Estimation of a thin flexible object with bipedal gaits

This paper discusses a dynamic nonprehensile manipulation of a thin flexible object where the object rotates on a plate. We have found that a thin flexible object shows bipedal-gaited motions when rotating on the vibrating plate and that the maximal angular velocity of the object is achieved by an appropriate plate motion with respect to the object's physical parameters. Based on such an object's behavior, in this paper, we propose how to estimate the physical parameters of a bipedal-gaited object, as an inverse problem. The relationship between the plate's angular frequency and the object's angular velocity shows a resonant curve based response. Focusing on this relationship, we employ a Lorentzian curve fitting to represent the dynamic characteristics of the object with a simple mathematical expression. Through simulation analysis, we show that two physical parameters, the first order natural angular frequency in bending and the friction between the object and the plate, dominate the Lorentzian curve characteristics: the former one determines the plate's rotational frequency leading to the object's maximal angular velocity, while the latter one determines a characteristic width of the Lorentz distribution. Based on the above correlations, we propose an estimation method in which the two physical parameters of an object can be obtained.