Graceful Transitions between Periodic Walking Gaits of Fully Actuated Bipedal Robots

We present a theoretical method for graceful transitions between distinct periodic orbits of a fully actuated walking robot. First, a family of hybrid periodic orbits depending smoothly on a parameter are generated via continuously varying constrained optimization. The family specifies a fiber bundle of periodic orbits, and a reference trajectory is designed based on the bundle connecting two periodic orbits. This reference trajectory is shown to have steps that are almost periodic and hence is defined to achieve graceful transitions between orbits. Next, an online Quadratic Program (QP) based feedback controller is used to track the reference trajectory subject to ground forcing constraints. The method is illustrated on a five degrees of freedom planar bipedal robot in simulation.