Global stability analysis for plane limit cycle walking models with feet and actuation

Biped robots based on limit cycle walking paradigm commonly need less energy than other models and generate pretty natural gait, because this paradigm has fewer artificial constraints to walking motion compared to other conventional ones. To increase performance and to realize a practical biped, the model needs further studies on its stability, disturbance rejection capability, and versatility, the ability to perform various gaits, etc. In this work, we tried to increase its stability, disturbance rejection capability. To have a stable walking gait, the walking model requires proper initial conditions. The set of proper initial conditions is called as basin of attraction. The larger of basin of attraction gives more stable walking and can resist to larger disturbances. Unfortunately, the basin of attraction for a purely passive walking model is very narrow. Some research showed the basin of attraction could be enlarged with swing leg actuation in the falling forward region. Firstly, we modified the foot shape of a purely passive walking model, the simplest walker which has pointed foot. Modified models have larger basin of attraction with varying parameters. Secondly, we applied another form of actuation to the simplest walker. The actuation such as toe-off can´t increase the basin of attraction.