Time-Scaling Trajectories of Passive-Dynamic Bipedal Robots

This paper presents a control law that time-scales reference trajectories of dynamical systems, yielding arbitrary velocities in arbitrary time. It is shown that, for unforced (passive) reference trajectories, constant time-scaling results in a potential energy-shaping control. Application to walking trajectories of bipedal robots is shown, extending the use of the control beyond purely continuous dynamical systems to a class of hybrid dynamical systems with discontinuities that are linear in velocity. Two biped models are used to demonstrate the control law: for the compass-gait biped, we illustrate time-scaling of a passive reference trajectory; for the biped with a torso, we show time-scaling of a semi-passive reference trajectory.