Instability-induced hierarchy in bipedal locomotion.

One of the important features of human locomotion is its instant adaptability to various unpredictable changes of physical and environmental conditions. This property is known as flexibility. Modeling the bipedal locomotion system, we show that initial-state coordination by a global variable which encodes the attractor basins of the system can yield flexibility. This model is based on the following hypotheses: (i) the walking velocity is a global variable, and (ii) the leg posture at the beginning of the stance phase is the initial state of the gait. Moreover, we confirm these hypotheses. We investigate the regions near the neutral states between walking and falling phases using numerical experiments and demonstrate that global variables can be defined as the dominant unstable directions of the system dynamics near the neutral states. We propose the concept of an "instability-induced hierarchy." In this hierarchy, global variables govern other variables near neutral states; i.e., they become elements of a higher level.