Editorial Board

2012B-7 The functional roles of time delay on flexible phase-locking in Bipedal locomotion (pp.123-133)

Author(s): Wulin Weng, Shin-Ichiro Ei and Kunishige Ohgane

J. Math-for-Ind. 4B (2012) 123-133.

Based on neurophysiological studies, a walking model has been proposed, which is the coupling of two oscillatory systems, i.e., a central pattern generator (CPG) and a musculoskeletal system (Body). The walking model can well reproduce human walking. However, time delays on a sensorimotor loop give a serious problem in motor control in general. Indeed even a short time delay induces the walking model to fall. Theoretical studies have shown that the walking model can overcome the time delays by the flexible-phase locking. It emerges from the following two conditions; 1) activity of CPG and Body has stability of limit cycle; 2) a sign differs between coupling coefficients of the connection from Body to CPG and from CPG to Body, i.e., the afferent and efferent connection. Physical or physiological interpretation of this two theoretical conditions is an important problem. The condition 1) has already interpreted [1]. In this paper, we gain a physical interpretation of the condition 2). We introduce the simplified model fit to best analyze. Analyzing the simplified model, this study leads to the interpretation in which signs of the coupling coefficients corresponding to the excitatory and inhibitory connection are regarded as a force to forward and backward shift the CPG activity, respectively. This is an essential element to yield the flexible-phase locking.

Keyword(s).  human walking, CPG, body, time delay, phase shift