Analysis of Instantaneous Kinematic Properties Regarding the Shape of Robotic Mechanisms

Abstract

A theoretical framework for analyzing instantaneous kinematic properties regarding the shape of robotic mechanisms is proposed. Conventional research on kinematic analysis regarding the shape has been conducted with the primary goal of approximating a target shape. In contrast, this study does not set a target shape, and instantaneous kinematic properties regarding the shape formed by multiple reference links are analyzed. The properties provide information about the shape change that is easy to achieve and about the controllability of the shape. Furthermore, in contrast to the standard kinematic analysis of robot manipulators that assumes having a single hand link configuration with respect to the base link, the kinematic analysis in this study is free from this assumption. When analyzing instantaneous kinematic properties regarding the shape, it is crucial to decompose motions of reference links into rigid and nonrigid components. After formulating this decomposition, the Jacobian matrices that relate active joint velocities and nonrigid motions are defined. The indices of instantaneous kinematic properties regarding the shape are defined on the basis of the Jacobian matrices. Moreover, application examples using the defined indices are demonstrated.