Standing stabilizability and stepping maneuver in planar bipedalism based on the best COM-ZMP regulator

The goal of this paper is to answer (i) how the stabilization performance of a biped controller can be evaluated on a certain invariant supporting region, (ii) how the standing stabilizer which performs the best on a given supporting region can be designed, (iii) how the system can be judged if it is stabilizable by the best standing stabilizer without deforming the current supporting region, and (iv) how the supporting region should be deformed if it is judged to be necessary. In order to answer these question, the stable standing region is defined. It gives a criterion to design the best standing stabilizer, to judge if the deformation of the supporting region is necessary to stabilize the system, and to maneuver the stepping motion in accordance with the standing stabilizability condition, which is also defined in the paper. It is found that the best standing stabilizer can be designed by a simple pole-assignment technique. This framework unifies the standing stability and the stepping stability of bipedalism, which have been separately considered in conventional studies. The discussion goes on an approximate planar COM-ZMP model, in which the total mass is concentrated at the center of mass, and the position of ZMP is regarded as the input. Though it is the simplest dynamical model of bipeds, it can conceal differences of body constitutions and represent the macroscopic dynamics. Therefore, this paper contributes to not only the biped robot controller design but also the biomechanical analyses.