymptotic stability.