Stability examination of biped model by Floquet theory

摘要

This study intends to reveal neural control mechanisms that can achieve stable biped human walking while maintaining flexibility. As a preliminary step, we develop an analytical methodology to evaluate the gait stability of biped models. To this end, we construct a simple 7-rigid-link biped model with feet. The model employs three parts of controlling torques, namely, feedforward and feedback control torques for a periodic desired joint motion, and feedback torques for postural balancing. Floquet multipliers are used for examining the gait stability. Root loci concerning the Floquet multipliers have been examined along with changes in the value of every feedback gain parameter, which validates effectiveness of Floquet method used for evaluating the gait stability. The method can also apply to modify the gain parameters to make an unstable gait dynamics stable. Features of the obtained root loci are summarized as follows. First, if the biped model is walking stably, all the eigenvalues are located within a unit circle of the complex plane and one located at (0,1). Second, bifurcations exist due to the nonlinearity of the model. Third, non-monotonic changes in the stability can be observed along with monotonic increasing/decreasing of the gain parameters. In summary, we show that the proposed method can describe how the gait stability changes as a continuous function of parameter values of the feedback gains. Thus, it could be used to elucidate parameter regions that can alleviate the rigidity of joint motion through reducing the values of the feedback gain parameters.