Symmetry in Biped Walking

Symmetry in running was observed by Marc Raibert and was applied to simplify the control of dynamic legged systems. In this paper, we show that symmetry also exists in biped walking and investigate it using two simplified 2D models, that are, the inverted pendulum (IP) model and the linear inverted pendulum (LIP) model, both leading to similar conclusions. To characterize the symmetry in biped walking, the concept of acceleration factor is proposed. Symmetry occurs when the acceleration factor is zero, which results in an unchanged mid-stance velocity. And an important property of symmetry is that the n-step reachable region and the n-step controllable region are exactly the same. This means that if we can achieve speed B from A in n steps, then we can also achieve speed A from B in n steps. Symmetry in walking helps us to better understand human walking and also provides an intuitive way to control robotic walking. As an example, we propose a feedforward controller and a feedback controller, respectively, which can regulate the walking speed very effectively. This work provides us some new insights to view biped walking.